Mrs. Taylor is planning a pizza party for her students. She plans to purchase cheese pizza and pepperoni pizza for her students to enjoy. Cheese pizzas cost $8 each and pepperoni pizzas cost $11 each. She needs to purchase at least 12 pizzas, while spending no more than $180.

Let x represent the number of cheese pizzas purchased and y represent the number of pepperoni pizzas purchased.

What are two combinations of cheese and pepperoni pizzas that Mrs. Taylor can purchase without exceeding her spending limit?

Verify the combinations, graphically.

Verify the combinations, algebraically.


What is one combination of cheese and pepperoni pizzas that does not meet the criteria?

Verify the combination, graphically.

Verify the combination, algebraically.

Answer:

Graph for (x^4+x-1)/(x-1)

Step-by-step explanation:

Graph for (x^4+x-1)/(x-1)

The required, divide is given by [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex]

Fraction of polynomial is, in the numerator and in the denominator of a fraction there is polynomial function

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

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

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

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

Thus the required, divide is [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex].

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Using the mid-point concept, we have that:

The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.

The center of the circle is the mid-point of the coordinates of the diameter, hence:

The radius is the distance between the center and the end-points of the diameter, hence, applying the formula for the distance between two points:

[tex]r = \sqrt{(5 - 2)^2 + (8 - 7)^2} = \sqrt{10} = 3.16[/tex]

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It looks like your equations are

7M - 2t = -30

5t - 12M = 115

Solving by substitution

Solve either equation for one variable. For example,

7M - 2t = -30   ⇒   t = (7M + 30)/2

Substitute this into the other equation and solve for M.

5 × (7M + 30)/2 - 12M = 115

5 (7M + 30) - 24M = 230

35M + 150 - 24M = 230

11M = 80

M = 80/11

Now solve for t.

t = (7 × (80/11) + 30)/2

t = (560/11 + 30)/2

t = (890/11)/2

t = 445/11

Solving by elimination

Multiply both equations by an appropriate factor to make the coefficients of one of the variables sum to zero. For example,

7M - 2t = -30   ⇒   -10t + 35M = -150 … (multiply by 5)

5t - 12M = 115   ⇒   10t - 24M = 230 … (multiply by 2)

Now combining the equations eliminates the t terms, and

(-10t + 35M) + (10t - 24M) = -150 + 230

11M = 80

M = 80/11

It follows that

7 × (80/11) - 2t = -30

560/11 - 2t = -30

2t = 890/11

t = 445/11

Answer:

Step-by-step explanation:

A rational number can be in the form of a whole/natural number, integers, fractions and recurring decimals

In this case, 5 is a whole number, integer (can be a fraction too) , and of course, is a rational number.

As of which options to choose, read the above sentence carefully :)

Answer:

Natural, Integer, Rational, Whole

Step-by-step explanation:

First, we should know the definition of the word choices.

1) Natural Numbers: We can also count it as 'counting numbers'. Natural numbers are numbers that are a whole excluding the number 0. Some examples are 1, 2, 3, 4, 5 ... and so on.

2) Irrationals: They are numbers that cannot be written in a fraction form. Some examples are [tex]\sqrt{2} , \sqrt{3} , \sqrt{4} , \pi ...[/tex] etc.

3) Integers: They are a whole number that can be a negative, positive, or even a zero. Natural numbers are included in integers. Examples are -2, -1, 0, 1, 2, and so on.

4) Rationals: They are numbers that can be expressed in a fraction form, so it is the opposite of 'irrationals'. Examples are -1/2, 1/2, 2/4, 2/1 ... etc.

5) Whole Numbers: They are numbers that aren't a fraction. It can only be a positive number and a zero, so some examples would be 0, 1, 2, 3, 4, 5 ... and so on.

With these in mind, we can now solve the question. The number 5 is a natural, integer, rational, and a whole number.

Answer:

KE = 1/2 mv²

In terms of Mass Velocity

KE = mv²

Answer: [tex]KE=\frac{1}{2} mv^{2}[/tex]

Step-by-step explanation:

- the correct equation is: [tex]KE=\frac{1}{2} mv^{2}[/tex]

- KE is kinetic energy

- m is mass

- v is velocity

besides that, i don't really know how to explain it but hope this helps :)

The slope-intercept form of the equation of the line containing the points (−2, 4) and (6, 0) will be y =0.5 x+ 5.

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The slope of the line is found as;

[tex]\rm m = \frac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{0-4}{6-(-2)} \\\\ m = \frac{-4}{8} \\\\ m = \frac{-1}{2}[/tex]

The standard line equation is;

y-y₁=m(x-x₁)

[tex]\rm y-4= \frac{-1}{2}(x-(-2)) \\\\ 2y-8 = x+2 \\\\ 2y =x+10 \\\\ y = 0.5 x + 5[/tex]

Hence, the slope-intercept form of the equation of the line containing the points (−2, 4) and (6, 0) will be y =0.5 x+ 5.

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Answer:

C

Step-by-step explanation:

to calculate these kinds of questions we can simply plug in the points given in the equation (x,y ) places where 4 is substituted in x place and 8 in y . so in choice "C" if we put 4 in x's place in the equation we would have to divide it by 2 and multiply by 1 which gives us 2 not 8.

El número máximo de ocupantes es el máximo común divisor de los dos números, es decir, 10 personas por cabaña. Se debe pagar siete cabañas para minimizar costes.

En esta pregunta desconocemos la capacidad de cada cabaña, solo conocemos que todas las cabañas tienen el mismo aforo. En consecuencia, puede haber más de una respuesta, aunque con la restricción de que cada cabaña tiene el mismo número de hospedados.

Inicialmente, descomponemos factorialmente los números de adultos y niños:

Niños

40 = 2³ × 5

Adultos

30 = 2 × 3 × 5

El número máximo de ocupantes por cabaña es el máximo común divisor de los dos números, es decir, 2 × 5 = 10. Por tanto, los excursionistas deben pagar siete cabañas para minimizar costes.

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Step-by-step explanation:

monthly interest rate calculation example convert the annual rate from a percent of a decimal by dividing by 100 / 100 is equal to 0.10.9 divide that number 12 to get monthly interest rate in the decimal forms 0.10 upon 12 is equal to zero zero eight three

Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.

According to the statement

Average sample =3700

SD sample =6500

Sample size =400

EV average =3700

SE average =325

Population size =3000

The boundaries of the 68% confidence interval are then 1 standard error from the estimated average:

EV average+1⋅SE average ​=3700+1⋅325=3700+325=4025

EV average−1⋅SE average =3700−1⋅325=3700−325=3375

Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.

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Answer:

C) Similar - SAS

Answer:

x^2 -4

Step-by-step explanation:

(x-2)(x+2)

We want to FOIL

First  x*x = x^2

Outer  x*2 =2x

Inner  -2 *x = -2x

Last  -2*2 = -4

Add them together

x^2+2x-2x-4

Combine like terms

x^2 -4

Explanation:

From the given graph of f(x) = √-x

After analyzing,

Above from all options, D.) The domain of the function is all real numbers less than or equal to 0.

Answer:

AB = 14

Step-by-step explanation:

We can add the segments together to find the total

AB + BC = AC

This will allow us to find x

4x+2 + 3x-1 = 22

Combine like terms

7x +1 = 22

Subtract 1 from each side

7x+1-1 = 22-1

7x = 21

Divide by 7

7x/7 = 21/7

x = 3

Now we can find the length of AB

AB = 4x+2 = 4(3)+2 = 12+2 = 14

Answer:

7

Step-by-step explanation:

5 x 27 = 135

135 ÷ 20 = 6.75

round up to 7

Answer:

Step-by-step explanation:

Answer:

[tex]\sf \boxed{ \sf y - 3 = \dfrac{3}{2} (x - 6)}[/tex]

Explanation:

[tex]\sf Given \ equation: y = \dfrac{3}{2} x - 5[/tex]

Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept.

