Answer:
658.24 m
Step-by-step explanation:
Let A be the point from where Elton started. Connect points A and C, you get triangle ABC with AB=500 m, BC=350 m and m∠B=100°. Use the cosine rule to determine the length of the segment AC:
[tex]AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot \cos \angle B,\\ \\AC^2=500^2+350^2-2\cdot 500\cdot 350\cdot \cos 100^{\circ},\\ \\AC^2=250000+122500-350000\cdot (-0.174),\\ \\AC^2\approx 433276.8622,\\ \\ AC\approx 658.24\ m.[/tex]
Answer:
658.24 m
Step-by-step explanation:
The figure makes a triangle with vertices abc.
Where ab = 500 m
bc = 350 m
The angle abc = 100°
Using the cosine rule we can find the distance ac.
ac² = 500²+350² - 2×500×350×cos100°
= 372,500 - -60,776.86
= 433,276.86
ac = √433,276.86
= 658.24 m
In a certain year the price of gasoline rose by 20% during January, fell by 20% during February, rose by 25% in March, and fell by x% in April. The price of gasoline at the end of April was the same as it had been at the beginning of January. Find the value of x.
Answer: The value of x is [tex]\frac{50}{3}[/tex]
Step-by-step explanation:
Let the original price of gasoline be y
Since we have given that
Price of gasoline rose by 20% during January fell by 20% during February rose by 25% in March and fell by x% in April.
So, According to question,
In January, Price became
[tex]\frac{100+20}{100}\times y=\frac{120}{100}\times y=\frac{6}{5}\times y=\frac{6y}{5}[/tex]
Similarly, In February, Price became
[tex]\frac{100-20}{100}\times \frac{6y}{5}=\frac{80}{100}\times \frac{6y}{5}=\frac{4}{5}\times \frac{6y}{5}=\frac{4}{5}\times \frac{6y}{5}=\frac{24y}{25}[/tex]
Similarly, in March, Price became,
[tex]\frac{100+25}{100}\times \frac{4\times 6y}{25}=\frac{125}{100}\times \frac{6\times 4y}{25}=\frac{5}{4}\times \frac{24y}{25}=\frac{5}{4}\times \frac{24y}{25}=\frac{6y}{5}[/tex]
similarly, in April , Price became,
[tex]\frac{100-x}{100}\times \frac{6y}{5}[/tex]
so, we have given that the price of gasoline at the end of April was the same as it had been at the beginning of January.
So, it becomes,
[tex]\frac{6y}{5}\times \frac{100-x}{100}=y\\\\6(100-x)=500\\\\600-6x=500\\\\600-500=6x\\\\100=6x\\\\x=\frac{100}{6}=\frac{50}{3}[/tex]
Hence, the value of x is [tex]\frac{50}{3}[/tex]
Answer:
x= 16 2/3
Step-by-step explanation:
Price will be p
The price in January increases by 20%, it will be 6p/5. The price in February decreased by 20%, it becomes 24p/25. The price in March rose by 25%, it will be 6y/5.
April: 6y/5 times 100-x/100 = p 6(100-x)=500 100=6x x= 16 2/3
Which value are solution of the inequality? 3r<4r-6
Answer: r > 6
Step-by-step explanation:
3r < 4r - 6
-4r -4r
-r < -6
÷-1 ↓ ÷-1
r > 6
Identify each graph as being a non-linear function, a linear function, or not a function.
Graph A- The first graph.
Graph B- The graph with a circle.
Graph C- Graph shaped like a V.
1. Graph A: not a function
Graph B: not a function
Graph C: linear function
2. Graph A: non-linear function
Graph B: not a function
Graph C: linear function
3. Graph A: not a function
Graph B: not a function
Graph C: non-linear function
4. Graph A: non-linear function
Graph B: not a function
Graph C: non-linear function
ANSWERS PLEASE!
Without explicit graphical representation, precise classification is challenging. Tentatively: Graph A could be a non-linear function, Graph B is not a function due to its circular form, and Graph C could be a linear function (or a piecewise linear function) as a 'V' indicates straight lines.
