randy just had a lap pool put in his backyard. The rectangle pool measures 5 feet by 18 feet and is 4.5 feet deep

jeyben [28]

Answer:

x = -2

Step-by-step explanation:

Given the point, (-2, 9) and the linear equation of a horizontal line, y = 6:

The linear equation of a horizontal line with a slope of zero (m = 0) is y = b, for which the y-intercept is (0, b). Perpendicular lines comprise of the intersection of two lines forming 90° angles.

Since we are given the equation of a horizontal line, then we can assume that the line that intersects a horizontal line must be a vertical line in order to form perpendicular lines.

The linear equation of a vertical line with an undefined slope is x = a, for which the x-intercept is (a, 0). Vertical lines have an undefined slope because these lines do not have any horizontal change. Thus, when you try to solve for its slope, the denominator will have a difference of 0, making the mathematical operation undefined.

We can use the x-coordinate of the given point, (-2, 9), to formulate an equation for a vertical line: x = -2.

Therefore, the equation of the line that goes through y = 6 is x = -2.

Attached is a screenshot of the graph of both equations, y = 6 and x = -2, showing that their intersection form 90° angles, making them perpendicular lines.

8 0

3 years ago

Factor completely 125x-27x^4 Step by step explanation

Vera_Pavlovna [14]

Answer:

125x - 33x⁴

Pull out like factors :

125x - 27x⁴ = -x • (27x3 - 125)

Factoring: 27x³- 125

Theory : A difference of two perfect cubes, a³ - b³ can be factored into

(a-b) • (a² +ab +b²)

(a-b)•(a²+ab+b²) =

a³+a²b+ab²-ba²-b²a-b³ =

a³+(a2b-ba²)+(ab²-b²a)-b³ =

a³+0+0+b³ =

a³+b³

Check : 27 is the cube of 3

Check : 125 is the cube of 5

Check : x³ is the cube of x¹

Factorization is :

(3x - 5) • (9x² + 15x + 25)

8 0

4 years ago

12 is 30% of ____ (Please explain)

natka813 [3]

Answer:

40

Step-by-step explanation:

In word problems, the word "of" usually means multiply. Thus, for example, 10% of $50 is $5. This is because we can write 10% as 0.10 or as 10/100 (which is 1/10) and then multiply: (1/10)(50) = 5

So, we often see equations like:

R = (1/2)D meaning R is 50% of D, or R is half of D

Let x = the number we want to find

This problem says:

"12 is 30% of what number?"

12 = (30/100) * x

12 = (3/10)x

(10/3)12 = x [multiply both sides by (10/3)]

40 = x

Checking (very important):

Is 12 = (3/10)(40) ?

12 = (3)(4) ?

12 = 12 ? yes

7 0

2 years ago

Read 2 more answers

Does anyone get this?? Pls help!!

Molodets [167]

Answer:no

Step-by-step explanation:

5 0

3 years ago

For each of the questions, find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to

Step2247 [10]

Answer:

1. D

2. D

3. C

Step-by-step explanation:

3 0

4 years ago