The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = 4 and the point (2, 1). Substitute:
[tex]y-1=4(x-2)[/tex] use distributive property
[tex]y-1=(4)(x)+(4)(-2)[/tex]
[tex]y-1=4x-8[/tex] add 1 to both sides
[tex]\boxed{y=4x-7}[/tex]
-x+2 > 3 whats the answer plz its urgent thanks
if y varies directly as x and y=8 when x=2, find y when x=6
Answer:
y = 8
Step-by-step explanation:
If y varies directly as x we can write y = kx where k is some constant.
Y = 8 when x = 2 so 8 = k*2
k = 8/2 = 4
so y = 4x
This is the equation of variation.
When x = 6, y = 4*6 = 24 (answer).
Answer:
y =24
Step-by-step explanation:
The equation for direct variation is
y =kx
If we know x and y we can solve for k
y=kx
8 =k*2
Divide each side by 2
8/2 = k2/2
4 =k
y =4x
We want to find y when x=6
y =4*6
y =24
Mrs hawk assigns her students an average of no more than 15 questions on each assignment mrs. hawks students had 11,10,13,14 and 14 questions write amd solve amd inequality that Mrs hawk can use to determine the number of questions she can have in the sixth assignment
Answer:
The number of questions in sixth assignment must be less than or equal to 28.
Step-by-step explanation:
The number of questions in first five assignments are 11,10,13,14 and 14.
It is given that Mrs hawk assigns her students an average of no more than 15 questions on each assignment. Therefore the average of six assignments is less than or equal to 15 questions.
Let the number of questions in sixth assignment be x
[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
Average of six assignments are
[tex]A=\frac{11+10+13+14+14+x}{6}[/tex]
[tex]A=\frac{62+x}{6}[/tex]
Since the average of questions is no more than 15, therefore
[tex]A\leq 15[/tex]
[tex]\frac{62+x}{6}\leq 15[/tex]
[tex]62+x\leq 90[/tex]
[tex]x\leq 28[/tex]
Therefore the number of questions in sixth assignment must be less than or equal to 28.
abcd is not drawn to scale. based on the diagonal measures given abcd
Answer:
DAB must equal 52 because same side interior angles are supplementary. Supplementary describes 2 angles whose measures add up to 180
Answer: May or may not be
Step-by-step explanation:
check the picture and trust me
Valerie and Robbie are playing a number game.
Valerie tells Robbie “I’m thinking of a number between 1 and 50. If I divide the number by 4, then add 5, that subtract 6, I get 6.”
What number is Valerie thinking of ?
In the number game that Valerie and Robbie are playing, based on Valerie's clues, the number she is thinking of can be determined using a mathematical equation: x/4 + 5 - 6 = 6. Solving this equation step-by-step, the number Valerie is thinking of is 28.
Explanation:In the given scenario, Valerie and Robbie are playing a number game. Valerie tells Robbie that she's thinking of a number which, when divided by 4, then added to 5, and subtracted by 6, equals to 6. This can be translated into a mathematical equation:
x/4 + 5 - 6 = 6
We can simplify this step-by-step. First, we can combine the constants:
x/4 -1 = 6
Next, add 1 to both sides to isolate x/4 on the left:
x/4 = 7
Finally, to find x, multiply both sides by 4:
x = 28
So, the number that Valerie is thinking of is 28.
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Select the correct rule for this Geometric Sequence:
3, 12, 48, 192, ...
Question 5 options:
A(n)=12−3n−1
A(n)=3⋅12n−1
A(n)=3⋅4n−1
A(n)=4⋅3n−1
A(n)=3+12n−1
Answer:
see explanation
Step-by-step explanation:
given the geometric sequence then the n th term rule is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] . [tex]r^{n-1}[/tex]
where r is the common ratio and [tex]a_{1}[/tex] the first term
here r = [tex]\frac{192}{48}[/tex] = [tex]\frac{48}{12}[/tex] = 4 and [tex]a_{1}[/tex] = 3, hence
[tex]a_{n}[/tex] = 3 . [tex]4^{n-1}[/tex] ← third option
Find the earnings for selling the same number of each type of sandwich use x to represent the number of each sandwich sold
The earnings for selling the same number of each type of sandwich, considering both Turkey and Ham with Pretzel Roll and Bagel options, amount to $48. This is derived from a simplified expression of $29.10x, factored by 11, indicating a total revenue of $4.30 per sandwich.