Explanation:In Mathematics, when we talk about functions, a linear function is one where the graph is a straight line. A non-linear function is anything that is not a linear function, including any graph that is not a straight line. If a graph does not pass the vertical line test, where any vertical line would touch the graph only once, it is considered not a function.
Based on the descriptions given:
Graph A, being the 'first graph,' isn't sufficient information for classification. However, as a placeholder, let's say it's a non-linear function.Graph B, being a circle, does not pass the vertical line test and is therefore not a function.Graph C, if shaped like a 'V,' would be a linear function, as it forms straight lines. However, if the point at which the 'V' changes direction occurs at a single point, it could be argued as a piecewise linear function.Learn more about Function Identification here:https://brainly.com/question/33409105
#SPJ3
1.Graph A: non-linear function
Graph B: not a function
Graph C: linear function
2. Graph A: non-linear function
Graph B: not a function
Graph C: linear function
3. Graph A: not a function
Graph B: not a function
Graph C: non-linear function
Graph A: non-linear function
Graph B: not a function
Graph C: non-linear function
How to categorize the graphsGraph A represents a non-linear function due to its curved shape, showcasing a relationship where the output doesn't change uniformly with respect to the input.
Graph B, resembling a circle, doesn't represent a function as it fails the vertical line test, indicating multiple outputs for a single input.
Graph C, displaying a V-shape, represents a linear function, depicting a consistent rate of change between the variables.
Linear functions maintain a constant slope, resulting in a straight line. Therefore, these classifications are based on the distinctive characteristics of the graphs concerning linearity and functional behavior.
Learn about graphs at: https://brainly.com/question/19040584
#SPJ3
Which is a Proportional Relationship?
A. x + y=3
B. y= 3x^2
C. y= 4x - 1
D. y= 12.5x
If x and y are proportional, then the quotient y and x is constant.
[tex]\dfrac{y}{x}=a-constant[/tex]
The equation of a Proportional Relationship:
[tex]\dfrac{y}{x}=a\qquad\text{multiply both sides by }\ x\neq0\\\\y=ax[/tex]
Therefore your answer is
D. y = 12.5xan auto transport truck holds 12 cars. A car dealer plans to bring in 1150 new cars in June and July. If an auto transport truck is filled for each delivery, except for the last one, how many full truckloads are needed and how many cars will be in the last truck?
Answer: 96 truckloads, 95 will be full, the last on will have 10 cars
Step-by-step explanation: 1150/12= 95.888> 95*12=1140, 1140+10=1150
What is the missing numerator?
2/7 = n/21
A. 3
B. 5
C. 6
D. 8
Answer:
C. 6
Step-by-step explanation:
2 n
-------- = -------------
7 21
We can use cross products to solve this.
2 * 21 = 7 * n
42 = 7n
Divide each side by 7
42/7 = 7n/7
6 =n
A zoo has 19 monkeys and 10 chimpanzees
Answer: It has 29 animals from this info.
The ratio comparing the number of monkeys to the number of chimpanzees in the zoo is[tex]\(19\) to \(10\), \(19:10\), or \(19/10\). This indicates that for every \(19\) monkeys, there are \(10\)[/tex]chimpanzees in the zoo.
The ratio comparing the number of monkeys to the number of chimpanzees in the zoo is expressed as [tex]\(19\) to \(10\), \(19:10\), or \(19/10\). This indicates that for every \(19\) monkeys, there are \(10\) chimpanzees in the zoo. Additionally, it can be written as \(10\) to \(19\), \(10:19\), or \(10/19\), showing the reverse comparison where for every \(10\) chimpanzees, there are \(19\) monkeys. Lastly, it can be represented as \(1.9:1\) or \(1.9/1\), highlighting that for every \(1.9\) monkeys, there is \(1\)[/tex]chimpanzee. These different representations offer flexibility in conveying the proportional relationship between the two quantities, allowing for a clearer understanding of the relative abundance of monkeys and chimpanzees in the zoo.
complete question
Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. (1 point) A zoo has 19 monkeys and 10 chimpanzees. 19 to 10, 19:10, [tex]19/10 10 to 29, 10:29, 10/19 19 to 29, 19 : 29, 19/29 10 to 19, , 10:19 10/19[/tex]
luz will buy a total of $9360 on her car loan. her monthly payment is $390. for how many months is the loan
Luz will have to pay $390 per month for 24 months to repay her $9360 car loan in full.
