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What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

aalyn [17]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

in this problem we have

the point $(5,12)$ is on the line of direct variation

so

Find the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

the equation is

$y=\frac{12}{5}x$

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

case A) point $(0,0)$

$x=0\ y=0$

Substitute the value of x and y in the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is true

therefore

the point $(0,0)$ is on the line of direct variation

case B) point $(2.5,6)$

$x=2.5\ y=6$

Substitute the value of x and y in the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is true

therefore

the point $(2.5,6)$ is on the line of direct variation

case C) point $(3,10)$

$x=3\ y=10$

Substitute the value of x and y in the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not true

therefore

the point $(3,10)$ is not on the line of direct variation

case D) point $(7.5,18)$

$x=7.5\ y=18$

Substitute the value of x and y in the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is true

therefore

the point $(7.5,18)$ is on the line of direct variation

case E) point $(12.5,24)$

$x=12.5\ y=24$

Substitute the value of x and y in the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not true

therefore

the point $(12.5,24)$ is not on the line of direct variation

case F) point $(15,36)$

$x=15\ y=36$

Substitute the value of x and y in the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is true

therefore

the point $(15,36)$ is on the line of direct variation

therefore

the answer is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

5 0

1 year ago

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Samantha is wall papering her bedroom and wants to make sure that she bought enough wall paper. Each wall in her room measures 1

Gala2k [10]

Answer:

17.60

Step-by-step explanation:

Look at the room carefully, the length of the room is 11 feet

And the height = 10 feet

The area of the 4 walls of the room = 4( 11×10) = 440 sq ft

Area covered by each roll = 25 sq ft

= 440/25 = 17.60 rolls

Therefore we require 17.60 rolls to cover a rectangular room on all four sides.

7 0

2 years ago

Mary Hernandez had a policy with a $250 deductible which paid 80% of her covered charges less deductible. She had medical expens

Nataly_w [17]

A. the insurance company's payment = $14,392
$18240 - $250 = 17990 x 80% = $14,392

b. the 20% copayment
17990 * 20% = $3598

c. Mary's total cost
$250 + $3598 = $3848

6 0

1 year ago

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What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the rati

steposvetlana [31]

Let

3x----> angle exterior 1

4x----> angle exterior 2

5x----> angle exterior 3

we know that

The exterior angles of any polygon add up to 360 degrees

so

3x+4x+5x=360-------> 12x=360----------> x=30°

The largest of exterior angles is equal to the smallest of interior angles

so

the largest of exterior angles is 5x------> 5*30=150°

the smallest of interior angles is 180°-150°=30°

therefore

the answer is

the smallest of interior angle measure 30 degrees

8 0

1 year ago

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Marcie wants to enclose her yard with a fence. Her yard is in the shape of a rectangle attached to a triangle. The formula for t

nydimaria [60]

Let

l------> the length side of the rectangle

w----> the width side of a rectangle

b----> the base of the triangle

h----> the height of the triangle

we know that

the area of the yard is equal to

$A=lw+0.5bh$

Solve for b------> ( that means clear variable b)

Subtract $lw$ both sides

$A-lw=lw+0.5bh-lw$

$A-lw=0.5bh$

Divide by $0.5h$ both sides

$(A-lw)/(0.5h)=0.5bh/(0.5h)$

$b=(A-lw)/(0.5h)$

therefore

the answer is the option B

The quantity A minus l times w all divided by 0.5 times h

8 0

2 years ago

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