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2 years ago

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Line AB has an equation of a line y = 5x − 2. Which of the following could be an equation for a line that is parallel to line AB

? y = 5x + 3 or y = 1/5x + 3 or y = −5x + 3 or y = −1/ 5x + 3

1 answer:

SpyIntel [72]2 years ago

4 0

Determine the slope of line AB
m = 5

Determine the slope of the lines from the options
First option: y = 5x + 3, the slope is 5
Second option: y = (1/5)x + 3, the slope is 1/5
Third option: y = -5x + 3, the slope is -5
Fourth option: y = (-1/5)x + 3, the slope is -1/5

Parallel lines are similar in the slope. So the line which is parallel to line AB must have the slope of 5.

The answer is first option.

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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

<u>case A)</u> 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

<u>case B)</u> 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

<u>case C)</u> 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

<u>case D)</u> 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

<u>case E)</u> 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

<u>case F)</u> 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

<u>the answer is</u>

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

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2 years ago

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chen is buying a ham. He wants to divide it into 6.5-ounce servings for 12 people. write and solve a division equation to find w

OLga [1]

Answer:

Amount of people to serve x Serving Size = Size of ham

12 x 6.5 = ?

=78

Step-by-step explanation:

Looking for size ham chen should buy = ?

Amount of people to serve = 12

Serving Size = 6.5-ounce

Equation=

Amount of people to serve x Serving Size = Size of ham

12 x 6.5 = ?

=78

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A goat is tethered by a 6 metre rope to the outside corner of a shed measuring 4 metres by 5 metres in a grassy field. What area

Naily [24]

(3/4)∗π∗62=27π
Also , the goat can reach around the corners by 2 on the short sides and 1 on long side.creating 2 90 degree sectors of additional grazing area.(1/4)∗π∗22=π
(1/4)∗π∗12=π/4
27π+π+π/4=28.25π

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2 years ago

Which of the following appear in the diagram below? Check ALL that apply.

Wittaler [7]

Answer:

∠ZXY and ZX

XYZ is not found on the diagram, as there is no line going from Z to Y, and YX is not a line segement in the diagram, its a full line.

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2 years ago

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A set of data points has a line of best fit of y=2.5x-1.5

castortr0y [4]

To solve this problem you must apply the proccedure shown below:

1- You must apply the following formula:

$R=yo-yp$

Where $R$ is the residual, $yo$ is the observed value $y$ and $yp$ is the predicted value $y$ .

2- You only need to substitute the $x=5$ into the equation $y=2.5x-1.5$ and then, you must apply the formula for calculate the residual:

$y=2.5(5)-1.5\\ y=11$

$R=12-11\\ R=1$

The answer is: The residual is $1$

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2 years ago

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