Explanation:To determine how many months Luz will need to pay for her car loan, we can use a simple division since the question doesn't mention anything about interest rates affecting the payments.
We divide the total loan amount she has to pay, which is $9360, by her monthly payment of $390.
Months to pay off the loan = Total loan amount ÷ Monthly payment
Months = $9360 ÷ $390
Months = 24
Luz will therefore have to make payments for 24 months to repay her car loan in full.
a farmer bought a number of pigs for $180. However, 3 of them died before he could sell the rest at a profit of 8 per pig. His total profit was $109. how many pigs did he originally buy?
The farmer originally bought 41 pigs.
Let x be the number of pigs the farmer originally bought.The total cost of the pigs is $180.After 3 died, he was left with x - 3 pigs.He sold these pigs at a profit of $8 per pig,Resulting in a total profit of 8(x - 3).We know his total profit was $109. So, we can set up an equation:Profit = Selling price - Cost price8(x - 3) = 109 (his total profit) + 180 (cost price)
Combining like terms:8x - 24 = 289
Adding 24 to both sides:8x = 313
Dividing both sides by 8:x = 39.125
Since the farmer can't buy parts of pigs, we round x up to the nearest whole number, which is 40.However, there's a slight discrepancy because the profit wouldn't be exactly $109 if he had 40 pigs. This is because the profit is calculated per pig, and a fraction of a pig wouldn't generate a proportional profit.Therefore, let's try with x = 41:Profit = 8(41 - 3)= 8 * 38
= $304
Total earnings = Profit + Cost price= $304 + $180 = $484
Since the cost price is $180 and the total earnings are $484,The profit would be $484 - $180 = $304, This matches the calculation with 8 pigs sold at a profit of $8 each.Therefore, the farmer originally bought 41 pigs.
In Maria's store, the customer count this week is 3000. Maria is planning a promotion and expects a 5% increase in customers next week. How many additional customers is Maria expecting?
Answer:
There will be an additional 150 customers.
Step-by-step explanation:
First, we need to find what 5% of 3000 is, to do this we need to use the following formula:
Amount x [tex]\frac{percentage}{100}[/tex]
Plug the values in:
3000 x [tex]\frac{5}{100}[/tex] = 150
So there will be an additional 150 customers!
Maria expects 150 additional customers next week, based on a 5% increase from her current customer count of 3000. The total number of customers anticipated is 3150. This calculation involves finding 5% of the current count and adding it to the original number.
To find out how many additional customers Maria is expecting, we need to calculate 5% of the current 3000 customers and then add this number to the original customer count.
Calculate 5% of the current customer count:
5% of 3000 = 0.05 * 3000 = 150 customers
Add the additional customers to the current customer count:3000 + 150 = 3150 customers
So, Maria is expecting an additional 150 customers next week due to the promotion.
About 9/10 of the weight of a watermelon is water how many pounds of water are in the watermelon if it weighs 20 pounds?
Answer: 18 pounds
Step-by-step explanation:
1) 9/ 10 = x/ 20
2) CROSS MULTIPLICATION: 10x/ 10= 180/10
3) Divide each side by ten and "x" is equal to 18
I hope this helped somewhat :)
Marissa is standing next to an 18 door tall flagpole that is casting a 12 foot long shadow. If Marissa's shadow is 3.5 feet long, how tall is Marissa
Answer:
5'3
Step-by-step explanation:
This question will look like this: 18/12 x/3.5. Remember about height/shadow.
You will need to cross multiply 18 and 3.5 and keep 12, x as 12x.
Now it will look like this: 12x=63. Divide that 63 with 12 and you will get 5.25.
Since there is a 5 next to that 2 you add 1 because 5 or higher add one and 5 or lower don't add anything.
You got rid of that 5 and added 1 to the 2, you will have 5'3
Hoped it helped!
What is the rate of change ???
Answer:
24 photos per day i believe
I believe it is A but I am not sure.
Answer: The answer is A
Step-by-step explanation: You use substitution because it says that 4-t is equal to r.
solving systems by elimination 3x+y=9
y=3x+6
[tex]\left\{\begin{array}{ccc}3x+y=9\\y=3x+6&\text{subtract 3x from both sides}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x+y=9\\-3x+y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad2y=15\qquad\text{divide both sides by 2}\\.\qquad\qquad\boxed{y=7.5}\\\\\text{Put the value of y to the first equation}\\\\3x+7.5=9\qquad\text{subtract 7.5 from both sides}\\3x=1.5\qquad\text{divide both sides by 3}\\\boxed{x=0.5}\\\\Answer:\ \boxed{x=0.5\ and\ y=7.5\to(0.5,\ 7.5)}[/tex]
Use Distributive property to rewrite each algebraic expression problem: 4(x+2
Answer:4x+8
Step-by-step explanation:
4x+8, 4*x+4*2 for the distributive property
In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=x2−16 , and CE=6x . What is AC ? Enter your answer in the box.
Answer:
AC = 96 units.Step-by-step explanation:
Given ABCD is a parallelogram.
And diagonals AC and BD intersects at point E.
Note: Diagonals of a parallelogram intersects at mid-point.
E is the mid point of diagonal AC
Therefore,
AE = CE.
Plugging expression for AE and CE, we get
[tex]x^2-16 =6x.[/tex]
Subtracting 6x from both sides, we get
[tex]x^2-16-6x = 6x-6x[/tex]
[tex]x^2 -6x -16 =0[/tex]
Factoring quadratic
(x+2)(x-8) =0.
x+2 =0 => x=-2.
x-8=0 => x=8.
We can't take the length by a negative number. Therefore, x=8.
Now, plugging x= 8 in CE =6x, we get
CE = 6(8) = 48.
We need to find the length of AC.
AC would be two times of CE.
Therefore, AC = 2 × 48 = 96.
Answer:
96
Step-by-step explanation:
What is BC?
Enter your answer in the box?
Answer:
18 is your answer
the tickmarks on the vertices of B and C mean that those angles are twins, which means that the sides AB = AC, which means is an isosceles triangle.
now if AB = AC, then
[tex]\bf 8x-4=5x+11\implies 3x=15\implies x=\cfrac{15}{3}\implies \boxed{x=5} \\\\\\ BC\implies 4x-2\implies 4(5)-2\implies 18[/tex]
The graph shows a production possibilities curve for Sabrina’s Soccer.
At which point on the graph are resources not used efficiently?
A) point A
B) point F
C) point X
D) point Y
Answer:
D
Step-by-step explanation:
A production possibilities curve shows the maximum amount of 2 goods that can be produced given the input is fixed.
The points that lie on the curve gives different combinations of output of 2 goods given that resources shifts from one to another.The point outside the curve are impossible combination because with current resources, this much of both goods cannot be produced.The point inside the curve shows inefficient use of resources because more could be produced of each good given the resources.So the point which uses resources inefficiently is the one inside the curve, which is Y.
Answer choice D is right.
Which algebraic rule describes the transformation?
A) (x, y) → (x + 2, y + 5)
B) (x, y) → (x − 2, y + 5)
C) (x, y) → (x + 2, y − 5)
D) (x, y) → (x − 2, y − 5)
Answer:
D
Step-by-step explanation:
The original figure was was moved 2 units to the left (-2), and 5 units down (-5).
Answer:
D is correct.
Step-by-step explanation:
In the given figure two rectangle MNOP and M'N'O'P'
To choose correct transformation rule from MNOP to M'N'O'P'
So, we change for point M
M(-2,3) → M'(-4,-2)
If shift M 2 unit left
M(-2,3) → M(-2-2,3)
Now, shift 5 unit down
M(-2-2,3) → M(-4,-2) ⇔M'(-4,-2)
So,
(x,y) → (x-2,y-5)
Rule: (x,y) → (x-2,y-5)
Using this rule get MNOP to M'N'O'P'
Valerie sold 42 tickets to the school play and mark sold 24 tickets. what is the ratio of the number of tickets Valerie sold to the number of tickets mark sold?
