Which box plot has the same data as the dot plot?

Answer:

[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]

Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.

Step-by-step explanation:

We are given that a frog leaps two feet, with the highest point in the jump being six inches.

Assuming the frog starts at (0,0), we want to find a quadratic function in vertex form for the path of the jump.

First, we will convert the length of the jump to inches. Two feet is equivalent to 24 inches.

Next, since the frog started at (0, 0), in order to jump a length of 24 inches, it must have ended at (0, 24). These two points will also be our two roots: x = 0 and x = 24. We can use the factored form of a quadratic:

[tex]f(x)=a(x-p)(x-q)[/tex]

Where p and q are the roots.

Substitute in the roots:

[tex]f(x)=a(x-0)(x-24)=ax(x-24)[/tex]

Now, since the frog reached a maximum height of six inches, the y-coordinate of the function at its vertex point is 6.

Since a parabola is symmetrical along its axis of symmetry, the axis of symmetry is always halfway between the two roots.

Therefore, the x-coordinate of our vertex is:

[tex]\displaystyle x=\frac{24-0}{2}=12[/tex]

So, when x = 12, f(x) = 6. Substitute:

[tex]6=a(12)(12-24)[/tex]

Solve for a:

[tex]\displaystyle- 144a=6\Rightarrow a=-\frac{1}{24}[/tex]

Therefore, our function is:

[tex]\displaystyle f(x)=-\frac{1}{24}x(x-24)[/tex]

Now, we can place this into vertex form:

[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

Our leading coefficient is -1/24, and the vertex is (12, 6). Hence, our function is:

[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]

Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.

Answer:

16/32

Step-by-step explanation:

Answer:

C, 8.5

Step-by-step explanation:

The area of a rectangular prism is Length times Width times Height. If the volume of the tank (which is a rectangular prism) is 1360, then the L x W x H is 1360. The area of the base of the tank is determined by multiplying the Length and the Width together, so that means that L x W = 160.

Our first equation

L x W x H = 1360

Our second equation

L x W = 160

We see that 1360 divided by 160 gets us the height of the prism.

1360 / 160 = 8.5, so the answer is C

Answer:

16π

Step-by-step explanation:

ooohhhh, that makes so much more sense, I wasn't actually supposed to substitute 3.14 for π, whoops, sorry

m is independent variable and p is dependent variable.

Because number of pair of shoes depend on the number of miles run by her.

Answer:

1/2

Step-by-step explanation:

Answer:

rectangular prism

Step-by-step explanation:

Answer:

244140625 or 5^12

Step-by-step explanation:

When it comes to multiplication, you add exponents IF the base (the 5 at the bottom is called base) is the same answer. for example: 1^16 x 1^9, since the exponents are the same you just add the exponents (16 & 9) which is 25 or 1^25

Dividing is the same as multiplying except your subtracting with the examples, adding and subtracting is simplifying and solving, for example

14^2 + 13^3

          14 * 14 = 196

                   13*13*13 =2,197

          196+2,197 = 2,393

Same thing for subtraction

13^3 - 14^2

2,197 - 196 = 2,001

Hope this helps

~R3V0

Answer:

D.

Step-by-step explanation:

As you can see, there is a total of 8 slices, and 5 are shaded. So, you know that it is 5/8. As you can also see, there is 5 of these. So, you would have 5/8 5 times, or:

5/8 x 5

Hope this helps!

Answer:

952 l

Step-by-step explanation:

Answer:

[tex]\frac{7}{22}[/tex], the total sum of the money is    

Step-by-step explanation:

1- [tex]\frac{5}{11}[/tex]= [tex]\frac{6}{11}[/tex]

[tex]\frac{6}{11}[/tex]*[tex]\frac{7}{12}[/tex]= [tex]\frac{7}{22}[/tex]

x* [tex]\frac{7}{22}[/tex]= 4500

4500/[tex]\frac{7}{22}[/tex]= about 14142.85

this is what I got out.

Answer:

20in

Step-by-step explanation:

To find the rate of which they are similar all you have to do is divide 10 by 4 or 15 by 6 to get a rate of 2.5 then multiply that rate by 8 to find your answer

Answer:

12+12=24x3

Step-by-step explanation:

Answer:

Yes this is a function.

Step-by-step explanation:

This graph is a function because it passes the vertical line test. The vertical line test ensures that no x value has more than one y value. You can take a pencil, hold it vertically, and move it horizontally across your paper to test whether or not the graph contains multiple y values for a single x value. If it passes this test, then the graph is indeed a function.

Answer:

follow the steps

Step-by-step explanation:

Answer:

Hello Love!

All range is in math Is the highest number subtracted by the smallest number so our equation is 15 - 0 = 15

so 15 is our range!

The way the question is worded is a little confusing.

I think I would say 10m. It could be 5m, but usually they list length first, then width. The perimeter, the whole distance around the outside, is 30 m (10 + 10 + 5 +5)

The length of the rectangle will be 10 m.

A rectangle is a two-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles.

Given that, a rectangle has sides that are 10 m, 10 m, 5 m, and 5 m.

We need to find the length of the rectangle,

We have the dimensions 5 m x 10 m,

Lengths in a rectangle tells that how much the rectangle is long and the width tells how much the width tells about the breadth of the rectangle,

So, we can say that,

Length = 10 m

Width = 5 m

Hence, the length of the rectangle is 10 m.

Learn more about rectangle click;

https://brainly.com/question/29123947

#SPJ2

Answer: Answer: C. 3.2 × 10^4

Step-by-step explanation: for this case the multiplication of the values with exponent are summed, as the exponent are the 6 and -3

6 - 3 = 3

this will be the exponent of the common value which is the 10.

after you only need to multiply 8 and 4 by separate the

8 * 4 = 32.

then we only need to place the values one by one

32 × 10^3

3 is the result of the sum of the exponent.

10 is the common value.

32 is the result of the product.

if we add another zero to the multiplication we get 3.2 and exponent finish with one more zero, then we get this result

3.2 × 10^4

because of that the C is the correct answer, keep in mind that the other answers do not apply correctly the rule of the exponent, because the rest of answer give us wrong answer with final result of the exponent.

Answer:

y = 60

Step-by-step explanation:

All triangle angles add up to 180 so:

y + y + y = 180

3y = 180

y = 60

Answer:

y=60

Step-by-step explanation:

this is something to remember

when the angles of a triangle are all the same, they are 60°

Answer:

6

Step-by-step explanation:

Answer:

i think that every time she rolls the dice, she is further away from the gym

Step-by-step explanation:

Answer:

Confusion

Step-by-step explanation:

what the heck are you asking?

Answer:

b

Step-by-step explanation:

Answer: 3/7

Step-by-step explanation:

im not sure but i thinks its 3/7

Answer:

the area of the figure below is 56mm

Answer:

88 mm 2

Step-by-step explanation:

The small top recatngle has an area of 16 and the large bottom one has an area of 72. Add them together and you get 88 mm 2.