True or false. The following lines are perpendicular. <br> Y = -x

40 POINTS!!! PLEASE HELP!!!!

vovangra [49]

Answer: They can complete the job in 1.43 hours.

Step-by-step explanation:

Let's define:

"moving a three-bedroom" as "one job"

We know that Kevin can complete one job in 5 hours, then he works at the rate:

K = (1 job)/(5 hours) = (1/5) job per hour.

Now if Q is the rate at which Quinton works and T is the rate at which Trey works, their combined rate is (Q + T), and they can complete the job in 2 hours, then:

(Q + T) = (1 job)/(2 hours) = (1/2) job per hour.

When Kevin, Quinton, and Trey wor togheter, the combined rate is:

(K + Q + T)

And we know that:

(Q + T) = (1/2) job per hour.

K = (1/5) job per hour.

If we replace these in the above sum we get:

(K + Q + T) = (1/5) job per hour + (1/2) job per hour

= (1/5 + 1/2) job per hour

= (2/10 + 5/10) job per hour

= (7/10) job per hour.

Then they need to work for T hours in order to complete 1 job, we have the equation:

[ (7/10) job/hour]*T = 1 job

T = ( 1 job)/(7/10) job/hour = 10/7 hours = 1.43 hours.

they can complete the job in 1.43 hours.

5 0

3 years ago

Read 2 more answers

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

RoseWind [281]

Answer:

a. The equation of the parallel line to the given line is y = -4x + 19

b. The equation of the perpendicular line to the given line is y = $\frac{1}{4}$ x + 2

Step-by-step explanation:

Parallel lines have the same slopes

If the slope of one of them is m, then the slope of the other is m

The product of the slopes of the perpendicular lines is -1

If the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$

To find the slope of a perpendicular line to a given line reciprocal the slope of the given line and change its sign

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are the points on the line

The form of the equation of a line is y = m x + b, where

m is the slope

b is the y-intercept

Let us solve the question

∵ The given line passes through points (1, 6) and (2, 2)

∴ x1 = 1 and y1 = 6

∴ x2 = 2 and y2 = 2

→ Substitute them in the rule of the slope to find it

∵ m = $\frac{2-6}{2-1}=\frac{-4}{1}=-4$

∴ The slope of the given line is -4

a.

∵ The line is parallel to the given line

∴ Their slopes are equal

∵ The slope of the given line = -4

∴ The slope of the parallel line = -4

→ Substitute its value in the form of the equation above

∴ y = -4x + b

→ To find b substitute x and y in the equation by the coordinates

of any point on the line

∵ The parallel line passes through the point (4, 3)

∴ x = 4 and y = 3

∵ 3 = -4(4) + b

∴ 3 = -16 + b

→ Add 16 to both sides

∴ 3 + 16 = -16 + 16 + b

∴ 19 = b

→ Substitute it in the equation

∴ y = -4x + 19

The equation of the parallel line to the given line is y = -4x + 19

b.

∵ The line is perpendicular to the given line

∴ The product of their slopes is -1

→ Reciprocal the slope of the given line and change its sign

∵ The slope of the given line = -4

∴ The slope of the perpendicular line = $\frac{1}{4}$

→ Substitute its value in the form of the equation above

∴ y = $\frac{1}{4}$ x + b

→ To find b substitute x and y in the equation by the coordinates

of any point on the line

∵ The perpendicular line passes through the point (4, 3)

∴ x = 4 and y = 3

∵ 3 = $\frac{1}{4}$ (4) + b

∴ 3 = 1 + b

→ Subtract 1 from both sides

∴ 3 - 1 = 1 - 1 + b

∴ 2 = b

→ Substitute it in the equation

∴ y = $\frac{1}{4}$ x + 2

The equation of the perpendicular line to the given line is y = $\frac{1}{4}$ x + 2

4 0

3 years ago

Read 2 more answers

Help solve ?<br> Need answer soon

galina1969 [7]

Answer:

A.

Step-by-step explanation:

It seems and makes the most sense. Anyways have a nice day/night :). Also if you can may I please have brainliest

6 0

3 years ago

PLEASE HELP ASAP

jek_recluse [69]

It is none of them
9x³ - 4x³ = 5x³
3x² - -2x² = 3x²+2x² = 5x²
-3 - 16 = 13
So :
5x³ + 5x² +13

5 0

4 years ago

Which shows the correct solution of the equation a to=50, when b=30?

Fed [463]

Answer:

yes the answer is 70 your correct i think

6 0

4 years ago

True or false. The following lines are perpendicular. Y = -x - 7 Y + x = 20