The ratio of tickets sold by Valerie to those sold by Mark is 7:4, after simplifying the original ratio of 42:24 by dividing both numbers by 6.
To find the ratio of tickets sold by Valerie to those sold by Mark, we simply compare the two quantities. Valerie sold 42 tickets, and Mark sold 24 tickets. Therefore, the ratio can be expressed as 42:24. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 6 in this case. Thus, after simplification, the ratio of tickets sold by Valerie to Mark is 7:4. This process illustrates the method of comparing quantities and simplifying ratios, providing a clear and concise representation of the relative ticket sales between Valerie and Mark.
3 equivalent ratios for 5/7
Answer:
10/14, 15/21, and 20,28
Step-by-step explanation:
You just need to multiply a number on the numerator and the denominator. Remember, whatever you do to the numerator you have to do on your denominator.
turn 6/5 into mixed mumber
Answer:
[tex]1\frac{1}{5}[/tex]
Answer:
1 1/5
Step-by-step explanation:
There is one whole(5/5) and then 1 extra 5th(1/5), so the answer is 1 1/5.
The original sale price of an item at markdowns is $110.95. You have an additional 20% off coupon for markdowns for purchases totaling $90.00 or more. Using the coupon, how much more do save when compared to the original sale price?
Answer:
$22.19
Step-by-step explanation:
20% off the original price = $110.95 - (20% x $110.95)
20% x $110.95 = $22.19
$110.95 - $22.19 = $88.76
difference = $110.95 - $88.76 = $22.19
Answer:
You will save $22.19 when compared to the original sale price.
Step-by-step explanation:
The original sale price of an item at markdowns is $110.95.
You have an additional 20% off coupon for markdowns for purchases totaling $90.00 or more.
So, this becomes:
[tex]0.20\times110.95=22.19[/tex] dollars
Hence, you will save $22.19 when compared to the original sale price.
in the figure below ABC = MPN find m P
Answer:
m∡P = 80°
Step-by-step explanation:
Because ABC = MPN, m∡B = m∡P. Therefore, m∡P = 80°.
What are the approximate solutions of 2x2 − 7x = 3, rounded to the nearest hundredth?
Answer:
-0.39 and 3.89
Step-by-step explanation:
By using the quadratic formula it will give you the answers of x= 7 + or - square root of 73 all over 4.
When you do the math of both of the equations it will give you the answers above
A geometric sequence is shown below: 66 a0, -11, 22, 56 a1, 88, -176. A) What is the common ratio for this geometric sequence? 69 a2 B) What are the missing terms in the geometric sequence shown above?
Answer:
Step-by-step explanation:
Given a geometric sequence as
66 a0, -11, 22, 56 a1, 88, -176
We have to find the common ratio and also the missing numbers.
A geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Hence by comparing two consecutive numbers let us find common ratio.
Consider 88 and -176. -176 = 88(-2) Hence common ratio is -2
a0 = -11/-2 = 5.5
a1 = 88/-2 = -44
Missing terms are -132 and 5.5
common ratio = -2
What is the square root of -15
Answer:
you cannot do a square root of a negative number so there is no answer.
Step-by-step explanation:
Can someone help? =
Betty saves $161 a month. She saves $141 less each month than Jack. How much will Jack save in 2 years?
I need to use a area model to the partial products of the algorithm.
Thanxs if u can!
Answer:
He will save $7,248 in 2 years.
Step-by-step explanation:
The whole explanation is in the picture :)
Answer:
jack earns 3624 a month
Step-by-step explanation:
?-141=161
141+161=302
jack earns 302 bucks a month
302 times 12 = 3624
10 2
300║3000 ║ 600 ║
2 ║ 20 ║ 4 ║
3000+600+20+4=3624
List the first 5 multiples, and find ALL the factors of 13
Answer:
13,26,39,52,65,78 are the multiples 13 and 1 are the all of the factors
Hi There!
List the multiples and factors of 13:
Multiples: 13, 26, 39, 52, 65...
Factors: 1, 13...
Hope This Helps :)