The pitch of a roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8, what is its slope expressed as a positive number?

Answers

Answer 1

If the pitch is 8, it means the roof raises 8 ft. per each horizontal 12 ft.
Since slope, m, is defined as the rise/run; then m = 8/12. Simplifying, we obtain a slope m = 2/3 In order to write the line of the roof as an equation, let's assume that the roof line starts at the origin (0, 0); it rises 8 units for every 12 it advances; up to the point (12, 8). At this point, the roof descends at the same rate until it reaches the point (0, 24). We need to set two equations with the given constraints: y = mx + b since the roof ascend from (0, 0) up until (8, 12) we use a positive slope: y = 2/3x + b If we use (0, 0) to define b, then the equation of this section of the roof will be:
y = 2/3x 〈0 ≤ x ≥ 12〉 At (12, 8) the roof starts descending at the same rate, then we use the negative slope m = -2/3: y = -2/3x + b Now, let's use (12, 8) to define b: 8 = (-2/3)(12) + b Simplifying, we obtain b = 16, ∴ the equation of this section of the roof will be: y = -2/3x + 16 〈12 ≤ x ≤ 24〉

Related Questions

(a) (4,4) is a point on a locus whose equation is y2 = kx. Show that (16,8) is another point on the locus.
(b) (2,3) is a point on a locus whose equation is 5x +by= 16. Show that (0,8) is another point of the locus

Answers

Step-by-step explanation:

plug the coordinate points into the equations and solve for the remaining variable.

b) (2,3) - 5(2) + b(3) = 16

10 + 3b = 16. 3b= 6. b = 2

(0,8) - 5(0) + 2(8) = 16. 0+ 16 = 16. ☆

a) (4,4) assume based on results you meant y squared. (y^2)

(4)^2 = 4k. 16 = 4k. k = 4

(8)^2 = 4(16). 64 = 64. ☆

Answer:

Please check the explanation.

Step-by-step explanation:

Given

(4,4) is a point on a locus whose equation is y²=kx

Putting (4, 4) in y²=kx

(4)² = k(4)

16 = 4k

k = 16/4

k = 4

Checking the point (16, 8) on the locus

y²=kx

Putting (16, 8) and k =4 in y²=kx

y²=kx

(4)² = 4×4

16 = 16

L.H.S = R.H.S

Therefore, (16, 8) is another point on the locus.

Given

(2, 3) is a point on a locus whose equation is 5x +by= 16

Putting (2, 3) in 5x +by= 16

5x+by=16

5(2)+b(3)=16

10+3b=16

3b=6

b=6/3

b=2

Putting (0, 8) and b=2 in 5x +by= 16

5x +by= 16

5(0)+2(8)=16

0+16=16

16=16

L.H.S = R.H.S

Therefore, (0, 8) is another point on the locus.

WILL GIVE BRAINLIEST!!!!!!1
Consider this system:
3x + 1/2y = 3
6x - y = 2
Which of the following operations would eliminate the y-terms if the two equations were added together afterward?

A. Multiply the first equation by -2.

B. Multiply the first equation by 2.

C. Multiply the second equation by -2.

D. Multiply the second equation by 2.

Answers

Answer:

B. Multiply the first equation by 2

hope this helps tell me if you need more :)

Multiply the first equation by 2 then the variable y will be eliminated. Then the correct option is B.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Consider this system:

3x + 1/2y = 3 ...1

6x - y = 2 ...2

The operations would eliminate the y-terms if the two equations were added together afterward will be

Multiply the first equation by 2. Then we have

6x + y = 6

6x - y = 2

Add the above equations, then we have

12x = 8

y is eliminated.

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ2

WILL GIVE BRAINLIEST

Answers

We Know that in geometry the Cos/Sin = Cotangent. And the abbreviation for this is cotø

The 10th power of t

Answers

Answer:

t¹⁰

Step-by-step explanation:

The 10th power of t:

t¹⁰

What does 24 square root using perfect squares look like?

