Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?It takes Aaron about 1 hour to mow 2 acres.
Aaron’s rate for mowing lawns is 0.5 acres per hour.
The ratio of acres to time is 5 acres to 3 hours.
The rate to mow a lawn is 0.6 hours per acre.

Answers

Answer 1
Answer:

Answer:

Aaron’s rate for mowing lawns is 0.5 acres per hour.

Step-by-step explanation:

We are given that  x denotes the time in hours it takes to mow a lawn and y denotes the size of the lawn in acres.

Now Two of his points are (3, 1.5) and (5, 2.5)

(x_1,y_1)=(3,1.5)

(x_2,y_2)=(5,2.5)

Slope : m=(y_2-y_1)/(x_2-x_1)

m=(2.5-1.5)/(5-3)

m=(1)/(2)

m=0.5

Thus Aaron’s rate for mowing lawns is 0.5 acres per hour.

Hence Option B is correct

Answer 2
Answer: The answer is "Aaron;s rate for mowing lawns is 0.5 acres per hour."
as
1.5 acres / 3 hours = 0.5 acres an hour
2.5 acres / 5 hours = 0.5 acres an hour

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Name the line and plane shown in the diagram.

Answers

the correct answer would be c

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A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be

Answers

18 yards and 22 yards are the length of trapezoid.

What is Trapezoid?

Trapezoids are quadrilaterals that have two parallel sides and two non-parallel sides

Given,

shorter base to be 3 yards greater than the height

b₁=h+3

longer base to be 7 yards greater than the height.

b₂=h+7

Area of trapezoid=1/2(b₁+b₂)h

150=1/2(h+3+h+7)h

150=(2h+10)h/2

150=2h²+10h/2

150=2h²+5h

h²+5h-150=0

h²+15h-10h-150=0

h(h+15)-10(h+15)=0

(h-10)(h+15)=0

h=10 or h-15

h value should be positive.

So b₁=h+3=15+3=18

b₂=h+7=15+7=22

Hence the bases be 18 yards and 22 yards.

To learn more on Trapezoid click:

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From your information 
Let shorter base = h +3 and longer base = h + 7 where h is the height.
Formula for area of a trapezoid is A = (1)/(2) (b_1 +b_2)h
Substituting into the formula we get the following equation.
150= (1)/(2)(h+3+h+7)h
150 = (1)/(2) (2h+10)h
150=h^2+5h
This is a quadratic equation which I will solve by factoring.
h^2+5h-150 =0
(h-10)(h+15)=0
h-10= 0 ..... h=10 this is a useable answer (it's positive and length must be nonnegative)
h+15=0 .... h=-15 can't use this answer
so shorter base = 10 + 3 = 13 yards and longer base = 10 + 7 = 17 yards

At the gas station, each liter of gas costs $ 3 $3dollar sign, 3, but there's a promotion that for every beverage you purchase you save $ 0.20 $0.20dollar sign, 0, point, 20 on gas.

Answers

The complete question is:

At the gas station, each liter of gas costs $3dollar but there's a promotion that for every beverage you purchase you save $0.20 dollar on gas. Is your total savings on gas proportional to the number of beverages you purchase?

Answer:

  • Yes, your total savings on gas is proportional to the number of beverages you purchase.

Explanation:

What is a proportional relationship?

A proportional relationship, also known as direct relation, between two variables exists when the ratio between every pair of data is constant.

In this case the variables are:

  • number of beverage purchased
  • savings

Thus, as per every beverage purchase you save $ 0.20 the ratio of total savings to the number of beverage purchases is:

  • savings / beverages purchase = $ 0.20 / beverage

That means that you can determine the savings by multipliying the number of beverages times $ 0.20.

For proportional relationships it is easy to build a table that shows the behavior of the variables. This shows you that:

Number of beverages   savings    ratio

         1                              $ 0.20      $0.20 / 1 beverage = 0.20

         2                             $ 0.40      $0.40 / 2 beverages = 0.20

         3                             $ 0.60       $0.60 / 3 beverages = 0.20

         4                             $ 0.80       $0.80 / 4 beverages = 0.20

Write a rule for the linear function in the table. x f(x) –3 –1 0 2 3 5 6 8 A. f(x) = x + 2 B. f(x) = 3x C. f(x) = x – 2 D. f(x) = x – 1

Answers

Answer:

The answer is A.

Step-by-step explanation:

In this kind of exercise the usual way to solve it is s kind of trial an error. We evaluate f(x) in the given values of x and check if it corresponds with the values of f(x) in the table. If only one of the calculations does not correspond we dismiss the function.

Let us start our analysis from D. to A.

D.  In this case f(x) = x-1, then f(-3) = -3-1=-4, and the result does not correspond to the values of the table (recall f(-3)=-1).

C. The same idea: we have f(x)=x-2, then f(-3)=-3-2=-5, and the result does not correspond to the values of the table (recall f(-3)=-1).

B. Here f(x)=3x, then f(-3)=3*(-3)=-9, and the result does not correspond to the values of the table (recall f(-3)=-1).

A. Now f(x)=x+2, then f(-3)=-3+2=-1, and the result does correspond to the values of the table (recall f(-3)=-1). So, we need to check the next values of the table:

f(0)=0+2=2, f(3)=3+2=5 and f(6)=6+2=8.

As all the values are equal to those in the table, we conclude that A. is the correct answer.

If you notice:

x = -3,  f(x) = -3 + 2 = -1

x = 0,  f(x) = 0 + 2 = 2

x = 2,  f(x) = 2 + 2 = 4

x = 3,  f(x) = 3 + 2 = 5

And so on...

By observation:    f(x) = x + 2.    Option (A).

I hope this helps.

What is 30 minutes as a percentage of an hour?

Answers


 30 minutes is half of an hour so it would be 50%.

Use the form y=mx +b for linear equations.Write the equation for the following relation.C = {(x, y): (6, 15), (8, 21), (10, 27), . . .}

Answers

I'm not sure if the answer is right, but here you go.

y=mx+b 

'm' is for gradient of the line. First, calculate the gradient.

Let's use (6,15) and (8,21)

Gradient, m = y_(2)y_(1)
                    --------------
                     x_(2)x_(1)
                 
                 =  21 - 15     = 6       = 3
                     -----------      ----   
                       8 - 6         2
           
Therefore, m = 3 . Now let's search 'b' .
Let's use (6,15) again. Substitute it into the equation.

y=mx+b 
15 = 3 (6) + b
b = -3

Thus, the equation : y=3x -3 



Answer: Use Desmos.com/calculator

Step-by-step explanation: