Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:

What is the direct variation equation that represents this situation? (worth 2
points)

How much will Eric spend if he buys 12 pizzas? (worth 2 points)

Explain how you calculated his total cost for pizzas. (worth 2 points)

Answer:

Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1).

The edge lengths of a cube that has a 1.728 cm³ volume is 1.2 cm

The volume of a cube is the given by the length of one edge raised to the power of 3

The volume of a cube, V = Length, L × Width, W × Height, H

Given that the lengths of the edges of a cube are equal, we have!

Length, L = Width, W = Height, H

Which gives;

The volume of a cube, V = L × L × L = L³

Therefore, for the given cube, we have;

L³ = 1.728 cm³

1.728 = 1728/1000

(a + b)³ = a³ + 3•a²•b + 3•a•b² + b³

Taking a = 10, and b = 3, we have;

(10 + 2)³ = 10³ + 3×10²×2 + 3×10×2² + 2³ = 1728

Therefore;

1728/1000 = (10 + 2)³/10³ = 12³/10³

Which gives;

L³ = 12³/10³

[tex] \displaystyle {L = \sqrt[3]{ \frac{{12}^{3} }{ {10}^{3} } } = 1.2}[/tex]

The edge lengths of the cube, L = 1.2 cm

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There are 12,565,671,261 ways to assign scores to the problems in discrete mathematics exam.

In this case, we must employ the combination as well as repetition formula.

C(n + r-1, r) = (n + r -1)!/ r! (n - 1) !

n = 10 is provided (The number of questions)

Every question is worth a minimum of 5 points.

For 10 question = 10×5 = 50 points.

The total are 100 (sum of the scores)

r = 100 - 50

r = 50

Applying the formula.

C(10 + 50 - 1 , 50) = (10 + 50 - 1)!/ 501 (10 - 1)!

C(59, 50) = 59!/50!9!

We get by clarifying the above factorial.

C(59, 50) = 12,565,671,261

Thus, there are 12,565,671,261 ways to assign scores to the problems in discrete mathematics exam.

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Answer:

2

Step-by-step explanation:

7y-14=0

7y=14

7y/7=14/7

y=2

The number of mathematics assignments are 69.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

Given : Brianna has 113 assignments in history, science and art.

Let x be the number of assignments that are in math section. There are 182 assignments in total.

The equation to represent this is

113 + x = 182

x = 182 - 113 = 69.

So the number of math assignments are 69.

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The answer will be .25 and .25 for both set of question. using probablity.

What is Probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.

Total number of students =1-juniors+chemistry+neither+both

(a) For both a junior and chemistry major =1/4 =. 25

(b) probability that she is also a chemistry major will be 1/4 =. 25

Hence The answer for the above two set of qustion will be .25 and .25.

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The slope of the line will be equal to 30.

Slope of a line may be defined as the steepness of a curve. Slope of line can be positive, negative or zero. Slope of a line is used to determine the equation of the line which is given as y = mx + b where m is the slope, b is y intercept and x and y are independent and dependent variables respectively. The slope of a line on points (x₁, y₁) and (x₂, y₂) is given by the formula, m = y₂ - y₁/x₂ - x₁.

According to the question the value of points is (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 60).

Now, the slope can be calculated as

m = (60 - 0)/(2 - 0)

=> m = 60/2

=> m = 30 which is the required slope.

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Answer:

3/2

Step-by-step explanation:

XY/Z

-2×-3/4

6/4

3/2

Answer:

x-3+4 = x+1

Step-by-step explanation:

x-3+4 = x+1.

NOTE -3 MUST MULTIPLY EVERYTHING IN THE BRACKETS.

[tex] = - 3(v) - 3(2) - 2v \\ = - 3v - 6 - 2v \\ = - 3v - 2v - 6 \\ = - 5v - 6[/tex]

GOODLUCK.

Answer: 20 x 1 x 0.1 + 8 + 1

              2 + 8 = 10

Answer:

y=2x+4

Step-by-step explanation:

get x is get two point let’s say (-2,0) and (0,4)

The 4-0/0-(-2)=4/2=2 so 2 is x and (0,4) is where it hit the y axis so 4 is b plug in

Y=2x+2

Answer:

f(n)=8n-63

15th term=57

Step-by-step explanation:

goes up by 8 each time therefore the coefficient of n is 8

take for example the 1st term,8n would be 8, to get to -55 from 8 you would have to subtract 63, therefore the nth term is 8n-63.

Some examples of ratios are:

There are 20 passengers on each bus

There are 2 red and 3 black balls in each box.

Some examples of unit rates are:

The man can run 10 miles in one hour.

I can type 100 words in 30 minutes.

A unit rate means a rate for one of something.

We write this as a ratio with a denominator of one. 

The ratio is the comparison of two quantities of the same units.

We have,

Ratio:

For every 1 car, there are 4 tires.

We can have some examples of ratios as:

1 - There are 20 passengers on each bus

2 - There are 2 red and 3 black balls in each box.

Unit rate:

Car driving 60 miles per hour.

We can have some examples of unit rates:

1 - The man can run 10 miles in one hour.

2 - I can type 100 words in 30 minutes.

Thus,

Some examples of ratios are:

There are 20 passengers on each bus

There are 2 red and 3 black balls in each box.

Some examples of unit rates are:

The man can run 10 miles in one hour.

I can type 100 words in 30 minutes.

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The answer is b(x)=f(x)-7, which is option B.

The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The parent linear function is given below.

f(x) = x

The function is shifted downward direction by 7 units. Then the function b(x) will be given as,

b(x) = f(x) - 7

The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.

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answer: associative property

Step-by-step explanation:

Answer:

Step-by-step explanation:

An equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .What is the Point-slope form?The equation of the straight line has its slope and given point.If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equationy-y₁ = m(x-x₁)Which is the required equation of a line in a point-slope form.WE havex + y = 6y = - x + 6Slope= -1Now, Use the same slope since the two lines are parallel to each other.Point-slope formula:y - 8 = -1 (x - - 4)y - 8 = -1 (x + 4)y - 8 + 8 = -x - 4 + 8y = - x + 4 (Slope-intercept form)Hence, an equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .Learn more about slope here: brainly.com/question/2503591#SPJ2

⇒Parallel lines have equal gradients . It means that to obtain the gradient of the new equation we should first find the gradient of the given equation by writing the given equation in the form y=mx+c

[tex]x-y=6\\y=x-6[/tex]

⇒The gradient of the given equation is 1 as we know that the gradient of the equation is the coefficient of the variable x

This means the equation of the new equation is also going to be 1 since I explained above why.   to find the value of c in the new equation we will substitute the known values in the general equation including the point.

[tex]5=1(-1)+c\\6=-1+c\\c=5+1\\c=6[/tex]

This means that the new equation is going to be:

[tex]y=x+6[/tex]

Answer:

3:7

Step-by-step explanation:

AR has 3 spaces while AB has 7 means its 3:7

Expressing [tex]\frac{x-1}{2x+1}[/tex]  in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]

Given that:

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

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

The Knowledge required here is substitution, the value of x is given. Substitute [tex]x=\frac{2a+3}{3a-2}[/tex] in any place x is seen in the numerator and the denominator.

The numerator

x - 1

substituting the value of x

[tex]\frac{2a+3}{3a-2}-1[/tex]

[tex]\frac{(2a+3)-(3a-2)}{3a-2}[/tex]

[tex]\frac{2a+3-3a+2}{3a-2}[/tex]

[tex]\frac{5-a}{3a-2}[/tex]

The denominator

2x + 1

substituting the value of x

[tex]2*\frac{2a+3}{3a-2} +1[/tex]

[tex]\frac{4a+6}{3a-2} +1[/tex]

[tex]\frac{(4a+6)+(3a-2)}{3a-2}[/tex]

[tex]\frac{7a+4}{3a-2}[/tex]

combining the fraction

Here the numerator and the denominator is brought together and division of fraction is used to solve

[tex]\frac{\frac{5-a}{3a-2}}{\frac{7a+4}{3a-2}}[/tex]

[tex]\frac{5-a}{3a-2}}*\frac{3a-2}{7a+4}[/tex]

[tex]\frac{5-a}{7a+4}[/tex]

Using substitution as required, then expressing the equation in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]

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Answer:

-87

Step-by-step explanation:

-4x^2 + 3x - 11

-4(-4)^2 + 3(-4) - 11

-4 * 16 + 3(-4) - 11

-4 * 16 - 12 - 11

-64 - 12 - 11

-76 - 11

-87

Hope this helps! :)

The line segment AB with endpoints (-10,0) and (6,8). The equation of the line segment is x-2y+10=0.

Given that,

The line segment AB with endpoints (-10,0) and (6,8).

We have to find the equation of the line segment.

The equation of the line formula is y-y₁=m(x-x₁).

Here we don't know the m value that is nothing but slope of the line.

First we have to find the slope of the line segment.

Slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=(8-0)/(6+10)

m=8/16

m=1/2

Now,

We know the equation of line is y-y₁=m(x-x₁)

y-0=1/2(x+10)

2y=x+10

x-2y+10=0

Therefore, The equation of the line segment is x-2y+10=0.

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Equation is 4x-1 =27. that means the correct answer is 27

The equals sign is used in mathematical formulas to show that two expressions are equal. In contrast to English, where an equation is defined as any well-formed formula that consists of two expressions joined by the equals sign, French defines an equation as containing one or more variables. The first stage in resolving a variable equation is determining the values of the variables that lead to equality.

Here, 4x-1 =27
We know that x=7
4x=27+1
4x= 28
Therefore x = 28÷4 = 7.
Hence, 4x-1 =27

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Answer:

22 is 20% of 110

Step-by-step explanation:

Answer:

1st[tex]7532 + 100y ^{2} + 100y^{2} - 1100[/tex]

2nd

[tex]200y ^{2} + 6432[/tex]

final answer

[tex]a = 200[/tex]

[tex]b = 6432[/tex]

Answer:

58.2 degrees

Explanation:

The given problem is illustrated using the diagram below:

The angle the ramp makes with the sidewalk is labeled x above.

Using trigonometry:

The angle the ramp makes with the sidewalk is 58.2 degrees.

Answer: See attached.

Step-by-step explanation:

     To graph this, we will look at the pieces they gave us. Slope-intercept form equations are written in y = mx + b.

   ➜ The slope, m, is the pitch of the line. It's "rise over run" and helps us know where the plot points. For this problem, we will rise one value and move 6 values right to the next point.

     ➜ The y-intercept, b, is where the line intercepts the y-axis. It helps us know where the first point goes (0, y). For this problem, we will graph (0, 4).

     Using these details, we will graph the line. View attached.

Answer:

5.625

Step-by-step explanation:

450÷80 I hope I'm right and it helps if not I'm sorry.

As per the linear function, the destination after 57 minutes of driving is 1055 miles.

Linear function:

The linear equation is defined as an algebraic equation of the form

y = mx + b.

involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given,

Trey is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes).

Trey has 49 miles to his destination after 37 minutes of driving, and he has 37.8 miles to his destination after 51 minutes of driving.

Here we need to find his destination after 57 minutes of driving.

In this one, first we have to find the linear equation for the situation.

For that, we need the slope and the intercept.

So, here we consider the distance as y axis and the corresponding time as x axis. then we get the points as,

(x1. y1) => (37, 49)

(x2, y2) => (51,37.8)

Then the slope of the line is calculated as,

m = (37.8 - 49) / (51 - 37)

m = -11.2/14

Now, the intercept is calculated using the point (37,49) and the slope m = -11.2/14 is,

49 = -11.2/14(37) + b

686 = -414.4 + b

b = 1100.4

So, the linear equation of the function is

y = -11.2/14x + 1100.4

Here we need to find the distance when the time is 57 minutes,

For that, we have to apply the value of x as 57, to get the value of y,

Therefore,

y = -11.2/14 (57) + 1100.4

y = -45.6 + 1100.4

y = 1055

Therefore, the destination after 57 minutes of driving is 1055 miles.

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