Here slope: 3/2 and y-intercept: -5

Parallel slope has the same tangent slope.

Pass through point (x, y) = (6, 3)

Equation:

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

[tex]\rightarrow \sf y - 3 = \dfrac{3}{2} (x - 6)[/tex]

The area of regular hexagon is 166.27688 inch².

The area is the amount of space within the perimeter of a 2D shape.

Given:

side = 8 inch

Using

Area of regular hexagon = 3 √3/2 * a²

= 3 √3/2 * 8*8

=96√3

= 166.27688 inch²

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Charlotte is 96 years old and Rachel is 292 years old

Let c represent Charlotte's age and r represents Rachels's age

From the question, we have:

c = r - 195

2 years later, we have:

r + 2 = 3(c + 2)

Expand the equation

r + 2 = 3c + 6

Subtract 2 from both sides

r = 3c + 4

Substitute r = 3c + 4 in c = r - 195

c = 3c + 4 - 195

Evaluate the like terms

-2c = -191

Divide by -2

c = 95.5

Approximate

c = 96

Substitute c = 96 in r = 3c + 4

r = 3*96 + 4

Evaluate

r = 292

Hence, Charlotte is 96 years old and Rachel is 292 years old

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Answer:

kskwnneokjwonannwknwonw

Answer:

Hence we prefer FOIL method when multiplying two binomials.

Step-by-step explanation:

Explanation

Answer:Answer: We know it has a length of 10 cm, and the width is h times 2.

Step-by-step explanation: So the equation we should write is volume = 10 x (h x 2) x h.

Step-by-step explanation:

The statement which correctly compares the two functions is that: A. they have the same y-intercept and the same end behavior as x approaches ∞.

A function is a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.

By critically observing the graph which models the function f (see attachment), we can logically deduce that the y-intercept is at four (4).

Also, from the table of function g (see attachment), we have:

At x = 0, g(x) = g(0) = 4.

In conclusion, the statement which correctly compares the two functions is that they have the same y-intercept and the same end behavior as x approaches infinity (∞).

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Complete Question:

The graph of function f is shown.

Which statement correctly compares the two functions?

A. They have the same y-intercept and the same end behavior as x approaches ∞.

B. They have different x- and y-intercepts but the same end behavior as x approaches ∞.

C. They have the same x- and y-intercepts.

D. They have the same x-intercept and the same end behavior as x approaches ∞.

Answer:

x + 5y = 40

Step-by-step explanation:

the equation of the line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{1}{5}[/tex] and c = 8 , then

y = - [tex]\frac{1}{5}[/tex] x + 8 ( multiply through by 5 to clear the fraction )

5y = - x + 40 ( add x to both sides )

x + 5y = 40 ← in standard form

⊰________________________________________________________⊱

Answer:

See Below.

Step-by-step explanation:

[tex]\large\begin{gathered}\sf{First, \ let's \ write \ the \ equation \ in \ slope-intercept \ form.}\\\sf{ Slope-Intercept \ form \ is \curvearrowright} \\\boxed{y=mx+b}}\\\sf{Substitute \ the \ pieces \ of \ information \ we \ have \curvearrowright\\\sf{ y=-\dfrac{1}{5}x+8}\\\sf{Now, if \ we \ multiply \ the \ entire \ equation \ by \ 5, \ we'll \ have:} \\\sf{5y=-x+40}\\\sf{And \ finally, move \ \bf{x} \ \sf{to \ the \ left \ with \ the \ opposite \ sign: x+5y=40.}\end{gathered} \bigstar \\\bigstar[/tex]

Done!!

⊱______________________________________________________⊰

[tex]\overbrace{C}\underbrace{A}\overbrace{L}\underbrace{L}\overbrace{I}\underbrace{G}\overbrace{R}\underbrace{A}\overbrace{P}\underbrace{H}\overbrace{Y}[/tex]

The tax paid by Rebecca on each cupcake was $0.15 or 15 cents, in the buying of 15 cupcakes for $47.25, where the cost of each was $3 plus taxes.

The tax is the amount paid to the government for buying and selling of goods are services.

In the question, we are informed that Rebecca bought 15 cupcakes, where each cupcake cost $3 plus taxes and the total bill to Rebecca was $47.25.

It implies that the cost of 15 cupcakes along with their taxes = $47.25.

Therefore, the cost of 1 cupcake along with its taxes = $47.25/15 = $3.15.

The cost of 1 cupcake is given as $3 plus taxes.

The total cost of 1 cupcake was $3.15.

Thus, the tax on 1 cupcake = $3.15 - $3 = $0.15 = 15 cents.

Thus, The tax paid by Rebecca on each cupcake was $0.15 or 15 cents, in the buying of 15 cupcakes for $47.25, where the cost of each was $3 plus taxes.

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The average rate of change of the function from n = 1 to n = 5 is 3.36 plants per day

The function is given as:

f(n) = 10(1.02)^n

The maximum height is 11.04

So, we have:

10(1.02)^n = 11.04

Divide by 10

1.02^n = 1.104

Take the log of both sides

n * log(1.02) = log(1.104)

Divide by log(1.02)

n = 5

Hence, the reasonable domain is 0 ≤ n < 5

We have:

f(n) = 10(1.02)^n

Set n to 0

f(0) = 10(1.02)^0

Evaluate

f(0) = 10

Hence, the y-intercept is 10

We have:

f(n) = 10(1.02)^n

Calculate f(1) and f(5)

f(1) = 10(1.02)^1 = 10.2

f(5) = 10(1.02)^5 = 10.2

The average rate is then calculated as:

m = (f(5) - f(1))/(5 - 1)

This gives

m =(11.04 - 10.2)(5 - 1)

Evaluate

m = 3.36

Hence, the average rate of change of the function f(n) from n = 1 to n = 5 is 3.36

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The answers to the question about the equations are as follows:

1) A. Only add to or remove from one side.

2) B. No

1) As can be seen, the equations' left sides vary, while their right sides remain the same.

We must eliminate the difference in order to make them equal.

Formula A: 5x -2 + x = x -4

Formula B. 5x + x = x- 4

Equation B is created by multiplying the left side of equation A by 2.

The available response in this instance is:

A. Only increase or decrease an amount from one side.

2) The answers to the equations will differ since they are not identical.

Answer option:

B. No

The question was incomplete. The complete question was as follows:

Give two answers about Equations A and B:

A. 5x-2+x = x-4

B. 5x+x = x-4

1) From Equation A, how do we derive Equation B?

A. Only increase or decrease an amount from one side.

B. Increase/decrease the same amount on both sides.

C. Use the distributive principle to rewrite one (or both) sides.

D. Rewrite one (or both) sides using similar wording.

2) Are the equations equal in the light of the initial response? Do they share the same solution, in other words?

(1) Yes (2) No

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Answer:

Step-by-step explanation:

The measure in radians for the central angle of the circle is; 0.9 radians.

Since, the length of the arc is given as 7.2cm and it's radius is 8cm.

It follows that the angle measure of the central angle can be evaluated as follows;

7.2 = (A/6.28) × 2× 3.14 × 8

7.2 = 8A

A = 7.2/8

A = 0.9 radians.

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The equation that shows the relationship between the number of baskets (b) made from outside the three-point line and the number of points scored (p) is p = 3b

In basket ball, If a shot is successfully scored from outside of the three-point line, three points are awarded.

where

Therefore, the equation that shows the relationship between the number of baskets (b) made from outside the three-point line and the number of points scored (p) is as follows:

p = 3b

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Answer:

y = -7/8x - 1 1/2

Step-by-step explanation:

m = y2 - y1/ x2 - x1 is how you find the m in y=mx+b

(I converted the fractions to decimals)

substitute you slope and (x,y)

y = mx + b

-5 = -0.875(4) + b

-5 = -3.50 + b

-1.50 = b

b = -1.50

then just convert back to a fraction