Answers
The function graphed below is
y = x³ - 3, x ≤ 2
= x² + 6, x > 2 ⇒ C
Step-by-step explanation:
The graph has two parts:
The first part start at x > 2 and its a part of parabola (quadratic function)The second part End at x = 2 and its a part of a cubic function∴ The graph represents two functions:
→ Quadratic function y = ax² + bx + c with domain x > 2
→ Cubic function y = ax³ + bx² + cx + d with domain x ≤ 2
∵ The answers have two functions:
→ y = x³ - 3 ⇒ cubic function
→ y = x² + 6 ⇒ quadratic function
∵ The domain of the cubic function is x ≤ 2
∵ The domain of the quadratic function is x > 2
∴ The answer is
y = x³ - 3, x ≤ 2
x² + 6, x > 2
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Answer:
y={x^3-3, x ≤ 2
{x^2+6, x>2
Step-by-step explanation:
a pex :)
Related Questions
Joshua wrote 13 articles for the school newspaper this year. Paulette wrote 7 more articles than Joshua. Jeff wrote as many articles as Paulette. How many articles did they write in all?
Answers
In the parallelogram below, X = ?
Answers
Answer:
46°
Step-by-step explanation:
The exterior angle marked 69° is the sum of the remote interior angles 23° and x. So ...
69° = 23° +x
x = 69° -23°
x = 46°
Answer:
46 degrees
Step-by-step explanation:
see attached
Which property is shown?
(c^4)^6 = c^24
Answers
For this case we have the following expression:
[tex](c ^ 4) ^ 6 = c^{24}[/tex]
By definition of power properties we have to meet:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
This property is known as "high power to power."
Answer:
The property shown is:
High power to power.
A triangle with sides measuring 8, 15 and 17 units is inscribed in a circle. What is the radius of the circle, in units?
A. 8.5 unitsB. 6 unitsC. 3 unitsD. 5 unitsE. 12 units
Answers
Answer: radius of the circle is 8.5 units
Step-by-step explanation:
The diagram of the circle and the inscribed triangle is shown in the attached photo. Looking at the length of each side of the triangle given, the lengths form a Pythagorean triple. We can confirm by applying Pythagoras theorem
Hypotenuse^2 = opposite side^2 + adjacent^2. It becomes
17^2 = 8^2 + ``15^2
289 = 64 + 225
289 = 289
This means that the triangle formed is a right angle triangle.
According to Thales theorem,
The diameter of the circle always subtends a right angle to any point on the circle. Since the diameter is the longest side of the circle and the angles is formed on a point on the circle,
Diameter = 17
Radius = diameter/2 = 17/2 = 8.5
Answer:
8.5
Step-by-step explanation:
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible
Answers
Answer: 80
Step-by-step explanation:
Given : Number of married couples = 5
Number of people required = 3
Since , the committee does not include two people who are married to each other,
We consider 1 married couple as one people , then the number of ways to select 3 persons =[tex]^{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5\times4\times3!}{3!\times2}=10[/tex]
Also, chances of selecting any partner = 2 (either Husband or wife)
So for 3 persons the total chances =(2) (2) (2)
Total number of ways to form the committee so that the committee does not include two people who are married to each other= 10 x (2) (2) (2) =80
Hence, the number of committees are possible = 80
At a restaurant, four people order fried crab claws and four people order a cup of gumbo, with a total bill of $32. If only two people had ordered the crab claws and one person ordered the gumbo, the bill would have been $12.5. How much are each order of fried crab claws and each cup of gumbo?
Answers
The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5
Step-by-step explanation:
Let,
Cost of each fried crab claw = x
Cost of each gumbo = y
According to given statement;
4x+4y=32 Eqn 1
2x+y = 12.5 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+y = 12.5)\\4x+2y=25\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 1
[tex](4x+4y)-(4x+2y)=32-25\\4x+4y-4x-2y=7\\2y=7[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{7}{2}\\y=3.5[/tex]
Putting y=3.5 in Eqn 2
[tex]2x+3.5=12.5\\2x=12.5-3.5\\2x=9[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{9}{2}\\ x=4.5[/tex]
The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5
Keywords: linear equation, subtraction
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The price for each cup of gumbo is $3.5.
The student's question poses a system of linear equations problem where we need to determine the cost of each order of fried crab claws and each cup of gumbo. We can define two variables: let x be the price of an order of fried crab claws and y be the price of a cup of gumbo. The first condition gives us the equation 4x + 4y = 32, and the second condition gives us the equation 2x + y = 12.5. Solving the system of equations by multiplying the second equation by 4 and subtracting from the first one yields:
8x + 4y = 50
4x + 4y = 32
(8x + 4y) - (4x + 4y) = 50 - 32
4x = 18
x = 4.5
Thus, the price for each order of fried crab claws is $4.5. Now, substituting x in one of the equations to find y we get:
2(4.5) + y = 12.5
9 + y = 12.5
y = 12.5 - 9
y = 3.5
So, the price for each cup of gumbo is $3.5.
Calico Company has two operating departments: Department A and Department B. Department A occupies 30% of the floor space of the company but accounts for 75% of the sales of the company. Department B occupies 70% of the floor space of the company but accounts for 25% of company sales. Cleaning expense (an indirect expense of the company), which consists primarily of vacuuming the carpet is $30,000 each year. How much cleaning expense should be allocated to Department B? $0 $7,500 $9,000 $21,000 $22,500 $30,000 Slide 6 Slide 6
Answers
Answer: $21,000
Step-by-step explanation:
Cleaning expense is only related to the floor space occupied by the department.
If the company spend a total of $30,00 on cleaning each year.
And Department B occupies 70% of the company floor.
Therefore, the company spends 70% of their cleaning expense on department B
Hence, the cleaning expense on department B is given as;
= 70% of $30,000
= $21,000
Department B should be allocated $21,000 for cleaning expenses, as it occupies 70% of the floor space and the total cleaning expense is $30,000.
Explanation:To determine how much cleaning expense should be allocated to Department B at Calico Company, you should consider the proportion of floor space occupied by the department. Since cleaning expenses are primarily based on vacuuming the carpet, it's reasonable to use floor space as the basis for allocation.
Department B occupies 70% of the company's floor space. With a total annual cleaning expense of $30,000, we can calculate Department B's share of the expense by multiplying the total expense by the percentage of space that Department B occupies:
Allocated expense to Department B = Total cleaning expense × Department B's percentage of floor space
Allocated expense to Department B = $30,000 × 70%
Allocated expense to Department B = $30,000 × 0.70
Allocated expense to Department B = $21,000
Therefore, $21,000 should be allocated to Department B for cleaning expenses.
500 people are enrolled in at least two of these three classes: art, drama, and piano. 170 are enrolled in both art and drama, 150 are enrolled in both piano and drama, and 300 are enrolled in art and piano. How many of the 500 people are enrolled in all three?
Answers
Answer: 60
Step-by-step explanation:
let x="students enrolled in all three"
"170 are enrolled in both Math and English" __ so 170-x are enrolled in ONLY Math and English
"150 are enrolled in both History and English" __ so 150-x are enrolled in ONLY History and English
"300 are enrolled in Math and History" __ so 300-x are enrolled in ONLY Math and History
"500 students are enrolled in at least two of these three classes"
so (170-x)+(150-x)+(300-x)+x = 500
620-2x=500
120=2x
60=x
Final answer:
By applying the principle of inclusion-exclusion, we can find that 60 people are enrolled in all three classes: art, drama, and piano.
Explanation:
To solve the problem of determining how many people are enrolled in all three classes (art, drama, and piano), we use the principle of inclusion-exclusion. The principle allows us to find the number of individuals enrolled in at least one of the classes by adding the numbers enrolled in each pair of classes and then subtracting the number counted twice. The formula for three sets A, B, and C is given by:
[tex]|A \union\ B \union\ C| = |A| + |B| + |C| - |A \intersect\ B| - |B \intersect\ C| - |A \intersect\ C| + |A \intersect\ B \intersect\ C|.[/tex] We are given the following information:
170 people are enrolled in both art and drama
150 people are enrolled in both piano and drama
300 people are enrolled in both art and piano
Let X represent the number of people enrolled in all three classes. The sum of people enrolled in at least two classes is 500. So, we need to solve the equation:
170 + 150 + 300 - 2X = 500
620 - 2X = 500
X = (620 - 500) / 2
X = 120 / 2
X = 60
Therefore, 60 people are enrolled in all three classes: art, drama, and piano.
After creating a new email address, Gareth initially receives n emails per year. The number of emails received increases by 7% each year after that. The following expression represents the number of emails received after x years.
n(1+0.07)^x
Which of the following best represents the expression?
A.
the product of the number of emails received initially and the factor of increase raised to a period of x years
B.
the product of the number of emails received initially and one plus the factor of decrease raised to the number of years that the amount of emails Gareth received has increased
C.
the product of the number of emails received initially and one plus the factor of increase raised to the number of years that the amount of emails Gareth received has increased
D.
the product of the number of emails received initially and the factor of decrease raised to a period of x years
Answers
n is the initial amount
0.07 is the factor of increase
x is the number of years that the emails increased
answer: C
Frank an active 11 year old male, consume 660 calories during breakfast. This is 30 percent of the recommended number of calories for the day for him. What is the recommended number is calories for an active 11 year old male?
Answers
Answer:
the recommended number of caories for a 11 year old male = 220.
Step-by-step explanation:
it is given that frank consumes 660 calories during breakfast.
660 calories is the 30 percent of recommended calories for a day.
let the number of calories required for a day be x.
therefore 30 percent of x = 660
therefore [tex]\frac{30}{100}[/tex]×x = 660
30x= 660×100
x=660×[tex]\frac{100}{30}[/tex]
x= [tex]\frac{10}{3}[/tex]×660
x= 2200
solving the equation we get x= 2200
there the recommended number of caories for a 11 year old male = 220.
Suppose your school is having a talent show to raise money for new music supplies. You estimate that 200 studens and 150 adults will attend.You estimate $200 in expenses.
Answers
The question is incomplete. Here is the complete question:
Suppose your school is having a talent show to raise money for new music supplies. You estimate that 200 students and 150 adults will attend. You estimate $200 in expenses. Write an equation to find what ticket prices you should set to raise $1000.
Answer:
[tex]200x+150y=1200[/tex]
Step-by-step explanation:
Let 'x' be price per student ticket and 'y' be the price per adult ticket.
Given:
Number of students = 200
Number of adults = 150
Total fund to be raised = $1000
Expenses cost = $200
Now, price of ticket for 1 student = 'x'
Therefore, price of tickets of 200 students = [tex]200x[/tex]
Price of ticket of 1 adult = 'y'.
Therefore, price of tickets of 150 adults = [tex]150y[/tex]
Now, total fund raised will be equal to the total money obtained from selling the tickets minus the expenses estimated.
∴ Total fund raised = Total money from tickets - Expenses.
⇒ [tex]1000=200x+150y-200[/tex]
⇒ [tex]200x+150y=1000+200[/tex]
⇒ [tex]200x+150y=1200[/tex]
Therefore, the equation to find what ticket prices you should set to raise $1000 is given as:
[tex]200x+150y=1200[/tex]
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? 1. 31 < p < 37 2. p is odd.
Answers
Answer:
1) [tex]31 < p<37[/tex]
For this case the values that satisfy the inequality are: 32,33,34,35,36
And we can analyze one by one the number:
[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1
[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1
[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1
[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1
[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1
So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.
2) For this cas this statement is FALSE, since we have a counterexample on this case:
[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1
And since we have one element that not satisfy the condition that's FALSE.
Step-by-step explanation:
For this question we need to use the following definition "If an integer p can b expressed as the product of two integers, each of which that is greater then 1, then the integer p can be considered as a composite number". And this number is not the same as prime number.
Part 1
[tex]31 < p<37[/tex]
For this case the values that satisfy the inequality are: 32,33,34,35,36
And we can analyze one by one the number:
[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1
[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1
[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1
[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1
[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1
So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.
Part 2
For this cas this statement is FALSE, since we have a counterexample on this case:
[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1
And since we have one element that not satisfy the condition that's FALSE.
The distance formula states that distance (d) is equal to the product of rate (r) and time (t).
Which equation could be used to solve the problem?
John ran at a constant rate of 200 mph. How many minutes did it take john to run 500 m?
A. t=500/200
B. t=500d/200
C. t=200/500
D. t=200r/500
Answers
Answer:
A. t=500/200
Step-by-step explanation:
If Distance = d
Product Rate = r
Time = t
and the equation states that;
d = r x t
then by dividing the equation by r we get;
t = d / r
By putting in the values of d = 500 and r = 200 in the above equation we get;
t = 500 / 200
Answer: B
Step-by-step explanation:
d = t * r
t = d/r
t = 500d/200
If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability that all 3 cards are queens.
Answers
Answer:
I think the answer is 3/52
Dana is purchasing a new car that costs $24,650. Although Dana will be financing her car, she must pay sales tax, title, and tag feed up front. If the sales tax rate is 3.5% and the title and tag fees total $376, what is the total amount that Dana must pay up front?
Answers
Dana must pay $1238.75 upfront.
Step-by-step explanation:
Given,
Cost of car = $24,650
Sales tax = 3.5%
Amount of sales tax = 3.5% of cost of car
Amount of sales tax = [tex]\frac{3.5}{100}*24650[/tex]
Amount of sales tax = [tex]\frac{86275}{100}=\$862.75[/tex]
Amount of title and tag fees = $376
Total upfront amount = Amount of sales tax + Amount of title and tag fees
Total upfront amount = 862.75+376 = $1238.75
Dana must pay $1238.75 upfront.
Keywords: percentage, sales tax
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Suppose your marginal cost of making a peanut butter and jelly sandwich is constant at $10, but the marginal benefit of eating the sandwich decreases from $12 for one sandwich, to $10 for two sandwiches, to $8 for three sandwiches, to $6 for four sandwiches. How many sandwiches would you eat?
Answers
According to marginal analysis in economics, the optimal consumption is where marginal cost equals marginal benefit. Given that the marginal cost is constant at $10 per sandwich, and marginal benefit decreases, the optimal consumption would be to eat two sandwiches.
Explanation:In your scenario, you are trying to determine the optimal number of peanut butter and jelly sandwiches to consume given a constant marginal cost and a decreasing marginal benefit. This is essentially a problem in the domain of Economics, particularly concerning the concept of marginal analysis.
The principle of marginal analysis states that optimal consumption occurs at the point where marginal cost equals marginal benefit. In numerical terms, this translates to the following: a $10 cost for each sandwich equals a $10 benefit. Therefore, this is the optimal point of consumption, meaning that you would ideally consume two sandwiches.
This is the result of the economic theory of consumer behavior, which predicts that consumers seek to maximize their utility while considering their budget constraints. Any further sandwiches would result in a negative gain, or a loss, because the marginal cost would exceed the marginal benefit (as the benefit from the third sandwich decreases to $8, from the fourth to $6, and so on). It should be noted that this analysis assumes rational behavior and no external costs or benefits associated with the consumption of more sandwiches.
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PLEASE HELP. WILL GIVE BRAINLIEST
Answers
Answer:
B, C and D.
Step-by-step explanation:
3m=36-6m
9m=36
m=4
-1/3m+2=-1
-1/3m=-3
m=9
So not it
B, c and d is the same as they all equal to 4.
Answer:
The answer to your question is b, c and d
Step-by-step explanation:
Equation given
3m = 36 - 6m
3m + 6m = 36
9m = 36
m = 36/9
m = 4
Equation a
-1/3 m + 2 = -1
-1/3 m = -1 - 2
-1/3 m = -3
m = -3 x -3
m = 9
Equation b
-2(-4m - 6.4) = 44.8
-4m - 6.4 = 44.8/-2
-4m = -22.4 + 6.4
-4m = -16
m = -16/-4
m = 4
Equation c
8m - 5 - 2m + 1 = 20
6m = 20 + 4
6m = 24
m = 24/6
m = 4
Equation d
7m + 6 = 9m - 2
7m - 9m = -2 - 6
- 2m = -8
m = -8/-2
m = 4
Tony tacos is selling 15 sodas for 10 dollars.Nicks nachos is selling 30 sodas for 20dollars. Write the ratios.Are the two ratios above proportional
Answers
Answer: The ratios are proportional
Step-by-step explanation:
Tony tacos is selling 15 sodas for 10 dollars.
Nicks nachos is selling 30 sodas for 20dollars. The ratio of the number sodas sold by Tony tacos to the number of sodas sold by Nicks nachos is 15/30 = 1/2
The ratio of the cost of sodas sold by Tony tacos to the cost of sodas sold by Nicks nachos is 10/20 = 1/2
So the number of sodas sold is proportional to the cost.
Enter the slope and y−intercept as decimals. The scatter plot with trend line below shows data comparing wind speed and wind chill. The trend line passes through (10, 9) and (35, 0). Enter an equation for the trend line.
The equation of the trend line is
y =---------x +----------
Answers
Answer:
[tex]y=-0.36x+12.6[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(10, 9) and (35, 0)
substitute the values in the formula
[tex]m=\frac{0-9}{35-10}[/tex]
[tex]m=-\frac{9}{25}=-0.36[/tex]
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
With the slope [tex]m=-0.36[/tex] and point (35,0) substitute in the equation and solve for b
[tex]0=-0.36(35)+b[/tex]
[tex]0=-12.6+b[/tex]
[tex]b=12.6[/tex]
therefore
The equation of the line in slope intercept form is
[tex]y=-0.36x+12.6[/tex]
Mark bought 3 bags of pretzels for $2.00 each. He also bought 2 bottles of juice for $1.50 each. Write an expression and find the total cost for the pretzels and juice.
Answers
Final answer:
The expression for the total cost is (3 × $2.00) + (2 × $1.50). After performing the calculations, the total cost for Mark's pretzels and juice is $9.00.
Explanation:
To calculate the total cost of the pretzels and juice that Mark bought, we need to multiply the quantity of each item by its price and then add the totals for each item.
The expression for the pretzels is 3 bags × $2.00 per bag, which equals $6.00. For the juice, the expression is 2 bottles × $1.50 per bottle, which equals $3.00. The total cost is the sum of these two amounts, so we have:
Total Cost = Cost of Pretzels + Cost of Juice
= (3 × $2.00) + (2 × $1.50)
= $6.00 + $3.00
= $9.00
Therefore, the total cost for the pretzels and juice is $9.00.
Ava puts $400.00 into an account to use for school expenses.The account earns 12percent interest ,compuonded annualy.How much will be in the account after 9 years?
Answers
Answer:$1109.23 will be in the account after 9 years
Step-by-step explanation:
Initial amount deposited into the account is $400 This means that the principal
P = 400
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 12%. So
r = 12/100 = 0.12
It was compounded for 9 years. So
n = 9
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 400 (1+0.12/1)^1×9
A = 400(1.12)^9 = 1109.23$
What is the equation of a circle with center (-4,7) radius 3?
Answers
Answer:
a. (x + 4)² + (y – 7)² = 3²
Step-by-step explanation:
General equation for a circle is:
(x – h)² + (y – k)² = r²
h and k are the center (h, k), and r is the radius.
They want a center of (-4, 7) so h=-4 and k=7
They want a radius of 3 so r=3
plug it into the equation.
(x – h)² + (y – k)² = r²
(x – (-4))² + (y – (7))² = (3)²
(x + 4)² + (y – 7)² = 3²
Answer: ( x + 4 )² + ( y - 7 )² = 3²
Step-by-step explanation:
Formula for the equation of a circle centre (a, b), radius r
= ( x - a )² + ( y - b )² = r²--------------------------------------------------------1
a = -4 and b = 7 while r = 3
Therefore substitute for a , b and r in the equation 1 above to get the equation of the circle.
( x - (-4 ) )² + ( y - 7 )² = 3²
open the brackets through direct or indirect methods gives
( x + 4 )² + ( y - 7 )² = 9
x² + 8x + 16 + y² - 14y + 49 = 9
x² + y² + 8x - 14y + 16 + 49 - 9 = 0
x² + y² + 8x - 14 y + 116 = 0
Conditional Distribution, Marginal Distribution, Joint Distribution.
What’s the difference?
Answers
Explanation:
Marginal distribution: This distribution gives the probability for each possible value of the Random variable ignoring other random variables. Basically, the values of other variables is not considered in the marginal distribution, they can be any value possible. For example, if you have two variables X and Y, the probability of X being equal to a value, lets say, 4, contemplates every possible scenario where X is equal to 4, independently of the value Y has taken. If you want the probability of a dice being a multiple of 3, you are interested that the dice is either 3 or 6, but you dont care if the dice is even or odd.
Conditional distribution: This distribution contrasts from the previous one in the sense that we are restricting the universe of events to specific condition for other variable, making a modification of our marginal results. If we know that throwing a dice will give us a result higher than 2, then to in order to calculate the probability of the dice being a multiple of 3 using that condition, we have two favourable cases (3 and 6) from 4 total possible results (3,4,5 and 6) discarding the impossible values (1 and 2) from this universe since they dont match the condition given (note that the restrictions given can also reduce the total of favourable cases).
The joint distribution calculates the probabilities for two different events (related to two different random variables) occuring simultaneously. If we want to calculate the joint probability of a dice being multiple of 3 and greater than 2 at the same time, our possible cases in this case are 3 and 6 from 6 possible results. We are not discarding 1 or 2 as possible results because we are not assuming, that the dice is greater than 2, that is another condition that we should met in the combination of events.
The concepts of conditional distribution, marginal distribution, and joint distribution are used in statistics to analyze relationships between two variables. The joint distribution represents frequencies or probabilities of different combinations of values, the marginal distribution focuses on each variable individually, and the conditional distribution focuses on subsets of the population based on a specific condition or value.
Explanation:The conditional distribution, marginal distribution, and joint distribution are concepts used in statistics to analyze relationships between two variables in a dataset.
The joint distribution represents the frequencies or probabilities of different combinations of values for the two variables. It is typically presented in a two-way frequency table or as a joint probability function.
The marginal distribution focuses on the frequencies or probabilities of each variable individually, disregarding the other variable. It represents the disconditional distribution focuses on subsets of the population defined by a specific condition or value of one variable. It represents the tribution of one variable while ignoring the other.
The distribution of one variable within a specific condition or value of the other variable.
For example, in a two-way table with gender and favorite sport, the joint distribution represents the frequencies of males and females who prefer different sports. The marginal distribution represents the frequencies of males and females overall, ignoring their sport preferences. The conditional distribution represents the frequencies of different sports within each gender.
A parabola and a circle are graphed into the standard (x,y) coordinate plane. The circle has a radius of 4 and is centered at (1,1). The parabola, which has a vertical axis of symmetry, has its vertex at (1,5) and a point at (2,4). How many points of intersection exist between the parabola and the circle?
Answers
Answer:
Correct answer: Two point of intersection and one touch point.
Step-by-step explanation:
Cartesian form of parabola is: y= a(x-1)² + 5 and point named A(2,4)
when we replace the coordinates of the point A in the formula we get
a = - 1 and parabola is y= - (x-1)² + 5 which means that it faces the opening downwards. The parabola touches the circle in vertex.
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One family spends 131 on 2 adult tickets and 4 youth tickets at an amusement park. Another family spends 139 on 4 adult and 2 youth tickets at the same park
Answers
Answer:the price of one adult ticket is $24.5
the price of one youth ticket is $20.5
Step-by-step explanation:
Let x represent the price of one adult ticket.
Let y represent the price of one youth ticket.
One family spends $131 on 2 adult tickets and 4 youth tickets at an amusement park. This means that
2x + 4y = 131 - - - - - - - - - -1
Another family spends $139 on 4 adult and 2 youth tickets at the same park. This means that
4x + 2y = 139 - - - - - - - - - - -2
Multiplying equation 1 by 4 and equation 2 by 2, it becomes
8x + 16y = 524
8x + 4y = 278
Subtracting
12y = 246
y = 246/12 = 20.5
Substituting y = 20.5 into equation 1, it becomes
2x + 4×20.5 = 131
2x + 82 = 131
2x = 131 - 82 = 49
x = 49/2 = 24.5
Given: ∆AMK, MP ⊥ AK , MP = 10 m∠A = 72º, m∠PMK = 50° Find AM, MK, AK
Answers
Answer:
Step-by-step explanation:
The diagram of triangle AMK is shown on the attached photo. To determine AM, we would apply trigonometric ratio since triangle AMP is a right angle triangle.
Sin# = opposite/hypotenuse
Sin 72 = 10/AM
AMSin72 = 10
AM = 10/Sin72 = 10/0.9511
AM = 10.51
To determine MK,
Cos# = adjacent/hypotenuse
Cos 50 = 10/MK
MKCos50 = 10
MK = 10/Cos50 = 10/0.6428
MK = 15.6
AK = AP + KP
Tan# = opposite/adjacent
Tan 72 = 10/AP
AP tan 72 = 10
AP =10/tan72 = 10/ 3.0777 = 3.25
Tan 50 = KP/10
KP = 10tan50
KP= 10× 1.1918 = 11.918
Therefore,
AK = 3.25 + 11.918 = 15.168
To find AM, MK, and AK in triangle AMK, use trigonometry and given angle measurements. Subtract the measure of angle PMK from 180 degrees to find the measure of angle A. Then, use the sine rule to find AK and AM.
Explanation:To find the lengths of AM, MK, and AK, we can use trigonometry and the given angle measurements. Firstly, we can find MK by subtracting the measure of angle PMK from 180 degrees to find the measure of angle A. Then, we can use the sine rule to find the lengths of AK and AM. Using the given information, we can set up equations and solve for the unknown lengths.
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Lena wants to put the monkey stickers in all album. She says she will use more pages if she puts 5 stickers on a page instead of 10 stickers on a page. Is she correct
Answers
Answer:
She is absolutely correct!
Step-by-step explanation:
Let the total no. of stickers with Lena be x.
If she sticks 5 stickers per page, the number of pages she will use=[tex]\frac{x}{5}[/tex]
If she sticks 10 stickers per page, the number of pages she will use=[tex]\frac{x}{10}[/tex]
We all know, that the smaller the denominator the larger the number.
Therefore, [tex]\frac{x}{5} >\frac{x}{10}[/tex]
Condition being that x is a positive quantity which it automatically is.
So, Lena is right in her reasoning that she will use more no. of pages.
Yes, Lena is correct because placing a smaller number of stickers per page (5 instead of 10) will indeed result in the use of more pages overall, as this reduces the stickers-to-page ratio.
Explanation:The question is asking if Lena will use more pages for her stickers if she places 5 stickers on a page instead of 10. We are working with a simple division concept here. When you have a fixed number of items (stickers, in this case) and you use fewer items per group (or page), you will end up with more groups (or pages).
If Lena puts 5 stickers on each page as opposed to 10 stickers on a page, she will indeed need more pages because she’s placing fewer stickers on each page. For instance, if she has 20 stickers: with 5 stickers per page, she will need 4 pages (20 stickers / 5 stickers per page = 4 pages). On the other hand, with 10 stickers per page, she will only need 2 pages (20 stickers / 10 stickers per page = 2 pages). Therefore, placing fewer stickers on a page results in more pages being used.
A rectangle has a perimeter of 60 units and one side of length 18 units. If it can be determined, what are the lengths, in units, of the other three sides?
A. 18,3,3
B. 18,12,12
C. 18,18,6
D. 18,21,21
E. Cannot be determined from the information given
Answers
Answer:
option B. 18,12,12
Step-by-step explanation:
perimeter= 60 units
(consider a rectangle with sides a,b,c & d in order)
a= 18 units (given)
c=18 units (since opp. sides of a rectangle are equal)
now the remaining length= 60-(18+18)
= 60 - 36
= 24
so the sum of the remaining sides, ie, b+d= 24
since b and d are equal (opp.sides of a rect.)
b=d=24/2=12
therefore, b=12; c=18; d=12
i really hope i'm clear...but if i'm not then please do ask...
Answer:
Step-by-step explanation:
Perimeter of a plane shape is the distance around the shape. The formula for determining the perimeter of a rectangle expressed as
Perimeter = 2(length + width)
The rectangle has for side. Two parallel and opposite sides are equal. There, if the length of one side of the rectangle is 18 units, it means that the length of the opposite side is also 18 units.
Since the perimeter of the rectangle is 60 units, it means that
2(18 + W) = 60
18 + W = 60/2 = 30
W = 30 - 18 = 12
Therefore, the lengths, in units, of the other three sides are 18 , 12 and 12 units
Which set of numbers would be included in the shaded portion of the Venn diagram
Answers
Answer:
it is D
Step-by-step explanation:
this is because D has integers which are multiples of 15 and are also even numbers
The set of numbers that would be included in the shaded portion of the Venn diagram is {30, 60, 90, 120}.
What is the Venn diagram?A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by intersections of the circles.
The universal set. ∪, is the set of all positive integers.
The multiples of 15 are;
15, 30, 45, 60, 75, ........
The odd multiplies of 15 are;
15, 45, 75, 105, ......
The even multiplies of 15 are;
30, 60, 90, and 120.....
Comparing the set of numbers that would be included in the shaded portion of the Venn diagram is a set of multiples of 30.
Hence, the set of numbers that would be included in the shaded portion of the Venn diagram is {30, 60, 90, 120}.
Learn more about the Venn diagram here;
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Marco wants to invest his savings in a bank for 3 years. He has borrowed £15,0000 to invest and receives offers from two banks. Bank 1 is:- 2.5 % per year compound interest and Bank 2 is:- 3.8% for 1st year and 1% for each extra year compound interest. Which bank should Marco choose to get the most interest over the 3 year period?
Answers
Answer:
Marcos Should invest with the first bank
Step-by-step explanation:
Formula for finding compound interest is: A = p(1+\frac{r}{n})^{nt}
where
A = the future value of the investment
P = the principal investment amount (the initial deposit)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested
If marcos choose to invest with the first bank
A = 15000(1+\frac{0.025}{12})^{12*3} = £16166.81
If he choose to invest with the second bank
His principal become 15570 in the first year because of the 3.8% offer from the bank and t becomes 2.
A = 15570(1+\frac{0.01}{12})^{12*2} = £15884.27
Comparing the future value of his investment from both bank, Marcos will get more interest from investing with the first bank.
Answer:
Marco should choose the first bank to get the most interest over 3 years (£1153.36)
Step-by-step explanation:
According to the question, Marco is trying to invest his savings of £15,000 in a bank for three (3) years.
Two banks presented an offer with different interest rates. Bank 1 offers 2.5% interes rate per year while Bank 2 offers 3.8% interest rate for the 1st year and 1% interest rate for subsequent years.
In order to calculate the interest amount offered by both banks, we use the formula:
I = P × R × T ÷ 100
Where P= Principal amount to be invested
R = interest rate
T= Time in years
I = Interest amount
We will calculate the interest amount for each year, hence, T is 1 for each year.
Bank 1:
For 1st year;
P= £15,000 , R= 2.5%, T=1
I = 15000 × 2.5 × 1 ÷ 100
I = 375
To get the principal amount for year 2, we add 15000 + 375 = 15375
2nd year;
P= £15,375 , R= 2.5%, T=1
I = 15375 × 2.5 × 1 ÷ 100
I = 384.375
Principal amount for year3= 15375 + 384.375= 15759.38
3rd year;
P= £15,759.38 , R= 2.5%, T=1
I = 15759.38 × 2.5 × 1 ÷ 100
I = 393.98
Amount for three years = 15759.38 + 393.98= £16153.36
Hence, for the first bank, a total amount of £16153.36 was realized after three years with a total interest amount of £16153.36 - £15000 = £1153.36
Bank 2:
For 1st year;
P= £15,000 , R= 3.8%, T=1
I = 15000 × 3.8 × 1 ÷ 100
I = 570
To get the principal amount for year 2, we add 15000 + 570= 15570
N.B: The interest rate has been reduced for following years
2nd year;
P= £15,570 , R= 1%, T=1
I = 15570 × 1 × 1 ÷ 100
I = 155.7
Principal amount for year3= 15570 + 155.7 = 15725.7
3rd year;
P= £15,725.7 , R= 1%, T=1
I = 15725.7 × 1 × 1 ÷ 100
I = 157.257
Amount for three years = 15725.7 + 157.257 = £15882.95
Hence, for the second bank, a total amount of £15,882.95 was realized after three years with a total interest amount of £15882.95 - £15000 = £882.95
The interest amount of Bank 1 (£1153.36) after three years of investing £15000 will be more than the interest amount (£882.95) of Bank2 after investing the same amount for 3 years. Hence, Marco should choose Bank 1 to invest his savings.