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2 years ago

For options A-E choose all of the expressions that are equivalent to 3(4x + 3).

Mathematics

1 answer:

dezoksy [38]2 years ago

5 0

E,D and B are all the correct choices that are equivalent to 3(4x+3)

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How do you write an equation in standard form given point (2,2) (0,-4)

notka56 [123]

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (2, 2) and (0, -4). Substitute:

$m=\dfrac{-4-2}{0-2}=\dfrac{-6}{-2}=3\\\\y-2=3(x-2)$

The standard form:

$Ax+By=C$

$y-2=3(x-2)$ <em>use distributive property</em>

$y-2=3x-6$ <em>add 6 to both sides</em>

$y+4=3x$ <em>subtract y from both sides</em>

$4=3x-y$

<h3>Answer: 3x - y = 4</h3>

6 0

3 years ago

EXERC

eimsori [14]

Answer:551.3212cm³

Step-by-step explanation:

Find the image attached

The volume is made up of a cone, cylinder and a hemisphere

Volume of the shape = Volume of cone + volume of cylinder + volume of hemisphere

Get the volume of the cone;

Volume of a cone Vc = 1/3πr²h

r is the base radius = 3.5cm

Height = 10cm

Vc = 1/3π(3.5)²(6)

Vc = 1/3π(12.25)(6)

Vc = 12.25 * 2π

Vc = 24.5π cm³

Get the volume of the cylinder;

Vcy = πr²h

r = 3.5cm

h = 10cm

Vcy = π(3.5)²(10)

Vcy = π(12.25)(10)

Vcy = π(122.5)

Vcy = 122.5π cm³

Get rhe volume of the hemisphere;

Volume of hemisphere = 2/3 πr³

r = 3.5cm

Vh = 2/3 π(3.5)³

Vh = 2/3π(42.875)

Vh = 28.58π cm³

Volume of the shape = VC + Vcy + Vh

Volume of the shape = 24.5π+122.5π+28.58π

Volume of the shape = 175.58π

<em>Volume of the shape = 551.3212cm³</em>

7 0

3 years ago

Shelby made 5quarts of juice. she said that she made 1 1\4of juice.expkain her mistake

docker41 [41]

Shelby mistake is 11;4 is not the correct mixed number

8 0

3 years ago

Which table represents a direct variation? Table A x 4 6 8 10 y 7 9 11 13 Table B x 4 6 8 10 y 12 18 24 30 Table C x 4 6 8 10 y

Greeley [361]

Answer:

We conclude that 'Table B' represents a direct variation.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the constant of proportionality.

Table A

x 4 6 8 10

y 7 9 11 13

Finding k for all the pairs of x and y

k = y/x

k = 7/4, k = 9/6 = 3/2, k = 11 / 8, k = 13/11

As constant of proportionality 'k' does not remain constant.

Hence, table A does not represent a direct variation

Table B

x 4 6 8 10

y 12 18 24 30

Finding k all the pairs of x and y

k = y/x

k = 12/4 = 3, k = 18/6 = 3, k = 24/8 = 3, k = 30/10 = 3

As the constant of proportionality remains constant.

Therefore, the value of k = 3 for all the points in the table.

Hence, table B represents a direct variation.

Table C

x 4 6 8 10

y 1 3 5 7

Finding k all the pairs of x and y

k = y/x

k = 1/4, k = 3/6 = 1/2, k = 5/8, k = 7/10

As the constant of proportionality 'k' does not remain constant.

Hence, table C does not represent a direct variation.

Table D

x 4 6 8 10

y 3 3 3 3

Finding k all the pairs of x and y

k = y/x

k = 3/4, k = 3/6, k = 3/8, k = 3/10

As the constant of proportionality 'k' does not remain constant.

Hence, table D does not a direct variation.

Therefore, we conclude that 'Table B' represents a direct variation.

8 0

2 years ago

Read 2 more answers

Simone builds a simple spinning engine by inserting straws through holes in a plastic cup. She then suspends the cup from a meta

Zinaida [17]

D. It is smaller In magnitude

3 0

3 years ago