Earnings for Selling Sandwiches
1: Identify the Given Information
We have two types of sandwiches: Turkey and Ham.
Each type comes in two types of bread: Pretzel Roll and Bagel.
Prices are provided for each combination:
Turkey Pretzel: $2.25
Turkey Bagel: $2.00
Ham Pretzel: $1.55
Ham Bagel: $1.30
2: Represent the Number of Sandwiches with a Variable
Let x represent the number of each type of sandwich sold (both Turkey and Ham, regardless of bread).
3: Calculate Earnings for Each Type of Sandwich
Turkey Sandwich: $11 (given price) * x (number sold) = $11x
Ham Sandwich: $11 (given price) * x (number sold) = $11x
Step 4: Calculate Earnings for Each Bread Type (excluding overlapping information)
Pretzel Roll: (Earnings from Turkey Pretzel + Earnings from Ham Pretzel) = ($2.25 * x) + ($1.55 * x) = $3.80x
Bagel: (Earnings from Turkey Bagel + Earnings from Ham Bagel) = ($2.00 * x) + ($1.30 * x) = $3.30x
5: Combine Earnings for Total Revenue
Total Earnings = Earnings from Turkey Sandwiches + Earnings from Ham Sandwiches + Earnings from Pretzel Rolls + Earnings from Bagels
Total Earnings = $11x + $11x + $3.80x + $3.30x = $29.10x
6: Simplify the Expression
Total Earnings = $29.10x
Since we are selling the same number of each type of sandwich, 11 is a common factor in all four terms.
We can factor out 11 to obtain:
Total Earnings = 11 * ($2.65 + $1 + $0.35 + $0.30) = 11 * $4.30 = $48
Therefore, the earnings for selling the same number of each type of sandwich are $48.
Order each step and justification that is needed to solve the equation below. 2/3y+ 15=9
[ Answer ]
Y = -9
[ Explanation ]
Subtract 15 from both sides:
2/3y + 15 - 15 = 9 - 15
Simplify:
2/3y = -6
Multiply each side by 3:
3 * 2/3y = 3 (-6)
Simplify:
2y = -18
Divide both sides by 2:
2y / 2 = -18/2
y = -9
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Using the simplification, it is proven that the y = -9 from the equation 2/3y + 15 = 9.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given that 2/3y + 15 = 9
Subtract 15 from both sides;
2/3y + 15 - 15 = 9 - 15
Now Simplify,
2/3y = -6
Multiply each side by 3,
3 (2/3y) = 3 (-6)
2y = -18
y = -9
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Use the equation and type the ordered-pairs. y = 2^x {(-1, ), (0, ), (1, ), (2, ), (3, ), (4, )}
Put the values of x to the equation y = 2ˣ:
[tex]x=-1\to y=2^{-1}=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right)\\\\x=0\to y=2^0=1\to(0,\ 1)\\\\x=1\to y=2^1=2\to(1,\ 2)\\\\x=2\to y=2^2=4\to(2,\ 4)\\\\x=3\to y=2^3=8\to(3,\ 8)\\\\x=4\to y=2^4=16\to (4,\ 16)[/tex]
Answer:
[tex]\left\{\left(-1,\ \dfrac{1}{2}\right);\ (0,\ 1);\ (1,\ 2);\ (2,\ 4);\ (3,\ 8);\ (4,\ 16)\right\}[/tex]
Rectangle ABCD has vertices A(-3, 1), B(5, 7), C(9, 4), and D(1, -2). Calculate the
area of rectangle ABCD.
It's not a rectangle. Look at the picture.
It is a parallelogram.
The area of the red rectangle:
[tex]A_{\boxed{ \ }}=(4+8)(6+3)=(12)(9)=108[/tex]
The areas of the right triangles:
[tex]A_1=\dfrac{1}{2}(3)(4)=6\\\\A_2=\dfrac{1}{2}(6)(8)=24[/tex]
The area of a parallelogram:
[tex]A=A_{\boxed{ \ }}-(2A_1+2A_2)\\\\A=108-(2\cdot6+2\cdot24)=108-(12+48)=108-60=48[/tex]
A coffee shop sold 1627 espressos, 2741 cappuccinos and 4226 lattes. how many cups of coffee were sold in total?
