A gas station sells unleaded regular and unleaded premium gasoline. The price per gallon charged by the station is$1.299 for unleaded regular and $1.379 for unleaded premium. The cost per gallon from supplier is$1.219 for unleaded regular and $1.289 for unleaded premium. If equals the number of gallons sold of regular and equals the number of gallons sold of premium:(a) Formulate the revenue function from selling and gallons of the two grades of gasoline respectively?(b) Formulate total cost for purchasing and gallons?(c) Formulate the total profit? d) what is the total profit expected to equal if the station sells 100,000 gallons of unleaded and regular and 40000 of unleaded premuim?

Answer:

option (4)

Step-by-step explanation:

The general form of a quadratic function is given by :

[tex]f (x) = ax^ 2 + bx + c[/tex]

Where a,b and c are real numbers and a is nonzero.

Option (1)

[tex]f (x) = 3x^ 2 + 12x + 5[/tex]

It is a quadratic function. Here, a = 3, b = 12 and c = 5

Option (2),

[tex]f (x) = x^ 2 + x + 1[/tex]

It is a quadratic function where a = 1, b = 1 and c =1

Option (3),

[tex]f(x)=5x^ 2 + 8x[/tex]

It can also be written as :

[tex]f(x)=5x^ 2 + 8x+0[/tex]

It is a quadratic function where a = 5, b = 8 and c = 0

Option (4),

It can also be written as :

f(x) = 5x + 3

It is a linear function. It is not a quadratic function.

Hence, option (4) is the correct option. It is not a quadratic function.

Answer:

14. [tex]y = -2x -1[/tex]

15. [tex]y = -\frac{3}{4}x +3[/tex]

16. [tex]y= 4x + 9[/tex]

17. [tex]y = -\frac{5}{3}x -2[/tex]

18. [tex]y= -\frac{2}{3}x -5[/tex]

19. [tex]y = 4x -3[/tex]

20. [tex]y = -3x -7[/tex]

Step-by-step explanation:

Solving (14):

Given

[tex](x_1,y_1) = (-7,13)[/tex]

[tex]Slope (m) = -2[/tex]

Equation in [tex]slope- intercept[/tex] form is:

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

Substitute values for y1, m and x1

[tex]y - 13 = -2(x -(-7))[/tex]

[tex]y - 13 = -2(x +7)[/tex]

[tex]y - 13 = -2x -14[/tex]

Collect Like Terms

[tex]y = -2x -14 + 13[/tex]

[tex]y = -2x -1[/tex]

Solving (15):

Given

[tex](x_1,y_1) = (-4,6)[/tex]

[tex]Slope (m) = -\frac{3}{4}[/tex]

Equation in [tex]slope- intercept[/tex] form is:

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

Substitute values for y1, m and x1

[tex]y - 6 = -\frac{3}{4}(x - (-4))[/tex]

[tex]y - 6 = -\frac{3}{4}(x +4)[/tex]

[tex]y - 6 = -\frac{3}{4}x -3[/tex]

Collect Like Terms

[tex]y = -\frac{3}{4}x -3 + 6[/tex]

[tex]y = -\frac{3}{4}x +3[/tex]

Solving (16):

Given

[tex](x_1,y_1) = (-5,-11)[/tex]

[tex](x_2,y_2) = (-2,1)[/tex]

First, we need to calculate the [tex]slope\ (m)[/tex]

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

[tex]m = \frac{1 - (-11)}{-2 - (-5)}[/tex]

[tex]m = \frac{1 +11}{-2 +5}[/tex]

[tex]m = \frac{12}{3}[/tex]

[tex]m = 4[/tex]

Equation in [tex]slope- intercept[/tex] form is:

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

Substitute values for y1, m and x1

[tex]y - (-11) = 4(x -(-5))[/tex]

[tex]y +11 = 4(x+5)[/tex]

[tex]y +11 = 4x+20[/tex]

Collect Like Terms

[tex]y= 4x + 20 - 11[/tex]

[tex]y= 4x + 9[/tex]

Solving (17):

Given

[tex](x_1,y_1) = (-6,8)[/tex]

[tex](x_2,y_2) = (3,-7)[/tex]

First, we need to calculate the [tex]slope\ (m)[/tex]

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

[tex]m = \frac{-7 - 8}{3- (-6)}[/tex]

[tex]m = \frac{-7 - 8}{3+6}[/tex]

[tex]m = \frac{-15}{9}[/tex]

[tex]m = -\frac{5}{3}[/tex]

Equation in [tex]slope- intercept[/tex] form is:

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

Substitute values for y1, m and x1

[tex]y - 8 = -\frac{5}{3}(x -(-6))[/tex]

[tex]y - 8 = -\frac{5}{3}(x +6)[/tex]

[tex]y - 8 = -\frac{5}{3}x -10[/tex]

Collect Like Terms

[tex]y = -\frac{5}{3}x -10 + 8[/tex]

[tex]y = -\frac{5}{3}x -2[/tex]

18.

Given

[tex](x_1,y_1) = (-6,-1)[/tex]

[tex]y = -\frac{2}{3}x+1[/tex]

Since the given point is parallel to the line equation, then the slope of the point is calculated as:

[tex]m_1 = m_2[/tex]

Where [tex]m_2[/tex] represents the slope

Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison

[tex]m = -\frac{2}{3}[/tex]

and

[tex]m_1 = m_2 = -\frac{2}{3}[/tex]

Equation in [tex]slope\ intercept\ form[/tex] is:

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

Substitute values for y1, m and x1

[tex]y - (-1) = -\frac{2}{3}(x - (-6))[/tex]

[tex]y +1 = -\frac{2}{3}(x +6)[/tex]

[tex]y +1 = -\frac{2}{3}x -4[/tex]

[tex]y= -\frac{2}{3}x -4 - 1[/tex]

[tex]y= -\frac{2}{3}x -5[/tex]

19.

Given

[tex](x_1,y_1) = (-2,-11)[/tex]

[tex]y = -\frac{1}{4}x+2[/tex]

Since the given point is parallel to the line equation, then the slope of the point is calculated as:

[tex]m_1 = -\frac{1}{m_2}[/tex]

Where [tex]m_2[/tex] represents the slope

Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison

[tex]m_2 = -\frac{1}{4}[/tex]

and

[tex]m_1 = -\frac{1}{m_2}[/tex]

[tex]m_1 = -1/\frac{-1}{4}[/tex]

[tex]m_1 = -1*\frac{-4}{1}[/tex]

[tex]m_1 = 4[/tex]

Equation in [tex]slope\ intercept\ form[/tex] is:

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

[tex](x_1,y_1) = (-2,-11)[/tex]

Substitute values for y1, m and x1

[tex]y - (-11) = 4(x - (-2))[/tex]

[tex]y +11 = 4(x +2)[/tex]

[tex]y +11 = 4x +8[/tex]

Collect Like Terms

[tex]y = 4x + 8 - 11[/tex]

[tex]y = 4x -3[/tex]

20.

Given

[tex](x_1,y_1) = (-10,3)[/tex]

[tex](x_2,y_2) = (2,7)[/tex]

First, we need to calculate the slope of the given points

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

[tex]m = \frac{7 - 3}{2 - (-10)}[/tex]

[tex]m = \frac{7 - 3}{2 +10}[/tex]

[tex]m = \frac{4}{12}[/tex]

[tex]m = \frac{1}{3}[/tex]

Next, we determine the slope of the perpendicular bisector using:

[tex]m_1 = -\frac{1}{m_2}[/tex]

[tex]m_1 = -1/\frac{1}{3}[/tex]

[tex]m_1 = -3[/tex]

Next, is to determine the coordinates of the bisector.

To bisect means to divide into equal parts.

So the coordinates of the bisector is the midpoint of the given points;

[tex]Midpoint = [\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2)][/tex]

[tex]Midpoint = [\frac{1}{2}(-10+2),\frac{1}{2}(3+7)][/tex]

[tex]Midpoint = [\frac{1}{2}(-8),\frac{1}{2}(10)][/tex]

[tex]Midpoint = (-4,5)[/tex]

So, the coordinates of the midpoint is:

[tex](x_1,y_1) = (-4,5)[/tex]

Equation in [tex]slope- intercept[/tex] form is:

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

Substitute values for y1, m and x1: [tex]m_1 = -3[/tex] & [tex](x_1,y_1) = (-4,5)[/tex]

[tex]y - 5 = -3(x - (-4))[/tex]

[tex]y - 5 = -3(x +4)[/tex]

[tex]y - 5 = -3x-12[/tex]

Collect Like Terms

[tex]y = -3x - 12 +5[/tex]

[tex]y = -3x -7[/tex]

Answer:

32

Step-by-step explanation:

The numbers and letters next to each other mean multiplication. Plus, we already know the values of y and z, so all you have to do is simplify the equation. 10y turns into 10 x 5, and 6z turns intro 6 x 3. So now the equation is 50 - 18, which equals 32. Hope this helps!

Value of expression 10y -6z if y = 5 and z = 3 = 32

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given

value of y = 5

value of z = 3

expression 10y - 6z

Putting value of y and z in the expression

10(5) - 6(3)

= 50 - 18

= 32

Hence, 32 is the value of expression 10y -6z if y = 5 and z = 3.

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Answer:

Mae ling would have made 2,302.

Step-by-step explanation:

Answer:

U can determine that lines e and f are not parallel

Step-by-step explanation:

By remembering vertical angles, u can find all the angles for the diagram. The top are: 110, 70, 70, 110. The bottom four are: 105, 75, 75, 105. As u can see they're not the same so the lines cannot be parallel

Answer:

No/ False.

Step-by-step explanation:

1.) Substitute the coordinates to the given inequality; x is 2, and y is 2. Then, solve.

[tex]2x-3y\geq 6\\2(2)-3(2)\geq 6\\4-6\geq 6\\-2\geq 6[/tex]

Negative 2 (-)2 is NOT GREATER THAN OR EQUAL to Positive 6 (+6), therefore it is a FALSE STATEMENT.

Answer:

no

Step-by-step explanation:

its in the picture. -2 is not greater than or equal to 6

Answer:

Value of theta Ф = 1.33 radians

Step-by-step explanation:

We are given :

S= 8

r = 6

We need to find angle Ф

The formula used is: S=rФ

Finding theta Ф by putting values in formula:

[tex]S=r\theta\\\theta=\frac{S}{r}\\ \theta=\frac{8}{6}\\\theta=1.33[/tex]

So, value of theta Ф = 1.33 radians

Here is your system of equations:

200x + 400y = 3200

y = 2x

Now plug into your calculator to see the graph.

Where the lines cross each other is the point that shows the solution.

Answer:

area of the big triangle is QS*RT, where we know the QS

so we need to derive the area of big triange

the big triange is sum of the larger triangle (QT*RT) + smaller one (TS*RT)

so RT*(5+2.2)=RT(5)+RT(2.2)

the rest is simple to solve

Step-by-step explanation:

Answer:

pretty good tired of the virus stuff but good

Step-by-step explanation:

Answer:

Im great... how bout you?

Step-by-step explanation:

Answer:

60 CDs

Step-by-step explanation:

Given that :

Price of program = $0.5

Price of music = $5

Cost of production :

Program = $0.15 per program

CD = $1.75 per CD

Revenue made= $400

Profit made = $265

Number of CD produced =?

Let Number of CD's = x and program = y

$(0.5y + 5x) = 400

Y = (400 - 5x) / 0.5

y = 800 - 10x

Production :

$(1.75x + 0.15y)

Total cost of production - Revenue made = profit

(1.75x + 0.15y) - (5x + 0.5y) = 265

1.75x + 0.15y - 5x - 0.5y = 265

1.75x - 5x 0.15y - 0.15y = 265

3.25x + 0.35y = 265 - - - (2)

Put y = 800 - 10x in (2)

3.25x + 0.35y = 265

3.25x + 0.35(800 - 10x) = 265

3.25x + 280 - 3.5x = 265

-0.25x = - 15

x = 15/ 0.25

x = 60

Answer:

For the first one wouldnt it be like:

ht=10(r)+5

Step-by-step explanation:

Answer:

h = -25.2

Step-by-step explanation:

To solve the equation, you want to isolate the h variable. To do this, move 12.6 to the other side of the equation. Since you were adding on the left side, use the inverse operation, subtracting, on the right. Simplify the result to get the answer.

h + 12.6 = -12.6

h = -12.6 - 12.6

h = -25.2

Answer:

Step-by-step explanation:

First we need to factorize the given area of the rectangle as shown;

Given

A(x) = x^2-10x+16

Factorize

A(x) = x²-8x-2x+16

A(x) = (x²-8x)-(2x+16)

A(x) = x(x-8)-2(x-8)

A(x) = (x-2)(x-8)

Since area of a rectangle = length ×width

Hence the binomial that represents the width of the pool is w(x) = x-2

b) If the width of the deck is 17feet

Width = x-2

17 = x-2

x = 17+2

x = 19feet

Get the length

Length = x-8

Length = 19-8

Length = 11

Get the perimeter

P = 2(L+W)

P = 2(17+11)

P =2(28)

P = 56feet

Perimeter of the deck is 56feet

Answer:

0

Step-by-step explanation:

To find the number of integer solutions there are to the inequality, we need to  separate [tex]x[/tex] so it is on its own.

[tex]17<5x-8 < 22[/tex] (given inequality)

[tex]25 < 5x < 30[/tex] (add [tex]8[/tex] )

[tex]5 < x < 6[/tex] (divide by [tex]5[/tex] )

Since there are no integers between [tex]5[/tex] and [tex]6[/tex], it means there are 0 integer solutions for the inequality [tex]17 < 5x - 8 < 22[/tex].

Hope this helps :)

Answer:

Step-by-step explanation:

a)

the sum of all angles in a quadrilateral must be 360º

y+88+25+35 = 360

y = 360=88-25-35

y = 212º

b)

the sum of all angles in an octagon must be 1080º

45+45+140+140+6y = 1080

6y = 1080-90-280

6y = 710

y = 710/6

y=~ 118,3º

Answer:10

Step-by-step explanation: it adds 10 every 2 hours

The hourly rate is $5 per hour that the company charges to rent a scooter.

Rate is a measurement to determine the change in one quantity with respect to another quantity.

Given that,

Company charges initial fees, and hourly rate to rent scooter,

Also given,

Cost of scooter for 3 hours = $25,

Cost of scooter for 5 hours = $35,

And cost of scooter for 7 hours = $45

From the given information,

The cost of scooter for 2 hours = $10

Cost of scooter for 1 hour  = $5

Hourly rate of scooter that company charges to rent a scooter is $5.

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A(X)=(7-2x)(x+5)-(21-6x)(2x-1)

A(X)=(7x+35-2x²-10x)-(42x-21-12x²+6x)

A(X)= -2x²-3x+35+12x²+48x-21

A(X)=10x²+45x+14

Answer:

3(3a+4)

Step-by-step explanation:

Answer:

I think you cannot add 9a + 12 because 12 does not have a letter in tonces, it will stay the same

Step-by-step explanation:

Answer:

g(-3) = -30

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define

g(x) = 2x² - 12

g(-3) is x = -3

Step 2: Solve

Answer:

The slope of 8 is 0 and the slope of 9 is undefined

Answer:

She sold 82 brownies

Step-by-step explanation:

164 / 2 = 82

82 x 2 = 164

The number of brownies veronica sale is 82 brownies.

We are given that;

Number of brownies made= 164

Now,

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

To find out how many brownies Veronica sold, we need to divide the total number of brownies she made by 2.

This is because half of something means one part out of two equal parts. Using this method, we get:

[tex]$\frac{164}{2} = 82$[/tex]

Therefore, by unitary method the answer will be 82 brownies.

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Answer:

b = 5/4

Step-by-step explanation:

Equations

Given the function:

[tex]f(x)=mx+b[/tex]

It's required to find the value of b such that:

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

Substituting:

[tex]5(mx+b)=5mx+b+5[/tex]

Operating:

[tex]5mx+5b=5mx+b+5[/tex]

Simplifying:

[tex]5b=b+5[/tex]

Subtracting b:

[tex]4b = 5[/tex]

Dividing by 4:

b = 5/4

Answer:

15

Step-by-step explanation:

Answer:

7.5 hours

Step-by-step explanation:

210 dived by 3= 70

So, 525 dived by 70= 7.5 hours

Brainliest?

Answer:

38260

Step-by-step explanation:

ur welcome

Answer:

38,260

Step by step instructions

Answer:

The answer is

[tex] \huge y = - \frac{5}{4} x - 3[/tex]

Step-by-step explanation:

To find an equation of a line in when given the slope and a point we use the formula

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

From the question we have

[tex]y + 8 = - \frac{5}{4} (x - 4) \\y + 8 = - \frac{5}{4} x + 5 \\ y = - \frac{5}{4} x + 5 - 8[/tex]

We have the final answer as

[tex]y = - \frac{5}{4} - 3 \\ [/tex]

Hope this helps you

Oksuruk diyaframincok ani kasilmasiyla olusan bir reflekstir.

Answer:

I would say A and E would be it.

Step-by-step explanation: