Sophia buys a supply of toilet paper from costco that comes in a pack 36. She immediately gives 4 rolls of toilet paper to her sister (who shared with her last month). She uses 2 rolls of toilet paper a per month.

(a) Write an expression that represents the situation

(b) Determine how many rolls of toilet paper she will have left after 1 year

EXPLAIN AND SHOW YOUR WORK

We can write equations by rewriting the important phrases of information using variables. These variables make the equation look neater and it is faster to write a letter instead of constantly repeating 'cost of student tickets', for example.

The important pieces of information lies in the second last sentence of this question.

Now, let's rewrite them into equations.

Given

x= cost of adult tickets

y= cost of student tickets

Assuming that your friend and her little sister are students, the two equations are:

To convert these equations into slope-intercept form, move all the terms that are not y to the right-hand side of the equation before dividing both sides by the coefficient of y. This is to ensure that the coefficient of y is 1 and that your equation is in y= mx +c, where m is the slope and c is the y-intercept.

From equation (1):

x +2y= 23

2y= -x +23

Divide both sides by 2:

[tex]\bf{y = - \frac{1}{2} x + \frac{23}{2} }[/tex]

From equation (2):

2x +3y= 39

3y= -2x +39

Divide both sides by 3:

[tex]\bf{y= - \frac{2}{3} x + 13}[/tex]

The solution to the system of equations is the point at which the two lines intercept on the graph. I have attached the graph as an image.

The solution is (9, 7).

The x coordinate is the cost of an adult ticket, while the y coordinate is the cost of a student ticket. This means that adult tickets cost $9 and student/ child tickets cost $7.

Answer:

Answer

d) 2 – i

Explanation

f(x) = x³ – 2x²

When x = i, we proceed as follows.

Note: i =

         i² =(√-1)(√-1) =  -1

         i³ = (√-1)(√-1)(√-1) = -1(√-1) = -1i = -i

f(x) = x³ – 2x²

f(i) = i³ – 2i²

    = -i – 2(-1)

    = -i + 2

     = 2 – i

Step-by-step explanation:

Answer:

Obliviousness: Being unaware of something.

Answer:

P, R

Step-by-step explanation:

If you dilate P, you can find out that P can be the same as R.

The factors of 36x^8 – 49 are  (6x^4-7)(6x^4+7).

We are given to factor the following polynomial completely:

36x^8 – 49.

We have to find the complete factor of the given polynomial.

Completely factor means to continuously factor terms until they are in simple terms, meaning you are no longer able to factor

The formula for (a^2-b^2)= (a+b) (a-b).

Therefore applying the given formula we have,

[tex]F=(6x^4)^2-7^2[/tex]

[tex]F=(6x^4)^2-7^2\\F=((6x^4)-7)(6x^4)+7)[/tex]

Thus, the required factors are

[tex]F=((6x^4)-7)(6x^4)+7)[/tex]

Therefore,option (C) is correct.

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The factors of 36x^8 – 49 are  (6x^4-7)(6x^4+7).

We are given to factor the following polynomial completely:

36x^8 – 49.

We have to find the complete factor of the given polynomial.

Completely factor means to continuously factor terms until they are in simple terms, meaning you are no longer able to factor

What is the formula for (a^2-b^2)?

The formula for (a^2-b^2)= (a+b) (a-b).

Therefore applying the given formula we have,

b

Thus, the required factors are

b

Answer:

Hope that the payment picture will help you.Please mark me brilliant

Answer:

Its B

Step-by-step explanation: on edg 2022

Answer:

(12, 6 )

Step-by-step explanation:

locate 12 cups of flour on the x- axis, then go vertically up to meet the line at (12, 6 )

that is 6 cups of sugar would be used with 12 cups of flour.

Answer:

60% chance a girl is picked

Step-by-step explanation:

There is 10 students in total. 6 out of 10 are girls. We can represent this in a fraction 6/10. Now we convert the fraction into a percentage 60%.

oliver bought 7 bags of candy each bags cost 1.50  

Answer-$10.50

Answer:

10.5

Step-by-step explanation:

you take 1.50 and times it by how many bags there are so 7

1.50×7=10.5

A) = 23.0 miles

B) 14.4 Miles

   [tex]sin60\textdegree\ =\frac{opp}{hyp}=\frac{z}{10}[/tex]

           [tex]z=10\times sin60\textdegree =10\times 0.8660=8.66\ miles[/tex]

                  [tex]use\ pythagores\ theorem\ to\ get\ the\ value\ of\ y.\ l,e[/tex]

                    [tex]y=\sqrt{{20}^2-z^2}=\sqrt{{20}^2-{8.66}^2}=\sqrt{325.0044}[/tex]

                                                                       [tex]=18.03\ miles[/tex]

    [tex]\therefore\ distance\ AD=5+18.03[/tex]

                               [tex]=23.03\\ 23.0\ miles[/tex]

[tex]< ABN=\varphi=30\textdegree\ \{Beary\ 4A\ from\ B=360\textdegree\ -60\textdegree\ =300\textdegree\}[/tex]

                                           [tex]AB=y.[/tex]

             [tex]\cos{\theta=\frac{ads}{h}p}\\ cos\ G\begin{matrix}0\\0\\\end{matrix}=\frac{x}{25}[/tex]

                     [tex]x=25\times cos\ 60\textdegree[/tex]

                        [tex]=12.5\ mle[/tex]

             [tex]cos\ 30\textdegree=\frac{xe}{y}=\frac{12.5}{y}[/tex]

                    [tex]\because\ y=\frac{12.5}{cos\ 30\textdegree}[/tex]

                            [tex]=14.Fmm'_\mathcal{i}(es[/tex]

I hope this helps you

:)

Answer:

14.4

Step-by-step explanation:

20.4-6 = 14.4

So his balls should grow 14.4 inches/feet/centimeters (whatever measuring tool you're asked to use)

Are you sure it's balls though

Answer:

20.4-6=14.4

since he wants his balls to grow you need to subtract how much he wants them tp grow by how tall the already are

Step-by-step explanation:

The factored expression ofx^3 - 7x^2 -5x +35 is (x^2 - 5)(x - 7)

An expression is an algebraic term used for a mathematical statement that includes addition subtraction multiplication and division

x^3 – 7x^2 – 5x + 35

factor the given equation

x^2(x – 7) – 5(x - 7)

Factor out x - 7

(x^2 - 5)(x - 7)

Therefore, the factored expression is (x^2 - 5)(x - 7)

To learn more about the factored expression visit:

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Answer:

c. (x^2 - 5)(x - 7)

Step-by-step explanation:

c. (x^2 - 5)(x - 7)

[tex]C = 7.2b[/tex]

From the question we have that,

27 boxes --------------- $194.40

 b boxes --------------- C

Using the Rule of Three we have that,

[tex]27C = 194.40b[/tex]

Since we want a function that represents C in terms of b ( C = f(b) ) we can isolate C on the equation,

[tex]C = \frac{194.40}{27}b = 7.2b[/tex]

Using the concepts of domain and range, it is found that for the function given in the graph:

The graph in this problem gives the height of a projectile after t seconds, hence:

More can be learned about the domain and range of a function at https://brainly.com/question/10891721

Answer:

Yes, It looks great! I would suggest moving on to a littler harder problems like dividing integers! You can also look up integers practice and they will give you problems to solvle! If you dont know how to do it yet then you can simply skip but, You are doing wonderful!!! Good job and Good luck!

Step-by-step explanation:

Answer:

45 degrees

Step-by-step explanation:

Since this angle is a right angle (1/4 of a full circle, or 360 degrees) its angle is 90. Since one part of it is 45 degrees. A=90-45=45

Area of semi circle = π r²/2

= π 20 × 20 / 2

= 200 π

= 628 cm² (approx)

Answer:

To the nearest whole number : 628

Step-by-step explanation:

The formula for the area of a circle is :

To work out the area you would first need to work out the radius. You can do this by dividing the diameter of 40 cm by 2, this gives you 20 cm. This is because the radius is half of the diameter.

Now that we have worked out the radius, the next step would be to work out the area. You can do this by multiplying pi by the radius of 20 squared, this gives you 1256.64.

The final step is to work out the area of this semi-circle. You can do this by dividing the area of 1256.64 by 2, this gives you 628.32 . This is because a semi-circle is half of a circle.

1) Divide 40 by 2.

2) Multiply pi by 20 squared.

3) Divide 1256.64 by 2.

There are 9 men and 10 women, including Julia, who are trying out for a team. so there are 31,752 possible teams that would include Julia.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

Each of the teams in a mixed volleyball league consists of 5 men and 5 women.

There are 9 men and 10 women, including Julia, who are trying out for a team.

The number of combinations for men

= (9 × 8 × 7 × 6 × 5)/(1 × 2 × 3 × 4 × 5)

=126.  

The number of combinations for women

= (10 × 9 × 8 × 7 × 6)/(1 × 2 × 3 × 4 × 5)

=252.

The number of the possible team would include Julia

(126 × 252) = 31,752.

Learn more about combinations;

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Answer:

Vendor 1 had a higher unit rate.

Step-by-step explanation:

The quotient of the equation is 1.5.

The quotient is the number that is generated when we perform division operations on two numbers. Basically, it is the result of the division method.

The given equation is;

[tex]\rm \dfrac{2m+4}{8}\div \dfrac{m+2}{6}[/tex]

By fraction, a quotient is a number obtained by dividing the dividend by the divisor which is a simple division of numerator and denominator.

The solution of the equation is determined in the following steps given below.

[tex]=\rm \dfrac{2m+4}{8}\div \dfrac{m+2}{6}\\\\=\rm \dfrac{2m+4}{8}\times \dfrac{6}{m+2}\\\\=\rm \dfrac{2(m+2)}{8}\times \dfrac{6}{m+2}\\\\=\dfrac{2\times 6}{8}\\\\=\dfrac{12}{8}\\\\=1.5[/tex]

Hence, the quotient of the equation is 1.5.

Learn more about quotient here;

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Answer:

2/3

Step-by-step explanation:

What is the quotient?

StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction

StartFraction 24 Over (m + 2) squared EndFraction

StartFraction (m + 2) squared Over 24 EndFraction

Two-thirds

Three-halves

Answer:

To find the inverse of:

[tex]f (x)=\dfrac{4}{x-2}-1[/tex]

Set the function to y:

[tex]\implies y=\dfrac{4}{x-2}-1[/tex]

Rearrange to make x the subject:

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

[tex]\implies (y+1)(x-2)=4[/tex]

[tex]\implies xy-2y+x-2=4[/tex]

[tex]\implies xy+x=2y+6[/tex]

[tex]\implies x(y+1)=2y+6[/tex]

[tex]\implies x=\dfrac{2y+6}{y+1}[/tex]

Swap x and y:

[tex]\implies y=\dfrac{2x+6}{x+1}[/tex]

Change y to the inverse of the function sign:

[tex]\implies f[/tex][tex]\:^{-1}(x)=\dfrac{2x+6}{x+1}[/tex]

Rewrite g(x) as a fraction:

[tex]g(x)=\dfrac{3}{x+2}-2[/tex]

[tex]\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}[/tex]

[tex]\implies g(x)=\dfrac{3-2(x+2)}{x+2}[/tex]

[tex]\implies g(x)=\dfrac{3-2x-4}{x+2}[/tex]

[tex]\implies g(x)=-\dfrac{2x+1}{x+2}[/tex]

Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other

D. 6.

We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].

We will use formula [tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(-2)-f(-4)}{-2--4}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6--6}{-2+4}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6+6}{2}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{12}{2}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=6[/tex]

Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.

Answer:

6

Step-by-step explanation:

because i am in credit recovery and i had a test on it

Answer:

i think

Step-by-step explanation:

sorry i dont know the answer im just a children's

Answer:

y= -0.5x² + 1x + 7.5

Step-by-step explanation:

I graphed the points in Desmos and saw they looked liked a parabola the point (1,8) is in between -3 and 5 for the x-coordinate.

I put the values in a table. and had desmos do a regression

Answer:

f(x) = (-1/2)(x^2 + 8x - 15)

Step-by-step explanation:

Hope this helps

Answer:

D

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ BCD is an exterior angle of the triangle , then

∠ BCD = 35° + 67° = 102°

Answer:

Humans

Explanation:

So I can have wings :)

Answer:

If I could put wings on any species of animal, I would choose a Unicorn because then the Unicorn can fly and look at all the enviroment.

Step-by-step explanation: