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3 years ago

There’s a button for the pic

Mathematics

1 answer:

Arlecino [84]3 years ago

7 0

A Multiply the input number by 6 because 2 times 6= 12, 6 times 6= 36, 8 times 6= 48, 9 times 6= 54, and 12 times 6= 72.

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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

AnnZ [28]

Answer:

$\textsf{Factored form}: \quad f(x)=2x(x-4)$

$\textsf{Vertex form}: \quad f(x)=2(x-2)^2-8$

Step-by-step explanation:

Factored form of a quadratic function

$f(x)=a(x-p)(x-q)$

where:

p and q are the x-intercepts
a is some constant

Given x-intercepts:

(0, 0)
(4, 0)

Therefore:

$\implies f(x)=a(x-0)(x-4)$

$\implies f(x)=ax(x-4)$

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

$\implies 2a(2-4)=-8$

$\implies -4a=-8$

$\implies a=2$

Therefore, the function's equation in factored form is:

$f(x)=2x(x-4)$

Vertex form of a quadratic equation

$f(x)=a(x-h)^2+k$

where:

(h, k) is the vertex
a is some constant

Given:

vertex = (2, -8)

Therefore:

$\implies f(x)=a(x-2)^2-8$

To find the constant a, substitute one of the x-intercepts into the equation and solve for a:

$\implies a(0-2)^2-8=0$

$\implies 4a-8=0$

$\implies a=2$

Therefore, the function's equation in vertex form is:

$f(x)=2(x-2)^2-8$

4 0

2 years ago

Read 2 more answers

On a test of 25 items, 18 were answered correctly. What percent were answered correctly?

gayaneshka [121]

Answer:

72%

Step-by-step explanation:

18*4=72%

3 0

3 years ago

Combine like terms -4a+8+3a-9

Sunny_sXe [5.5K]

Answer: -a+1

Step-by-step explanation:

-4a+8+3a-9

=-4a+3a+8-9

=(-4a+3a)+(8-9)

=-a+1

Hope this helps!! :)

5 0

3 years ago

Read 2 more answers

Marissa claims that stacking 6 blocks with dimensions of One-half times 1 times 1 will give the same volume as stacking 9 blocks

quester [9]

Answer:

(A)Six of the one-half cubes would have a volume of 3 cubic units.
(D)Three of the one-third cubes will make 1 unit cube.
(E)Two of the one-half cubes will make 1 unit cube.
(F)Both stacks will have a volume of 3 cubic units.

Step-by-step explanation:

Marissa claims that stacking 6 blocks with dimensions of $\frac{1}{2}X1X1$ will give the same volume as stacking 9 blocks with dimensions of $\frac{1}{3}X1X1$ .

First, let us examine the volume of each of the blocks.

For Block 1

The dimensions are: $\frac{1}{2}X1X1$

Volume of 1 block = $\frac{1}{2}X1X1= \frac{1}{2} $ cubic units$

Volume of 6 blocks of dimension $=6* \frac{1}{2} =3$ cubic units$

For Block 2

The dimensions are: $\frac{1}{3}X1X1$

Volume of 1 block = $\frac{1}{3}X1X1=\frac{1}{3} $ cubic units$

Volume of 9 blocks of dimension $=9*\frac{1}{3} =3$ cubic units$

The following statements out of Marissa's claim are true:

(A)Six of the one-half cubes would have a volume of 3 cubic units.

(D)Three of the one-third cubes will make 1 unit cube.

$3*\frac{1}{3} =1$ cubic units$

(E)Two of the one-half cubes will make 1 unit cube.

$2*\frac{1}{2} =1$ cubic units$

(F)Both stacks will have a volume of 3 cubic units.

8 0

3 years ago

Determine the lateral area and surface area of the given prism. Round answers to the nearest whole number.

vazorg [7]

Answer:

Lateral Area = Area of 2 triangle + Area of slant rectangle + area of back rectangle

Lateral Area = (5m)(3m) + (6m) (36m) + (3m) (36m)

LA = 15m² + 216m² + 108m²

LA = 339 m²

SA = (5m)(3m) + (6m) (36m) + (3m) (36m) + (5m)(36m)

SA = 15m² + 216m² + 108m² + 180 m²

SA = 519 m²

3 0

3 years ago