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What is an equation of the line that is parallel to y=5x−7 and passes through (1, 11) ? Enter your equation in the box.

d1i1m1o1n [39]

ANSWER

$y = 5x + 6$

EXPLANATION

The equation of the given line is

$y=5x-7$

This line is in the slope -intercept form,

$y = mx + c$

where

$m = 5$

is the slope.

The line which is parallel to this line and passes through (1,11) also has slope

$m = 5$

Let the equation of this line be

$y = mx + b$

This implies

$y = 5x + b$

We substitute x=1 and y=11 to get

$11 = 5(1) + b$

$b = 11 - 5 = 6$

The required equation is

$y = 5x + 6$

6 0

3 years ago

Megan got paid $2,156 for babysitting this year. If she makes $11 an hour, how many hours did she babysit this year

Elenna [48]

Answer:

she worked 196 hours

Step-by-step explanation:

just divide 2156 by 11 :p i hope im right lol.

4 0

3 years ago

So far, Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days. What fraction of the book does

lesya [120]

Answer:1/6

Step-by-step explanation:

8 0

3 years ago

The DiMonte Corporation invented a new type of sunglass lens. Their variable expenses are $12.66 per unit, and their fixed expen

Sladkaya [172]

Answer:

a)one lens: 111,212.66

15000 lenses: 301,100

b)y=111,200+12.66x

slope: 12.66

c)12.66 dollars per unit of lens produced

d) 20.07

e) 19.2

f)decreases

Step-by-step explanation:

a) Cost of producing one lens

fixed expenses+variable expenses=111,200+12.66=111,212.66

Cost of producing 15,000 lenses

fixed expenses+variable expenses=111,200+12.66(15,000)=301,100

b)Expense function:

let y be the expense cost

let x be the number of lenses produced

y=111,200+12.66x

Slope:

The function is a line equation: y=mx+b where m is the slope.

In this case b=111,200 and m=12.66. So the slope is 12.66

c) the cost increases 12.66 dollars per unit of lens produced

d) The cost of producing 15000 lenses is:

111,200+12.66(15,000)=301,100

If DiMonte produces 15000 lenses, the average cost per lens is:

301,100/15000=20.073≈20.07

e)The cost of producing 17000 lenses is:

111,200+12.66(17,000)=326,420

If DiMonte produces 17000 lenses, the average cost per lens is:

326,420/17,000=19.2

f)The average per lens decrease.

8 0

4 years ago

Dominic is driving on a long road trip. He currently has 10 gallons of gas in his car. Each hour that he drives, his car uses up

Nostrana [21]

Answer:

(a) Equation: $T_n = 11.25 - 1.25n$

(b) 7.5 gallons

Step-by-step explanation:

Given

Current Gas = 10 gallon

Every Hour = -1.25 gallon

Solving for (a): An equation for the scenario

This question represents an Arithmetic Progression and will be solved using the following formula:

$T_n = a + (n - 1)d$

Where

$a = 10$

$d = -1.25$

Substitute these values in the formula

$T_n = 10 + (n - 1) * -1.25$

$T_n = 10 -1.25n +1.25$

Collect Like Terms

$T_n = 10 + 1.25 - 1.25n$

$T_n = 11.25 - 1.25n$

Solving for (b): In this case, n - 3

Substitute 3 for n in $T_n = 11.25 - 1.25n$

$T_3 = 11.25 - 1.25 * 3$

$T_3 = 11.25 - 3.75$

$T_3 = 7.5$

<em>7.5 gallon of gas left</em>

6 0

3 years ago