Answers

Each side is 6 square roots

Answer:

4.899

Step-by-step explanation:

4.899×4.899=24

I know cause I googled :)

Please I will give brainylest if the answer is correct

Answers

Answer:

a^n +3

Step-by-step explanation:

simpify: a^na^3:\quad a^{n+3}

a^{n+3}

Alicia is setting up a volleyball net and needs to support the posts with a rope. The volleyball post is 8 feet tall and Alicia placed a stake 6 feet from the
base of the post. The rope needs to reach from the top of the post to the stake. How long does the rope need to be?

Answers

According to my examination I have confirmed that I do NOT repeat do NOT know the answer to this question. Good luck!

Answer: answer is 10

Step-by-step explanation:

8 x 8 = 64

6 x 6 = 36

64 + 36 = 100 cm2

100 cm2 = 10

Grace and Zoe like to jump rope grades jump 66 times a minute Zoe jumps 56 times a minute they both Count Their jumps today and together they jump 1266 times in the total of 21 minutes how long did each girl jump

Answers

Answer:

Grace jumps for 9 minutes.

Zoe jumps for 12 minutes.

Step-by-step explanation:

Let the time for which Grace jumps the rope = [tex]x[/tex] minutes

Let the time for which Zoe jumps the rope = [tex]y[/tex] minutes

As per question statement:

[tex]x+y=21 ..... (1)[/tex]

Number of times Grace jumps in one minute = 66

Number of times Zoe jumps in one minute = 56

Number of times Grace jumps in [tex]x[/tex] minutes = 66

Number of times Zoe jumps in [tex]y[/tex] minutes = 56

As per question statement:

[tex]66x+56y=1266 ...... (2)[/tex]

Multiplying equation (1) with 66 and subtracting equation (2) from it:

[tex]10y = 1386 - 1266\\\Rightarrow 10y=120\\\Rightarrow y =\bold{12\ min}[/tex]

By equation (1):

[tex]x=21-12=\bold{9\ min}[/tex]

Therefore, the answer is:

Grace jumps for 9 minutes.

Zoe jumps for 12 minutes.

A town has a population of 10000 and grows at 5% every year. What will be the population after 5 years, to the nearest whole number?

Answers

Answer:12500

Step-by-step explanation:

10000 x 5% = 500. 500 x 5 = 2500. 10000 + 2500 = 12500

Answer:

12763

Step-by-step explanation:

Got it right on deltamath.

If 25⋅26=n, then which division equation is also true?

n÷26=25

26÷25=n

25÷n=26

25÷26=n

Answers

9514 1404 393

Answer:

n÷26=25

Step-by-step explanation:

Starting with the equation ...

25·26 = n

you can divide both sides of it by 26 to get ...

25 = n ÷ 26 . . . . matches choice A

ASAP FOR BRAINLIEST!

Answers

Answer:

-4

Step-by-step explanation:

down 4, right 1

-4/1

Answer:

-4

Step-by-step explanation:

Points: (-1,3) and (0,-1)

m = y2 - y1/x2 - x1

m = -1 - 3/0 - (-1)

m = -1 - 3/0 + 1

m = -4/1

m = -4

Question 10
Evaluate 122 – 3 [4 () – (18)].

Answers

Answer:

here is the answer -(12)/(-3)

Step-by-step explanation:

PLEASE MARK BRAINILIEST!

What is the area of the triangle?
10 km
10 km
square kilometers

Answers

The answer is 50 because the formula for the area of a triangle is base x hight x 1/2. So if we plug both the 10s into the formula you get 10x10 which = 100 then divide that by 2 and you get 50. Hope it helps :)

CORRECT ANSWER GETS BRAINLIEST!!!

The least-squares regression equation
y = 120 + 40x can be used to predict the cost of renting a backhoe for x hours. Suppose it costs $325 to rent a backhoe for 5 hours.
Calculate the residual for renting the backhoe for 5 hours, to the nearest hour.
The residual is _____

Answers

Answer:

Step-by-step explanation:

just did on edge

The residuals is $5

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given, The least-squares regression equation

y = 120 + 40x

This equation can be used to predict the cost of renting a backhoe for x hours

If it costs $325 to rent a backhoe for 5 hours.

We need to Calculate the residual for renting the backhoe for 5 hours,

Plug 5 in place of x in equation

y=120+40(5)

y=120+200

y=320

Since the The observed value is $325.

To find residual for renting the backhoe for 5 hours

We have to separate 320 from 325

325-320=5

Hence the residual is 5.

To learn more on Equation:

https://brainly.com/question/10413253

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The expression (x3)(x-15) is equivalent to xn. What is the
value of n?

Answers

Answer:

-45 is xn

The x=3 and x=-15 multiply them together which is the answer to xn

Pls help !!! I've already failed it twice this is my last try please help there's other questions on my account.

Answers

Answer:

A, C

Step-by-step explanation:

Maybe A and C because its reflecting in the opposite direction which is 180

asap I have 3 minutes

Answers

The second choice is the answer

Solve for the missing arc measure, angle measure, or variable.

m < C is how many degrees??

Pls help! I’ll give brainliest!

Answers

Answer:

m<C I believe is 25 degrees

Step-by-step explanation:

Answer:

the answer is 25 degrees

use the picture to create a ratio between the football and baseball

Answers

Answer:

there are no pics

ya I can't see one

Answer:

3,6 1 to 2

Step-by-step explanation:

Number 2.
A homeowner is wanting to pave his
drive way. He was quoted for every 240
bricks it would cost $30. Find the unit
rate.

Answers

240/30 is 8 i believe the answer is 8

Brielle's piggy bank has all nickels and dimes. The total value of the money in her piggy bank is
$7.80. If Brielle has 66 nickels, write and solve a linear equation to find the number of dimes she
has.
What’s the linear equation

Answers

Answer:

Step-by-step explanation:

7.80=66(.05)+.10(x)

7.80=3.30+.10(x)

7.80=3.30+.10x

4.50=.10x

x=45

Check

66 nickels at .05=3.30

45 dimes at .10= 4.50

3.30+4.50= 7.80

how do you solve
x-3y=-5
x+3y=1

Answers

Answer:

I got you fam

Step-by-step explanation:

First One:

x -3y = -5

x = -5 + 3y

x -3y = -5

-3y = -5 -x

y = 5/3 + x/3

Second one:

x +3y = 1

x = 1 - 3y

x + 3y = 1

3y = 1 -x

y = 1/3 - x/3

Use elimination
x - 3y = -5
x + 3y = 1
Subtract both sides
-6y = -6, y = 1
x - 3(1)= -5
x - 3 = -5, x = -2
Final answer: x = -2, y = 1

What is the y-intercept of y = 4x?

Answers

Answer:

It depends on what x is

Step-by-step explanation:

I cant help

Answer:

Step-by-step explanation:

well if its just 4, then that means it doesnt have a y value

state the value of digit 2 in the number 1326g , in base ten

Answers

Answer:

Step-by-step explanation:

2*10

= 20

PLS GIVE BRAINLIEST

i think 64 I’m not sure though

Pls help with this asap

Answers

Answer:

Step-by-step explanation:

5227 in ^3
Hope this helps

Jay is 3 years less than 4 times Nelly’s age ( n ). Which expression represents Jay’s age?

Answers

Answer:

Step-by-step explanation: 3x4= 12 -3=9

Answer:

what's nelly's age

Step-by-step explanation:

4x divided by 3?

Hey everyone I need help on the questions please!:)

Answers

Answer:

a. 1/2

b. 1 hair cut

c. 2.5

Step-by-step explanation:

4/8 divde by 4 to simplify and that gets you 1/2

8/4 is 2 so he does one hair cut every two hours

so you know how many he can do in 2 hours so add it up. It’s going to be 2 people in four hours so it will be half a hair cut in 5 hours

Which of the following numbers is divisible by both 5 and 10

Answers

Answer:

Step-by-step explanation:

Answer:

1 or 5

Step-by-step explanation:

cuz 1 divided by 5 =5 and 10 divided by with 1 =10

but 5 divided by 1 = 5 and 10 divided by 5 = 2

What is 6^4 x 6 1/4????

Answers

Answer:

8100

Step-by-step explanation:

if angle ABC=2x and angle CBD=4x and they are a linear pair, solve for x

Answers

2x+4x=180(linear pair)
->x=30

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