All categories

3 years ago

A pump moves 42 gallons in seven minutes. what is the unit rate?

2 answers:

mote1985 [20]3 years ago

8 0

You need to divide both numbers by 7 because you currently know how many gallons are pumped in 7 minutes, and we want to find out how much is pumped in one minute.

42 ÷ 7 = 6.
7 ÷ 7 = 1.

So it pumps 6 gallons per minute.

kupik [55]3 years ago

8 0

The correct answer is:

6 gallons per minute.

Explanation:

In order to have a unit rate, we must have a rate with a denominator of 1. Our rate is 42/7. To make this a unit rate, we need to divide the denominator by 7. What we do to the denominator, we must also do to the numerator; this means we have (42÷7)/(7÷7) = 6/1. This is a rate of 6 gallons per minute.

You might be interested in

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

Find the area of the rectangular playground

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

Can someone add these up and tell me what my final grades would be

denis23 [38]

Answer:

yea sure

Step-by-step explanation:

math pretty sure its A

civics B

LA b

pretty sure i am right

4 0

2 years ago

Read 2 more answers

Please Help Me On These Math Questions!!!!! Solve Each System By Elimination

nekit [7.7K]

11) -x + y = -1 ; 2x - y = 0
y = -1 + x ; 2x - (-1+x) = 0 ⇒ 2x + 1 - x = 0 ⇒x = -1
y = -1 + (-1) ⇒ y = -2

12) -2x + y = -20 ; 2x + y = 48
y = -20 + 2x ; 2x + (-20 + 2x) = 48 ⇒ 2x -20 + 2x = 48 ⇒ 4x = 48 + 20
4x = 68 ⇒ x = 68/4 ⇒ x = 17
y = -20 + 2(17) ⇒ y = -20 + 34 ⇒ y = 14

13) 3x -y = -2 ; -2x + y = 3
y = 3 + 2x ; 3x - (3 + 2x) = -2 ⇒ 3x - 3 - 2x = -2 ⇒ x = -2 + 3 ⇒ x = 1
y = 3 + 2(1) ⇒ y = 3 + 2 ⇒ y = 5

14) x - y = 4 ; x - 2y = 10
x = 4 + y ; (4 + y) - 2y = 10 ⇒ 4 + y - 2y = 10 ⇒ 4 - y = 10
⇒ -y = 10 - 4 ⇒ -y = 6 ⇒ y = -6
x = 4 + (-6) ⇒ x = 4 - 6 ⇒ x = -2

15) x + 2y = 5 ; 3x + 2y = 17
x = 5 - 2y ; 3(5-2y) + 2y = 17 ⇒ 15 - 6y + 2y = 17 ⇒ -4y = 17 - 15
⇒ -4y = 2 ⇒ y = -2/4 ⇒ y = -1/2
x = 5 - 2(-1/2) ⇒ x = 5 + 2/2 ⇒ x = 5 + 1 ⇒ x = 6

5 0

3 years ago

Read 2 more answers

Calculate the area of a right-angled triangle of sides 30 cm, 40 cm, 50 cm.

grin007 [14]

The correct answer is 60cm^2 because the area of a triangle is half base*height -> 30/2*40

5 0

3 years ago

Write the equation of the line that passes through (2,3) and (4, 1) in point-slope form. Use (2,3) for (x1, y1).

earnstyle [38]

Answer:

y-2 = -(x-2)

Step-by-step explanation:

To find the slope

m = (y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are two points on the line

= (1-3)/(4-2)

=-2/2

=-1

The point slope form is

y-y1 = m(x-x1) wher m is the slope and (x1,y1) is a point on the line

y-3 = -1(x-2)

y-2 = -(x-2)

5 0

3 years ago