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zzz [600]
2 years ago
8

A swimming pool already contains

Mathematics
1 answer:
xenn [34]2 years ago
6 0

Answer:

Rate of change = <u>3 gallons/minute</u>

Starting volume = 30 gallons

Step-by-step explanation:

A graph of the pool's water level would be useful.  The slope of the line would represent the rate of change for filling the pool.  It will also help us determine the amount of water that was in the pool to start.  Although it is tempting to say the rate of fill is 45gallons/5 minutes, or 9 gallons/minute, it is not correct.  The pool already started with an unknown volume of water.  The rate of change after 5 minutes, however, can be used.  The problem states it is being added at a constant rate.  Let's find an equation for a line, in the format of y=mx+b, where m is the slope (rate of change) and b is the y-intercept.

We'll let y represent the volume of water in the pool, and x will be the time in minutes.  The y-intercept will give us the amount of water in the pool at the start (x = 0).

The slope can be determined between the two given points:

(5,45) and (30,120):

Slope = Rise/Run [The change in y divided by the change in x].

Rise = (120 - 45) = 75

Run = (30-5) = 25

Slope = 75/25 or 3

The line, so far, becomes y=3x + b

The slope of <u>3 has units of gallons/minute.  It is the rate at which the pool is being filled.</u>

We can find b, the starting volume of water, by using one of the two points in the equation and solving for b:

y=3x + b   [I'll use (5,45)]

45 = 3*(5) + b

<u>b = 30 gallons</u>

<u>The pool had 30 gallons to start (at x = 0(minutes))</u>

See the graph of the line, attached.

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7 0
2 years ago
Just need help on #7 thru 8(a), b and c
Stella [2.4K]

7

a. The slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

b. The distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

c.  The midpoint of the R(3, 5) and H(-1,2) is  (2, 4)

8.

a. The transformation rule is  (x,y) → (x + 1, y - 1)

b.

  • The x-coordinate is shifted 1 unit to the left and
  • The y - coordinate is shifted 1 unit downwards.

c. The image of B' the pre-image of B(5, 6) is (6, 5)

<h3 /><h3>7 a. How to find the slope of the line?</h3>

The slope of a line passing through the points (x₁, y₁) and (x₂,y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

So, m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 5)/(-1 - 3)

m = -3/-4

m = -3/4

So, the slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

<h3>b. The distance between the points</h3>

The distance between two points (x₁, y₁) and (x₂,y₂) is d = √[(y₂ - y₁)² + (x₂ - x₁)²]

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

d = √[(2 - 5)² + (-1 - 3)²]

d = √[(-3)² + (-4)²]

d = √[9 + 16]

d = √25

d = 5 units

So, the distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

<h3>7 c How to find the midpoint of the R(3, 5) and H(-1,2) </h3>

The midpoint of the the points (x₁, y₁) and (x₂,y₂) is (x, y)  = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

So, the midpoint (x, y)  = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(x, y)  = [(3 + (-1))/2, (5 + 3)/2]

(x, y)  = [(3 - 1)/2, (5 + 3)/2]

(x, y)  = [4/2, 8/2]

(x, y)  = (2, 4)

So, the midpoint of the R(3, 5) and H(-1,2) is  (2, 4)

<h3>8. a The rule for the transformation of point A(1, 4) to point B(2, 3)</h3>

Given that point A(1, 4) and point B(2, 3) we see that point B(1 + 1, 4 - 1).

Let pont A be (x,y).

So, point B = (x + 1, y - 1)

So, the transformation rule is  (x,y) → (x + 1, y - 1)

<h3>b. Describe the transformation</h3>

Since the transformation rule is   (x,y) → (x + 1, y - 1), we see that

  • the x-coordinate is shifted 1 unit to the left and
  • the y - coordinate is shifted 1 unit downwards.
<h3>c. The image of B' the pre-image of B(5, 6)</h3>

Since the transformation rule is  (x,y) → (x + 1, y - 1) and point B is (5, 6), thus the image of B' is

(x,y) → (x + 1, y - 1)

(5,6) → (5 + 1, 6 - 1)

(5,6) → (6, 5)

So, the image of B' the pre-image of B(5, 6) is (6, 5)

Learn more about slope of a line here:

brainly.com/question/1617757

#SPJ1

3 0
2 years ago
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Nastasia [14]

f(x) = 5x^2 - 4x

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Therefore f - g = 5x^2 - 4x - (5x + 1)

= 5x^2 - 4x - 5x -1

= 5x^2 -9x - 1


Hope it helps :)











8 0
3 years ago
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