If anyone could help that would be greatly appreciated!

Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 8 minutes to fill the swimmi

tester [92]

Answer:

The rate the swimming pool is filled is 9 gallons of water per minute

Step-by-step explanation:

Let's review the information provided by Ronald to us to help him to find the answer to the question:

Time it takes to fill the swimming pool = 8 minutes

Amount of water the swimming pool can hold = 72 gallons

2. At what rate does the swimming pool fill, in gallons per minute?

Rate the swimming pool is filled = Amount of water the swimming pool can hold /Time it takes to fill the swimming pool

Replacing with the real values, we have:

Rate the swimming pool is filled = 72/8 = 9 gallons of water per minute

4 0

3 years ago

Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four

gregori [183]

Answer and step-by-step explanation:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = -5x + 750

Next we divide both sides by 2:

2y/2 = -5x/2 + 750/2

y = -2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x(-2.5x+375)

A = -2.5x² + 375x

This is a quadratic equation, with values a = -2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation

x = -b/2a

x = -375/2(-2.5) = -375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = -2.5x² + 375x

A = -2.5(75)² + 375(75) = -2.5(5625) + 28125 = -14062.5 + 28125 = 14062.5

6 0

3 years ago

Which angles are corresponding angles?

konstantin123 [22]

Answer:

A. 7 and 3

&

B. 1 and 5

Step-by-step explanation:

Corresponding angles are a pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

The answers are:

•8 and 4

•5 and 1

•7 and 3

•6 and 2

I hope this helps! I'm sorry if it's wrong.

3 0

3 years ago

16x+14y=8 -63x-14y=133

artcher [175]

Answer:

(-3, 4)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination
Solving systems of equations by graphing

Step-by-step explanation:

Step 1: Define Systems

16x + 14y = 8

-63x - 14y = 133

Step 2: Solve for x

Elimination

Combine 2 equations: -47x = 141
Divide -47 on both sides: x = -3

Step 3: Solve for y

Define original equation: 16x + 14y = 8
Substitute in x: 16(-3) + 14y = 8
Evaluate multiplication: -48 + 14y = 8
Add 48 on both sides: 14y = 56
Divide 14 on both sides: y = 4

Step 4: Graph Systems

Check the solution set.

4 0

2 years ago

An observer, whose eyes are 1.98 m above the ground, is standing 39.2 m away from a tree. The ground is level, and the tree is g

lozanna [386]

Answer:

The tree is 16.25 m tall.

Step-by-step explanation:

Attached is a diagram that better explains the problem.

From the diagram we see that the distance between the top of the tree and the line of sight of the observer is x.

To find the height of the tree, we need to first find x and then add it to the height of the observers line of sight from the ground.

Using SOHCAHTOA trigonometric function:

tan(20) = x/39.2

=> x = 39.2 * tan(20)

x = 39.2 * 0.364

x = 14.27m

Hence, the height of the tree is:

(14.27 + 1.98)m

16.25m

The tree is 16.25 m tall.

5 0

3 years ago