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Answer:

(a)

[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]

(b) Rate = 5

(c) Rate = 5

Step-by-step explanation:

Given

The attached graph

Solving (a): The piece-wise function

For the first line

Calculate the slope of the first line

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (5,25)[/tex]

So, the slope is:

[tex]m = \frac{25 - 0}{5 - 0}[/tex]

[tex]m = \frac{25}{5}[/tex]

[tex]m = 5[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (0,0)[/tex]

[tex]y = 5(x - 0) + 0[/tex]

[tex]y = 5(x) + 0[/tex]

[tex]y = 5x[/tex]

So, the function of the first line is:

[tex]f(x) = 5x;\ 0 < x \le 5[/tex]

For the second line

Calculate the slope of the second line

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (5,20)[/tex]

[tex](x_2,y_2) = (9,40)[/tex]

So, the slope is:

[tex]m = \frac{40 - 20}{9 - 5}[/tex]

[tex]m = \frac{20}{4}[/tex]

[tex]m = 5[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (5,20)[/tex]

[tex]y = 5(x - 5) + 20[/tex]

[tex]y = 5x - 25 + 20[/tex]

[tex]y = 5x -5[/tex]

So, the function of the second line is:

[tex]f(x) = 5x -5;\ x>5[/tex]

Hence, the piece-wise function is:

[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]

Solving (b): The rate at which customers that buy up to 5lb buy.

[tex]x = 5[/tex]

This question implies that, we determine the rate at which this customer buys.

For [tex]x = 5[/tex]

[tex]f(x) = 5x;\ 0 < x \le 5[/tex]

The slope of the above function is 5.

So, this customer buys at the rate of $5 per lb

Solving (b): The rate at which customers that buy more than 5lb buy the extra pounds above 5lb.

For [tex]x > 5[/tex]

[tex]f(x) = 5x -5;\ x>5[/tex]

Assume x = 6

[tex]f(6) = 5 * 6 - 5[/tex]

[tex]f(6) = 30 - 5[/tex]

[tex]f(6) = 25[/tex]

Express as 20 + 5

[tex]f(6) = 20 + 5 * 1[/tex]

Assume x = 7

[tex]f(7) = 5 * 7 - 5[/tex]

[tex]f(7) = 35 - 5[/tex]

[tex]f(7) = 30[/tex]

[tex]f(7) = 20 + 10[/tex]

Express 10 as 5 * 2

[tex]f(7) = 20 + 5 * 2[/tex]

So, we have:

[tex]f(6) = 20 + 5 * 1[/tex]

[tex]f(7) = 20 + 5 * 2[/tex]

This can be generalized as:

[tex]f(x) = 20 + 5(x - 5)[/tex]

For the above functions;

20 represents the amount they buy the first 5

5 represents the rate at which they buy extra pounds above 5

Hence, they buy the extra pounds at the rate of $5 per pound

Answer:

2.5 cm

Step-by-step explanation:

Since the triangles are similar, we can use ratios to solve

AC          BC

-------- = ---------

FH             GH

12            15

-------- = ---------

18             x

Using cross products

12x = 15*18

Divide each side by 12

12x/12 = 15*18/12

x = 2.5

Answer:

-10

Step-by-step explanation:

a= -4

b = -2

5(a-b)

5( -4 - (-2))

5( -4 + 2)

5(-2)

-10

Answer:

120.2 or in other words, the answer is the last option, D

Answer:

The first graph is not a function because it has two values at x = 3. Definition of a function is that it is a relation that assigns exactly one value for each value on its domain

Answer:

1.) [tex]\left(x-3\right)\left(x+6\right)[/tex]

2.) [tex]\left(a-3\right)^2[/tex]

3.) [tex]=\left(t+8\right)\left(t-9\right)[/tex]

4.) [tex]=\left(b+7\right)^2[/tex]

Step-by-step explanation:

2.) [tex]=a^2-2a\cdot \:3+3^2[/tex], [tex]\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2[/tex].

[tex]a=a,\:b=3[/tex]

[tex]=\left(a-3\right)^2[/tex]

3.) [tex]=\left(t^2+8t\right)+\left(-9t-72\right)[/tex][tex]=t\left(t+8\right)-9\left(t+8\right)[/tex], [tex]\mathrm{Factor\:out\:common\:term\:}t+8[/tex].

[tex]=\left(t+8\right)\left(t-9\right)[/tex]

Answer:

7040 yards

Step-by-step explanation:

1 mile = 1760 yards

1 x 4 miles = 1760 x 4 yards

4 miles = 7040 yards

Answer:

JONATHAN WILL NEED 14 PAGES.

Explanation:

33 + 67 = 100

100 - 12 = 88

88 ÷ 6 = 14.6666667

14.6666667 ⇒ 14

(Round 14.6666667 down to 14 because Johnathan does not have .6666667 of a page.)

Answer:

radius = 1.4

Step-by-step explanation:

The formula for circumference is as follows:

[tex]C = d\pi[/tex]

or

[tex]C = 2r\pi[/tex]

However, these formulas are the same, because the diameter is equal to the radius times 2. I prefer to use the first (it gives you less values to work with).

Anyhow, We would substitute like this:

[tex]8.8 = d\pi[/tex]

We know that pi, is going to be equal to: 3.14159

So we work from there...

[tex]8.8=d(3.14159)\\2.8011=d[/tex]

Diameter divided by 2 would be the radius, and thats:

1.4006

or 1.4

Answer:

130 square feet

Step-by-step explanation:

Answer:

just upload the file

Step-by-step explanation:

Answer:

1:Add the x for the number of tbs 2: Add all the values together.

Step-by-step explanation:

Hope this helped!

Answer:

64 inches

Step-by-step explanation:

There are 12 inches in a foot

12 x 5 is 60

64 is greater then 60

The two numbers have 1 as a common factor and nothing else. Hence 1 is the HCF. This proves that the HCF of any two consecutive numbers is always a one.

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Answer:

90

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers. 

Answer:

96 ft

Step-by-step explanation:

Well add the given numbers up and calculate unkown sides using given measurments

Answer:

Percy’s strengths is his loyalty to his friend. When he was in danger, he could have escaped and saved his own life. But he showed loyalty by choosing to stay and fight to help his friend. He says, “… there was Grover, needing my help.” Percy’s only weakness in this section is becoming frozen by his fear. When his mother tells him to run, he can’t. The text says, “But I just stood there, frozen in fear, as the monster charged her.”

Step-by-step explanation:

Answer:

x=30.6

Step-by-step explanation:

Answer:

16.1

Step-by-step explanation:

Answer:

I believe the answer is x = 16.1

Step-by-step explanation:

Solution :

It is given that we have a null and an alternative hypothesis. The hypothesis are :

[tex]$H_0: \mu = 240,000$[/tex]

[tex]$H_a : \mu < 240,000$[/tex]

We have to find if the cost of average home has decreased or not in this month.

So it is given that the test statics is -1.79, so the p value associated with the test statics is less than ( α ) 0.01

Therefore, we can conclude that the cost of the average house is less than $ 240,000.

Answer:

48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

21.4476105895

Step-by-step explanation:

Using a calculator [tex]\sqrt{460\\}[/tex]

Answer:

approximately 21.448 or 2 times the square root of 115

Step-by-step explanation:

Answer:

m<B, m<C, m<A

Step-by-step explanation:

The length of sides and angle measures correspond. This means the angle opposite to the longest side is the largest, etc. The shortest side is AC, which is the opposite of <B, making it the smallest. Then, the same logic can be applied to <C which is the middle, and <A which is the largest. Therefore, from least to greatest the angles are m<B, m<C, m<A.

Answer:

A

Step-by-step explanation:

Answer:

A) less than -5

Step-by-step explanation:

If it is lesser than -5, that means the line will be going to the left. This also means that the circle will be an open circle, not shaded.

Answer:

Step-by-step explanation:

4y - 2(5 - y + 4) = 4y - 2(9 - y)

                         = 4y + 9*(-2) - y *(-2)

                         = 4y  - 18 + 2y      {Combine like terms 4y and 2y}

                         = 6y - 18

6y - 18 = 6*y - 6*3

           = 6(y - 3)

6y- 18 =  2 *3y - 2*9

          = 2(3y -9)

2(3y - 9) and 6(y- 3 ) are equivalent to 4y - 2(5- y +4)

Others are not equivalent