Parabolas y=3x2 and y=−3x2+k intersect at points M and N that are in the first and the second quadrants respectively. Find k if length of the segment MN is 6.

Answers

Answer 1

Answer:

[tex]k=54[/tex]

Step-by-step explanation:

Find the coordinates of points M and N in terms of k. Solve the system of two equations:

[tex]\left\{\begin{array}{l}y=3x^2\\ \\y=-3x^2+k\end{array}\right.\Rightarrow \left\{\begin{array}{l}y=3x^2\\ \\y=-y+k\end{array}\right.\\ \\2y=k\\ \\y=\dfrac{k}{2}\\ \\\dfrac{k}{2}=3x^2\\ \\x^2=\dfrac{k}{6}\\ \\x=\pm\sqrt{\dfrac{k}{6}}[/tex]

Two points have the coordinates [tex]M\left(\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex] and [tex]N\left(-\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex]

Find the distance between M and N:

[tex]MN=\sqrt{\left(\sqrt{\dfrac{k}{6}}-\left(-\sqrt{\dfrac{k}{6}}\right)\right)^2+\left(\dfrac{k}{2}-\dfrac{k}{2}\right)^2}=\sqrt{4\dfrac{k}{6}}=\sqrt{\dfrac{2k}{3}}[/tex]

Since MN = 6, you have

[tex]\sqrt{\dfrac{2k}{3}}=6\\ \\\dfrac{2k}{3}=36\\ \\2k=108\\ \\k=54[/tex]


Related Questions

You can also write an equation for equivalent ratios. The equation at the right can be used to find the actual length x of the sculpture room in the museum. Complete the equation and explain what each part represents

Answers

The equation relates the scale drawing of the sculpture room to its actual dimensions using equivalent ratios. By setting the actual length corresponding to 6 cm on the drawing to 30 m, we can solve for the unknown actual length, which is 6 meters. So, the actual length of the sculpture room in the museum is 6 meters.

Completing the equation:

The equation in the image is missing a part: it should be:

1 cm : 5 m = x cm : 30 m

Explanation of the equation:

1 cm: This represents the length of the sculpture room on the scale drawing, as indicated by the scale 1 cm : 5 m.

5 m: This represents the actual length corresponding to every 1 cm on the scale drawing.

x cm: This is the unknown variable we're trying to solve for. It represents the actual length of the sculpture room in the museum.

30 m: This is a constant value, chosen because we want to find the length corresponding to 6 cm on the scale drawing (since the sculpture room in the drawing is 6 cm long).

What each part represents:

The colon (:) separates the two equivalent ratios.

The first ratio (1 cm : 5 m) represents the scale factor, which is the conversion factor between the scale drawing and the actual museum dimensions. It tells us that every 1 cm on the drawing corresponds to an actual length of 5 m.

The second ratio (x cm : 30 m) represents the unknown ratio we want to solve for. It relates the unknown actual length (x cm) to the desired actual length of 30 m (corresponding to 6 cm on the drawing).

Solving for x:

To solve for x, we can cross-multiply the two ratios:

(1 cm) * (30 m) = (5 m) * (x cm)

Simplifying the equation, we get:

30 m = 5x cm

Finally, dividing both sides by 5, we get:

x = 6 m

Therefore, the actual length of the sculpture room in the museum is 6 meters.

The sum of three consecutive even numbers is 84. What is the smallest of the three numbers?

Answers

Answer: 26

Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.

Consecutive even numbers can be represented as x, x + 2, and x + 4.

Since the sum of these is 84, our equation reads

x + (x + 2) + (x + 4) = 84.

Simplifying on the left we get 3x + 6 = 84.

Subtract 6 from both sides and we have 3x = 78.

Divide both sides by 3 and x = 26.

So our smallest number is 26.

Final answer:

To find the smallest of three consecutive even numbers that sum up to 84, we set up an equation and solve for 'x', where 'x', 'x+2', and 'x+4' represent the numbers. Solving this gives us the smallest number, which is 26.

Explanation:Finding the Smallest of Three Consecutive Even Numbers

If the sum of three consecutive even numbers is 84, we can find the smallest number by setting up an equation. Let's denote the smallest even number as 'x'. The next consecutive even number would be 'x + 2', and the one after that would be 'x + 4'. The sum of these three numbers should equal 84:

x + (x + 2) + (x + 4) = 84

Simplifying this equation, we get:
3x + 6 = 84

Subtracting 6 from both sides, we have:
3x = 78

Now, dividing both sides by 3 gives us:
x = 26

Therefore, the smallest of the three consecutive even numbers is 26.

95-a (b+c) when a=9, b= 3, and c = 7.4

Answers

95-9 (3+7)
95-9 (10)
86 (10)
= 8600

Answer:

95-9 (3+7)

95-9 (10)

86 (10)

= 8600

Step-by-step explanation:

What is the complete factorization of 64x2 - 48x + 9?
O A. (8x - 3)(8x+3)
B. (8x - 3)2
OC. 4(4x - 3)2
D. 4(4x - 3)(4x+3)
Please helppp

Answers

B. (8x-3)^2
You can’t factor anything out, because there’s no greatest common factor. That leaves the first two, and because the first one is a conjugate pair, the middle term will cancel.

Answer:

B)  (8x-3)²

Step-by-step explanation:

64x2 - 48x + 9= (8x)² - 2*8x*3 + 3²

Compare with a² - 2ab +b² = (a-b)²;  a = 8x and b =3

=(8x-3)²

32 loaves of bread total, wheat loaves has 8 more then the rye loaves. How many wheat loaves are there?

Answers

Answer:

Step-by-step explanation:

Let the no. Of rye bread = x

Wheat bread = x + 8

The total bread is 32

: x + x + 8 = 32

2x = 32 - 8

2x = 24

x = 24/2

x = 12

No. Of wheat bread = x + 8 = 12+8

No. Of wheat bread = 20

Answer:

Wheat loaves is 20

Step-by-step explanation:

Let wheat loaves be A

And rye loaves be B

A + B = 32

Hence A = B + 8

So, B + B + 8 = 32

2B = 24

B = 12

A = 20

Help please, giving brainliest.

Answers

Answer:

3

Step-by-step explanation:

30 x 3

Tabitha earns $8.50 per hour at her summer job. She wants to save money to buy a tablet that costs $289 plus 6% sales tax. Tabitha has already saved $75. write and solve an inequality that shows how many hours Tabitha will need to work to have enough money to buy the tablet.

Answers

Answer:

The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].

Tabitha needs to work at least 28 hours to buy the tablet.

Step-by-step explanation:

Amount earn per hour = $8.50

Amount already saved = $75

Cost of tablet = $289

Sales tax = 6%

We to write and solve the inequality number of hours Tabitha will need to work to have enough money to buy the tablet.

Solution:

Let the number of hours she need to work be 'x'.

First we will find the total amount required to buy tablet.

Amount of sales tax = [tex]\frac{6}{100}\times289 = \$17.34[/tex]

Now Total cost to buy tablet will be equal to sum of Cost of tablet and Amount of sales tax.

framing in equation form we get;

Total cost to buy tablet = [tex]289+17.34 = \$306.34[/tex]

Now we can say that;

Amount already saved plus Amount earn per hour multiplied by Amount earn per hour should be greater than or equal to Total cost to buy tablet.

framing in equation form we get;

[tex]75+8.5x\geq 306.34[/tex]

hence The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].

On solving the above Inequality we get;

First we will subtract both side by 75 we get;

[tex]75+8.5x-75\geq 306.34-75\\\\8.5x\geq 231.34[/tex]

Dividing both side by 8.5 we get;

[tex]\frac{8.5x}{8.5}\geq \frac{231.34}{8.5}\\\\x\geq 27.21[/tex]

Hence Tabitha needs to work at least 28 hours to buy the tablet.

find the discriminant 7x^2-5x+1=0​

Answers

Answer:

Therefore,

[tex]Discriminant=-3[/tex]

Step-by-step explanation:

Given:

[tex]7x^{2}-5x+1=0[/tex]

To Find:

Discriminant = ?

Solution:

For a Quadratic Equation ax²+bx+c=0

The Discriminant is given as

[tex]Discriminant=b^{2}-4ac[/tex]

On comparing we get

[tex]a=7\\b=-5\\c=1[/tex]

Substituting the values we get

[tex]Discriminant=(-5)^{2}-4\times 7\times 1\\Discriminant=25-28\\Discriminant=-3[/tex]

Therefore,

[tex]Discriminant=-3[/tex]

When one end of a seesaw is 9 inches above the ground and the other one is 21 inches above the ground how far are the ends above the ground when the seesaw is level

Answers

Answer:

15

Count down from 21 and count up from 9 till you have the same number.

21 9

20 10

19 11

18 12

17 13

16 14

15 15

Now they are the same height.

Step-by-step explanation:

Final answer:

When a seesaw is level, the height of both ends above the ground is the average of the heights when one end is lifted. In this case, both ends are 15 inches above the ground when the seesaw is level.

Explanation:

The question is asking for the height of the ends of a seesaw when it is in a level or balanced position. A seesaw balances when it is level, and both ends are at the same height. Considering the given details, one end is 9 inches and the other is 21 inches above ground, when they switch positions due to the seesaw's pendulum-like movement. But when the seesaw is level, both ends are at the same height. Therefore, the height of both ends of the seesaw when it is level is the average of 9 inches and 21 inches. You calculate this average by adding the two given distances and dividing by 2. So:

((9 inches + 21 inches) / 2) = 15 inches

So, when the seesaw is level, both ends are 15 inches above the ground.

Learn more about seesaw here:

https://brainly.com/question/21623981

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Simplify the expression 2j+4j+j+7

Answers

Answer:

7j+7

Step-by-step explanation:

2j+4j+j+7

combine like terms

7j+7

Sorry I don't really know how to explain it, but you just have to combine terms with the same unit

Your neighbor has decided to enlarge his garden. The garden is rectangular with width 6 feet and length 15 feet. The new garden will be similar to the original one, but will have a length of 35 feet. Find the perimeter of the original garden and the enlarged garden.

Answers

Answer:

Original garden: 42 feet

Enlarged garden: 98 feet

Step-by-step explanation:

Perimeter = length (2) + width (2)

Original perimeter:

P = 15(2) + 6(2)

P = 30 + 12

P = 42 feet

In this problem, similar is proportional, so the new garden will be proportional to the old one.

If the original length was 15 and the new length is 35, then 15 would have had to have been multiplied by 2 1/3. That means you need to multiply 6 by 2 1/3, which is 14. That means the dimensions of the enlarged yard is 14 (width) × 35 (length).

Enlarged perimeter

P = 35(2) + 14(2)

P = 70 + 28

P = 98 feet

Final answer:

The perimeter of the original rectangular garden is 42 feet, and the perimeter of the enlarged garden, which is similar in proportion to the original, is 98 feet.

Explanation:

The original garden has a width of 6 feet and a length of 15 feet. The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter of the original garden is 2(6 feet + 15 feet) = 2(21 feet) = 42 feet.

Since the new garden is similar to the original one, and its length is 35 feet, it means that the width will also increase in the same proportion. The original length to width ratio is 15:6 which simplifies to 5:2. Applying this ratio to the new length of 35 feet will give us the new width:

35 feet / 5 = 7 feet (per unit of the ratio)
7 feet * 2 = 14 feet (new width)

The perimeter of the enlarged garden is then 2(14 feet + 35 feet) = 2(49 feet) = 98 feet. So, the perimeter of the original garden is 42 feet and the perimeter of the enlarged garden is 98 feet.

how many solutions does the system of inequalities graphed below have?
A. 0
B. 1
C. 2
D. infinitely many​

Answers

Answer:

A 0

Step-by-step explanation:

because the lines are a paraell and they don't touch

Answer:  A) 0

A solution is a point that is in both shaded regions at the same time. This is impossible due to the fact the regions do not overlap. This is like saying there is a number larger than 1 and this same number is less than -1 at the same time. This is why there are no solutions to this system of inequalities.

Word Problem: You are traveling to your aunt's house that is 239 miles away. If you are currently twice as far from home as you are from your aunt's, how far have you traveled?

Answers

Answer:

119.5

Step-by-step explanation:

evaluate the variable expression when a=-4, b=2, c=-3, and d =4. b-3a/bc^2-d​

Answers

Answer:

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]

Step-by-step explanation:

Evaluate:

[tex]\dfrac{b-3a}{bc^{2}-d}[/tex]

When a=-4, b=2, c=-3, and d =4

Solution:

Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get

[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\[/tex]

[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1[/tex]

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]

A school charges $4.99 per child, $6.00 per adult, and $2.50 per baby, to go see the school play. How much money would they collect if 12 kids, 25 adults, and 6 babies came to see the play?​

Answers

Answer:

$224.88

Step-by-step explanation:

4.99×12= 59.88 for kids

6×25=150 for adults

2.50×6=15 for babies

59.88+150+15= $224.88 collected in total

Will mark brainliest and 15 points

Answers

Answer: its going in straight lines

Step-by-step explanation:

sum of (-3y-5)+(5m+7y)+(6+9m)

Answers

Answer:

4y+14m+1

Step-by-step explanation:

Remove the brackets

-3y-5+5m+7y+6+9m

Rearrange the terms

7y-3y+5m+9m+6-5

Adding like terms

4y+14m+1

4 2/5 divided by 1 1/5

Answers

the answer is: 3 and 1/3

22/5 divided by 6/5.......................
22/5 times 5/6 = 110/30
110/ 30 = 3 1/3
The answer is 3.6 as a decimal or 18/5 as a fraction

Under a dilation centered at the origin, the point (-4 , 3) has image at (8 , -6) The dilation is

Answers

Answer:

Balanced chemical equations only show formulae, not names. A balancing number, written in normal script, multiplies all the atoms in the substance next to it.

What is the remainder when 16,055 is divided by 16? Please i need help

Answers

Answer:

16,055/16 = 1003

The remainder would be 7

Step-by-step explanation:

What is the solution to the system of equations?
(3x+2y = 39
(5x-y=13
O (4,7)
O (7,4)
O (12,5)
(5, 12)

Answers

Answer:

X = 5

Y= 12

Step-by-step explanation:

3x + 2y = 39 —> (1)

5x - y = 13 —> (2)

Multiply (2) with 2

10x - 2y = 26 —> (b)

(1) + (b)

This will eliminate the y factor, leaving:

13x = 65

Therefore, x = 65/14

X= 5. Put this value of 5 in equation 1, which gives;

15 + 2y = 39

2y = 39-25

2y = 24

Y = 12

Answer:

x=5

y = 12

Step-by-step explanation:

3x + 2y = 39

2y = 39 - 3x

y = (39 - 3x) / 2

5x - y = 13

5x - ((39 - 3x) / 2) = 13

5x - 39/2 + 3/2x = 13

5x + 3/2x = 13 + 39/2

13/2x = 65/2

x = 65/2 * 2/13

x = 65/13

x = 5

y = (39 - 3x) / 2

y = (39 - 3*5) / 2

y = (39 - 15) / 2

y = 24/2

y = 12

hemraj made $135 for 9 hours of work. at the same rate, how many hours would he have to work to make $165?

Answers

Answer:

11 hrs

Step-by-step explanation:

so he made 135 for 9 hrs.....thats (135/9) = $ 15 an hr

so if he made 165, he would have to work (165/15) = 11 hrs <==

Find the value of the polynomial 3xy+7x^2−3x^2y+3y^2x−2x^2−2xy+4x^2y−2y^2x, when x=1 and y=−2

Answers

Answer:

[tex]5[/tex]

First Method:

Substitute the given values in for [tex]x[/tex] and [tex]y[/tex].Solve.

This isn't the only method, but it seems the least likely to result in an incorrect answer.

If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]

Substitute [tex]1[/tex] for [tex]x[/tex] and [tex]-2[/tex] for [tex]y[/tex].

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)(-2)+7(1)^2-3(1)^2(-2)+3(-2)^2(1)-2(1)^2-2(1)(-2)+4(1)^2(-2)-2(-2)^2(1)[/tex]

Wow. That's a lot. Let's try simplifying things. I'd start by multiplying all our [tex]1[/tex]'s because any number multiplied by [tex]1[/tex] is that very same number, so we can easily reduce the length of our equation without much worry for messing up our math in the process.

[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]

It still looks like torture trying to figure out this equation, but let's take it in chunks instead of all at once.

[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]

First, I'm going to deal with all the exponents, and turn them into integers.

[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)[/tex]

Notice that things are starting to look less complicated. We are taking our math in chunks. This will make it less likely for us to mess up, although it is more time consuming.Now, let's do multiplication. Any number within a parentheses is going to be multiplied by the number next to it. Remember that this only applies when there is no sign between them. I'm going to go one at a time.

[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2+4+4(-2)-2(4)\\-6+7+6+12-2+4-8-2(4)\\-6+7+6+12-2+4-8-8\\[/tex]

This is a lot of steps, but hopefully it doesn't looks as bad after seeing that I just did multiplication over and over. I'll go over another method after this that may make things less complicated.Now, we add these together. It doesn't matter what order you do this in.

[tex]-6+7+6+12-2+4-8-8\\7+4+6+12-6-2-8-8\\11+18-8-16\\29-24\\5[/tex]

Our final answer is [tex]5[/tex].

Here's another method:

If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]

Because we know that any number multiplied by [tex]1[/tex] will be that same number, let's just substitute in [tex]x[/tex] for now.

[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\[/tex]

Now, just like before, we can multiply [tex]1[/tex] without doing complicated math. Just basically get rid of it even when it's squared because [tex]1^2=1*1=1[/tex].

[tex]3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\3y+7-3y+3y^2-2-2y+4y-2y^2\\3y^2-2y^2+3y-3y-2y+4y+5\\y^2+2y+5[/tex]

Looks a LOT less complicated. Substitute [tex]-2[/tex] in for [tex]y[/tex] and get your final answer.

[tex]y^2+2y+5\\(-2)^2+2(-2)+5\\4-4+5\\5[/tex]

I’m so cunfused! Help please?

Answers

Answer:

36

Step-by-step explanation:

To obtain the required number, multiply 27 by the inverse of [tex]\frac{3}{4}[/tex]

The inverse of [tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex] ( fraction turned upside down ), thus

[tex]\frac{4}{3}[/tex] × 27 ← divide 3 and 27 by 3

= 4 × 9 = 36

The answer would be 36

At present, a man is 5 times older than his daughter. In 7 years, the man is 3 times as old as his daughter. What are their present ages?

Answers

The present age of father is 35 and daughter is 7.

Step-by-step explanation:

Let,

Age of father = x

Age of daughter = y

According to given statement;

A man is 5 times older than his daughter.

x = 5y      Eqn 1

In 7 years, the man is 3 times as old as his daughter.

x+7 = 3(y+7)

[tex]x+7=3y+21\\x=3y+21-7\\x=3y+14\ \ \ Eqn\ 2[/tex]

Putting value of x from Eqn 2 in Eqn 1

[tex]3y+14=5y\\14=5y-3y\\14=2y\\2y=14[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{14}{2}\\y=7[/tex]

Putting y=7 in Eqn 1

[tex]x=5(7)\\x=35[/tex]

The present age of father is 35 and daughter is 7.

Keywords: linear equation, substitution method

Learn more about substitution method at:

brainly.com/question/8929610brainly.com/question/8908016

#LearnwithBrainly

Final answer:

The present ages of the man and his daughter are 35 years and 7 years, respectively.

Explanation:

The question asks us to find the current ages of a man and his daughter, given that the man is currently five times older than his daughter and that after 7 years, he will be three times as old as her. To solve this, we can set up two equations based on the information provided:

Let D be the daughter's current age, the man's current age is 5D (since he is five times older).In 7 years, the daughter's age will be D+7 and the man's age will be 5D+7. At that time, the man will be three times as old as his daughter, so we have 5D+7 = 3(D+7).

Now, we solve the equation from step 2 to find the daughter's age:

5D + 7 = 3(D + 7)5D + 7 = 3D + 215D - 3D = 21 - 72D = 14D = 7

So, the daughter is currently 7 years old. To find the man's age, we multiply the daughter's age by 5:

Man's age = 5 x 7 = 35 years old

Therefore, the man is currently 35 years old and the daughter is 7 years old.

write the expression in the standard form a+bi (showing all work)
(2-i)^3

Answers

[tex]2-11i \text{ is the standard form of given expression }[/tex]

Solution:

The standard form of complex number is: a + bi

where a is the real part and bi is the imaginary part

Given expression is:

[tex](2-i)^3[/tex]

Expand the above expression using algebraic identity

[tex](a-b)^3=a^3-b^3-3ab(a-b)[/tex]

[tex]\text{For } (2-i)^3 \text{ we get, a = 2 and b = i}[/tex]

Thus on expanding using the above algebraic identity we get,

[tex](2-i)^3=(2)^3-(i)^3-3(2)(i)(2-i)[/tex]

Simplify the above expression

[tex](2-i)^3=8 -i^3-6i(2-i)\\\\(2-i)^3=8 -i^3-12i+6i^2[/tex]

We know that,

[tex]i^2 = -1\\\\i^3 = -i[/tex]

Substituting in above simplified expression, we get,

[tex](2-i)^3=8-(-i)-12i+6(-1)\\\\(2-i)^3=8 + i -12i -6\\\\\text{Combine the like terms }\\\\(2-i)^3=8 - 6 + i -12i\\\\(2-i)^3=2-11i[/tex]

Thus the given expression is expressed in standard form

How dose 4x+7=19. Work

Answers

Answer:

3

Step-by-step explanation:

4x+7=19

4x=19-7

4x=12

x=12/4

x=3

What is the measure of angle x, in degrees, in the figure shown? A triangle with angle measure 60 degrees and 53 degrees. The third angle has an unknown measure, x degrees.

Answers

Answer: x = 67

Step-by-step explanation:

60+53+x = 180

The degrees of a triangle always equal 180

113+x = 180

Subtract the 113 from the 180

x= 67

Answer:113

explanation: hope it helps☺

20 POINTS FOR REAL please answer
The data on the graph show the foot lengths and forearm lengths for a group of people. The line of best fit for the data is shown. Use the equation of the line of best fit to predict the length of a person’s forearm if the length of their foot is 8 inches.

A graph is labeled as Foot Length versus Forearm Length. The horizontal axis is labeled as Length of Foot left parenthesis inches right parenthesis and the vertical axis is labeled as Length of Forearm left parenthesis inches right parenthesis. The values on the horizontal axis range from 0 to 15 in increments of 1 and the values on the vertical axis range from 0 to 15 in increments of 1. Several points are scattered throughout the graph and a line is shown which passes between these points and the equation of the line is labeled as y equals 1 decimal point 1 1 x minus 0 decimal point 8 3.

A.
8.88 inches

B.
6.94 inches

C.
9.16 inches

D.
8.05 inches

Answers

Answer:

Option D.

8.05 inches

Step-by-step explanation:

Let

x ----> Length of Foot in inches

y ----> Length of Forearm in inches

we have

[tex]y=1.11x-0.83[/tex]

For x=8 in

substitute the value of x in the linear equation and solve for y

[tex]y=1.11(8)-0.83=8.05\ in[/tex]

The test scores for a math test are displayed in the following box plot. What percent of the students scored at least 75 on the test?

Answers

Please show the picture of the box plot otherwise your question is unanswerabe.

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