By using the simple addition operation, the total number of cups of coffee sold in the coffee shop, counting espressos, cappuccinos, and lattes, is 8,594 cups.
Explanation:To find the total number of cups of coffee sold, we should add up the number of espressos, cappuccinos, and lattes. This principle is known as simple summation or addition operation in mathematics. As per the numbers given:
Espressos sold: 1627Cappuccinos sold: 2741Lattes sold: 4226When we add these together, we get the total cups of coffee sold as:
1627 (Espressos) + 2741 (Cappuccinos) + 4226 (Lattes) = 8594 cups of coffee in total
So, the coffee shop has sold a total of 8594 cups of coffee.
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job starting salary of 81,000 and gets a 2% raise every year.what is the expected salary after the eight year ? please explain how to do step by step. really need help.
Answer:
hell have 120,000
Step-by-step explanation:
The velocity of a car increases from 2.0 m/s to 16.0 m/s in a time period of 3.5 s. What was the average acceleration?
The average acceleration of the car is 4 m/s²
The given parameters:
initial velocity of the car, u = 2 m/s
final velocity of the car, v = 16 m/s
time of motion of the car, t = 3.5 s
To find:
the average acceleration of the carThe average acceleration of the car is calculated as the change in velocity per change in time.
The formula for average acceleration is given below;
[tex]a = \frac{\Delta v}{\Delta t} = \frac{v- u}{t} = \frac{16 - 2}{3.5} = 4 \ m/s^2[/tex]
Thus, the average acceleration of the car is 4 m/s²
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Please help me, ASAP!
A candy mixture is made from 6 pounds of sugar sticks of $10 per pound and 14 pounds of jelly beans of $8 per pound. Find the price of the candy mixture per pound.
Answer: The price per pound is $18
Write an explicit formula for the sequence given by the recursive definition a(1)=1 and a(n+1)=a(n)+7
Answer:
an = -6+n
or
an = 1 + 7(n-1)
Step-by-step explanation:
a(1)=1 and a(n+1)=a(n)+7
The explicit formula is
an = a1+ d (n-1)
we know a1 =1
Looking at a(n+1)=a(n)+7
We are adding 7 each time so the common difference is +7
an = 1 + 7(n-1)
We can simplify this
an = 1 + 7n -7
an = -6+n
You can use either formula
-2/7 multiply by -5 2/3
Answer:
1.61904761905
Step-by-step explanation:
-5 2/3 is equal to -17/3. We then multiply the two fractions: -2/7 *-17/3, the answer is 1.61904761905 as a decimal or 34/21( or 1 13/21).
Hope this helps! <3
In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find AC, if CD = 6 sqrt 3
Final answer:
Since ΔACD is an isosceles right triangle, the two legs AC and CD are equal. Given CD = 6 √ 3, AC is also 6 √ 3 units.
Explanation:
In triangle ΔABC, we are given that m∠ACB = 90°, meaning that ΔACB is a right-angled triangle. We are also given that CD is perpendicular to AB and that m∠ACD = 45°. Since CD is perpendicular to AB at D, triangle ΔACD is also a right-angled triangle with a 45° angle, which makes it an isosceles right triangle. In an isosceles right triangle, the lengths of the legs are equal. Therefore, AC will be equal to CD which is given as 6 √ 3.
The length of AC in triangle ΔACB can be found using Pythagoras' theorem, AC = √(AB² + BC²). But here we need only the length of AC in the right-angled ΔACD where AC equals CD.
Hence, AC = 6 √ 3 units.
which choice shows how to find the greatest common factor of 18 and 72 through prime factorization
[tex]\begin{array}{c|c}18&2\\9&3\\3&3\\1\end{array}\\\\18=\boxed2\cdot\boxed3\cdot\boxed3\\\\\begin{array}{c|c}72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\72=2\cdot2\cdot\boxed2\cdot\boxed3\cdot\boxed3\\\\GCF(18,\ 72)=\boxed2\cdot\boxed3\cdot\boxed3=\boxed{\boxed{18}}[/tex]
The greatest common factor of 18 and 72 can be found through prime factorization, by identifying the prime factors of each number, finding the common factors, and multiplying them together. In this case, the greatest common factor is 18.
Explanation:To find the greatest common factor (GCF) of 18 and 72 through prime factorization, follow these steps:
First, obtain the prime factors of each number. For 18, the prime factors are 2, 3, and 3. For 72, the prime factors are 2, 2, 2, 3, and 3. Next, identify the common prime factors. Both 18 and 72 have the prime factors 2, 3, and 3 in common. Then multiply these common factors together. This gives 2*3*3 = 18. So, the greatest common factor of 18 and 72 is 18.Learn more about Greatest Common Factor here:
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(03.02 LC)
Look at the figure below:
Triangle ABC with a segment joining vertex A to point D on side BC.
Which information is required to prove that angle ABD is congruent to angle ACD? (6 points)
Segment AC is congruent to segment AB.
Segment AD is congruent to segment AC.
Segment BD is congruent to segment AD.
Segment AB is congruent to segment BD.
Answer:
SEgment AC is congruent to segment AB
Step-by-step explanation:
given is a triangle ABC with a segment joining A to D on side BC.
To prove that ABD is congruent to ACD
Let us compare these two triangles.
AD = AD (reflexive) Thus one side is equal.
IF AB = AC, then by isosceles triangles property we have angle B = angle C
Thus we get two sides equal. But this is a necessary condition not sufficient.
Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB
Thus if either AD is angle bisector, or D is mid point besides AC = AB we get
the two triangles are congruent.
3/5 (10+5x)−1/3(6x+3)=9 ok answer fast
Answer: x = 4
Step-by-step explanation:
[tex]\dfrac{3}{5}(10 + 5x) - \dfrac{1}{3}(6x + 3)=9[/tex]
[tex]\dfrac{3}{5}(10 + 5x)(15) - \dfrac{1}{3}(6x + 3)(15)=9(15)[/tex] multiplied by common denominator
3(10 + 5x)(3) - 1(6x + 3)(5) = 9(15) reduced all fractions
90 + 45x - 30x - 15 = 135 distributed
15x + 75 = 135 simplified (added like terms)
15x = 60 subtracted 75 from both sides
x = 4 divided 15 from both sides
The unchanging value of the ratio between two proportional quantities is
Answer:
The proportional
Step-by-step explanation:
twenty of the students in Hannah's class, or 80% of the class, voted to have pizza for lunch every Wednesday. How many students are in Hannah's class?
Answer:
There are 25 students in Hannah's class.
Step-by-step explanation:
If 20 students in Hannah's class is 80% of the total amount of students, we can use a variable to figure out the total amount of students.
Let's say x is the total amount of students. We can use this equation to solve the problem:
[tex]20 = .8x[/tex]
This is saying 20 equals 80% (.8 when you move the decimal 2 times) of x, or the total amount of students. Let's solve.
20 = .8x
Divide by .8
25 = x
There are 25 students in Hannah's class.
Percentage of a number is the part of the number in every hundred. The total number of students in Hannah's class is 25.
Given information
Total number of students in Hannah's class voted for the pizza is 20.
The total percent of students in Hannah's class voted for the pizza is 80.
What is percentage of a number?Percentage of a number is the part of the number in every hundred. A percentage of a number is the ratio expressed as fraction of hundred.
Suppose the total number of student in Hannah's class is x.
As total number of students in Hannah's class voted for the pizza is 20 and total percent of students in Hannah's class voted for the pizza is 80.
Therefore the the 80 percent of the total student of the class is equal to the number 20. The 80 percent of a number is 20 thus,
[tex]\begin{aligned}\\\dfrac{80}{100} \times x&=20\\\dfrac{4}{5} \times x&=20\\x&=\dfrac{20\times5}{4} \\x&=25\\\end[/tex]
Thus the total number of students in Hannah's class is 25.
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which expression is equivalent to (7x^2-4)(5x+7)
Expand to get 35x^3+49x^2-20x-28
Answer:
3x(3x + 2)
Step-by-step explanation:
251,589 divided by 252
Answer:
The answer would be 998.4
Step-by-step explanation:
251,589 divided by 252 = 998.36
round it to 998.4
last year the attendance at the homecoming football game was 300.This year , 360 attended What was the percent increase from last year to this year ?
Answer:
20%
Step-by-step explanation:
Percent increase is difference/original
360-300) / 300
60/300 / 60/60 = 1/5 * 20/20 = 20/100
Percent is out of 100
An airplane must clear a 60-foot pole at the end of a runway 500 yards long determine the angle of elevation at which the airplane must ascend to clear the pole.
Answer:
2.3 degrees.
Step-by-step explanation:
Please find the attachment.
We are told that an airplane must clear a 60-foot pole at the end of a runway 500 yards long.
Let us convert 500 yards to feet.
1 yard= 3 feet.
500 yards= 3*500 feet= 1500 feet.
We can see from our attachment pole and runway are in form of a right triangle. The pole is opposite to angle of elevation of plane and length of runway is adjacent.
Since tangent represents the relation between opposite and adjacent of right triangle, So we will use tangent to find angle of elevation that plane must ascend to clear the pole.
[tex]tan(\theta)=\frac{60}{1500}[/tex]
[tex]\theta=\tan^{-1}(\frac{60}{1500} )[/tex]
[tex]\theta=\tan^{-1}(0.04)[/tex]
[tex]\theta=2.290610042639[/tex]
Therefore, the airplane must ascend 2.3 degrees to clear the pole.
3x + 5 equals 19 - 4x what does x equals to
Answer:
x = 2Step-by-step explanation:
3x + 5 = 19 - 4x subtract 5 from both sides
3x = 14 - 4x add 4x to both sides
7x = 14 divide both sides by 7
x = 2
Answer:
x=2
Step-by-step explanation:
3x + 5 = 19 - 4x
Add 4x to each side
3x + 5 +4x= 19 - 4x+4x
7x+5 = 19
Subtract 5 from each side
7x+5-5 =19-5
7x =14
Divide each side by 7
7x/7 = 14/7
x = 2
1. 5h-9+-16+6h
2. 4x+4=9x-36
3.which of the following equation has an infinite number of solutions?
A. 3x-3+-4x B.2y+4-y+16 C. 7x+5=4x+5+3x D.6y-2+2(y=1)
Answer:
1) 11h - 25
2) 8
3) C
Step-by-step explanation:
1) 5h-9+-16+6h
+ and - together makes -
5h - 9 - 16 + 6h
Arrange the like terms together
5h + 6h - 9 - 16
= 11h - (9+16)
= 11h - 25
2) 4x+4=9x-36
Subtract 4x from both sides
4x+4-4x = 9x-36-4x
Cancl out 4x and -4x from the left side
4 = 9x - 4x -36
=> 4 = 5x -36
Add 36 to both sides
4+36 = 5x -36 + 36
Cancel out -36 and +36 from the right side
=> 40 = 5x
Flip both the sides of the equation
5x = 40
Dividing both sides by 5
[tex]\frac{5x}{5} = \frac{40}{5}[/tex]
Cancel out the 5's on the top and bottom of the left side
x = 8
3) 7x+5 = 4x+5+3x
Arrange the like terms together on the right side
7x+5 = 4x+3x+5
=> 7x+5 = 7x+5
Subtract 5 from both sides
7x+5-5 = 7x+5-5
Cancel out +5 and -5 on both the sides
7x = 7x
Divide both sides by 7
[tex]\frac{7x}{7} = \frac{7x}{7}[/tex]
Cancel out the 7's from the top and bottom of both sides
x = x
which can be true for infinite value of x like 1=1, 2=2, 3=3,.............
Find the area of rectangle PLUM
If entering your answer as a decimal, round your final answer to the nearest hundredth.
PL= sqrt(4^2+12^2)=4sqrt(1+9)=4sqrt(10)
Using similarity gives that AM=4/3.
ML=40/3
[PLMU]=40/3 * 4 = 160/3 (53.33)
Or
PM= sqrt(4^2+16/9)=sqrt(160/9)=4sqrt(10)/3
4sqrt(10)*4sqrt(10)/3=160/3 or approximately 53.33
Which equation demonstrates the distributive property? A) 15 + 40 = 55 B) 15 x 40 = 40 x 15 C) (3 + 8)5 = 5(3 + 8) D) 15 + 40 = 5(3 + 8)
The distributive property: a(b + c) = ab + ac.
Answer: D) 15 + 40 = 5 · 3 + 5 · 8 = 5 · (3 + 8)Answer:
d 15+40=5(3+8)
Step-by-step explanation: