What is the quotient of 228 ÷ 12?

Answer:

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

Angel

Guests --- Charges

10 -------- $180

15 -------- $255

25 -------- $405

30 -------- $480

Solving (a): Who charges the greater flat fee?

We have that the flat fee of Rose is:

[tex]Flat\ Fee = \$50[/tex]

For Angel, we need to determine the equation of the given table

Start by calculating the slope (m) of the table

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

Where x and y represent any two corresponding values of the guests and the charges.

[tex](x_1,y_1) = (10, 180)[/tex]

[tex](x_2,y_2) = (30, 480)[/tex]

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

[tex]m = \frac{480 - 180}{30 - 10}[/tex]

[tex]m = \frac{300}{20}[/tex]

[tex]m = 15[/tex]

Next, we calculate the equation using:

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

Where

[tex]m = 15[/tex]

[tex](x_1,y_1) = (10, 180)[/tex]

[tex]y - 180 = 15(x - 10)[/tex]

[tex]y - 180 = 15x - 150[/tex]

Add 180 to both sides

[tex]y - 180 + 180 = 15x - 150 + 180[/tex]

[tex]y= 15x + 30[/tex]

From the equation above:

The slope = 15 --- This represents the hourly rate

and

y intercept = 30 --- This represents the flat fee

This is better represented as:

Angel

[tex]Flat\ Fee = \$30[/tex]

[tex]Rate = \$15[/tex]

and

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

By comparison, Angel has a greater flat fee

Solving (b): Difference between total charges of 50 guests for both caterers.

For angel, the equation is:

[tex]y= 15x + 30[/tex]

and x = 50.

So:

[tex]y = 15 * 50 + 30[/tex]

[tex]y = 750 + 30[/tex]

[tex]y = 780[/tex]

For Rose,

First, we need to determine the equation.

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

The equation is:

[tex]y = Flat\ Fee + Rate * x[/tex]

[tex]y = 50 + 12 * x[/tex]

So, the total charges for 50 guests is:

[tex]y = 50 + 12 * 50[/tex]

[tex]y = 50 + 600[/tex]

[tex]y = 650[/tex]

The difference is then calculates as:

[tex]Difference = 780 - 650[/tex]

[tex]Difference = \$130[/tex]

Option B - The worker earns $8 per hour is the correct alternative.

We have a graph that shows the relationship between the number of dollars a worker earns and the number of hours worked.

We have to select the statement which best describes the rate of change for this situation.

The slope of a line can be calculated using -

[tex]$m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

According to the question, we have two coordinate points marked on the graph -

P(20, 60)

Q(40, 320)

Using the formula to calculate the slope of a line, we get -

[tex]$m = \frac{320-160 }{40 -20 }[/tex]

m = 8

We know that the slope of the line represents the rate of change of y with respect to x. Therefore, the worker earns $8 per hour.

Hence, Option B is correct.

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Answer:

y = x - 6

Step-by-step explanation:

find slope

m = -2 - (-9) / 4 - (-3)

m = 7 / 7

m = 1

find y intercept using slope formula

y = mx + b and plug in any points given

-2 = 1(4) + b

b = - 6

put it together

y = x - 6

Answer:

11 bags of grapefruits; 2 bags of lemons

Step-by-step explanation:

Create a system of equations.

Let x be the number of grapefruit bags. Let y be the number of lemon bags.

x + y = 13

10x + 8y = 126

Rearrange the first equation to solve for x:

x = 13 - y

Substitute x in for x in the second equation:

10(13 - y) + 8y = 126

130 - 10y + 8y = 126

-2y = -4

y = 2

Plug y back into the first equation to solve for x.

x = 13 - 2

x = 11

Answer:

Option D

Step-by-step explanation:

Given → Two sides of the triangle are equal in measure.

Therefore, given triangle is an isosceles triangle.

By the property of isosceles triangle, opposite angles of the equal sides of a triangle are equal in measure.

m∠A = m∠B = 70°

m∠A + m∠B + m∠C = 180°

70° + 70° + m∠C = 180°

m∠C = 180 - 140 = 40°

Since, m∠C = (2x + 16)°

(2x + 16)° = 40°

2x = 40 - 16 = 24

x = 12

Therefore, Option D will be the correct option.

Answer:

g(2) = -11

Step-by-step explanation:

So, g(-2), basically meaning that x = -2.

Since we know that, we need to plug -2 into all of the x's.

g(2) = 3(-2) - 5

g(2) = -6 - 5

g(2) = -11

The required value of g(2) would be -11.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The function is given in the question following as:

g(x) = 3x-5

We have to determine the value of g(2) to the given function.

As per the given question, we have

⇒ g(x) = 3x-5

So, g(-2), this meaning that x = -2.

Now, substitute the value of x = -2 in the given function,

⇒ g(2) = 3(-2) - 5

⇒ g(2) = -6 - 5

Apply the addition operation, and we get

⇒ g(2) = -11

Therefore, the required value of g(2) would be -11.

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Answer:

To find the inverse you switch x and y

Step-by-step explanation:

3y-4x=6

So 3y = 4x+6

and Y = 4/3x + 2

Answer:

y=(6-3x)/-4

Step-by-step explanation:

to get the inverse we make y the subject of the equation

3x-4y=6

-4y=6-3x

y=(6-3x)/-4

Answer:

2,000 + 0.03x

Step-by-step explanation:

Answer:

Answer is 9 Broski mark as brainliest

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

The slope is the rise over run or the change in y over the change in x. In this case, the y decreases by 3 while the x increases by 1. Since one value increases while the other decreases the slope must be negative. So if we put the 3 over 1 and make it negative the answer is -3/1, which simplifies to -3.

Answer:

Fourth choice (9,-2)

Step-by-step explanation:

Fourth choice (9,-2)

Answer:

Step-by-step explanation:

35

Answer:

Yes, the graph is a function because the lines do not overlap one another (vertical line test)

- I hope this helps have a great night

Answer:

it is diff because o the parentheses

Step-by-step explanation:

Answer:

156.63 ft squared

Step-by-step explanation:

The bedroom is a rectangle.

Area of a rectangle- A=length times width

multiply the two numbers and you will get 156.63.

Be sure to add the units (feet).

Answer:

25

Step-by-step explanation:

a2+b2=c2

3^2+4^2=c^2

9+16=25

25^2=625

Sqrt of 625 = 25

Answer:

x = 5

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 4² + 3² = 16 + 9 = 25 ( take the square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

(2x + I) (2x-I) = 4x^2 + 1

Using the complex arithmetic rule:

(A + bi)(a-bi) = a^2 + b^2

A would be the 2x and b would be the i

So you would have:

(2x)^2 + (i)^2

(2x)^2 = 2x times 2x = 4x^2

i ^2 = 1

Final answer is 4x^2 + 1

Answer:

Wouldn't it be 8?

Step-by-step explanation:

You crack 2 eggs and cook them, then eat them. If we cracked 2 eggs, cooked 2 different eggs, and ate 2 different eggs, that doesn't make sense.

Answer:

8

Step-by-step explanation: you can crack, cook, and eat with 1 egg

so if you cracked 2 cooked 2 and ate 2, it means that you only used 2

Answer: 22

Step-by-step explanation: 65 divided by 3 is 22

Answer:

21or22

Step-by-step explanation:

65/3

Answer:

-3, -2, -1, 0, 1, 2, 3

Step-by-step explanation:

I am pretty sure you are trying to ask this but don't mind if it's not. If it's not just ignore it.

-3 is the smallest, so you go see the integers above it that are equal or less than 3.

Integers are numbers that can be negative or positive, but cannot be a decimal, square root, X and more.

So then the answer should be

-3, -2, -1, 0, 1, 2, 3

The top one is x-intercept, and the bottem one is y-intercept. Also the gray boxes are your answer

The graph of the x-intercept at x = -5 and y-intercept at y = -2 is given below.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

x-intercept = (-5, 0)

This means,

It is a vertical line at x = -5.

y-intercept = (0, -2)

This means,

It is a horizontal line at y = -2.

Thus,

The graph is given below.

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Answer:

-6.28576e+81

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

Answer is B

Answer:

Concept: Evaluating Functions

Answer:

h(5)=59

Step-by-step explanation:

The function h(t) should be h(t)=2t²+9 NOT 2f²+9

With that said,h(5)=2(5²)+9

h(5)=50+9=59

Answer:

721

Step-by-step explanation:

dog you in elementary school

Answer: C

Step-by-step explanation:

Answer:

$12,500 per year

Step-by-step explanation:

rate of change = change in dollars/change in years

So,

(245000 - 120000)/(2017 - 2007) = 125000/10 = $12,500 per year