A store is having a sale where school supplies are 30% off their oiriginal price. A backpack is on sale for $11.20. What was the original price of the backpack

The domain is all of the x-values.  The x-values are also considered the input values.

Side Note: the range is all of the y-values, which represent the output values.

Answer: A

For this one, there are a few steps that will make it easier towards the end.

First lets solve for y

y+3x=8

subtract 3x from both sides

y=-3x+8

Now you are ready to plug in each of the x values and solve for y.

x vaues: -1, 0, 3

Here is what it would look like for each:

y=-3(-1)+8

y=3+8

y=11

y=-3(0)+8

y=8

y=-3(3)+8

y= -9+8

y=-1

So your final answer would be y= {-1, 8, 11}

~be careful putting it into the system, that one is sensitive~

Hope this helps!

First, subtract 90 from his total

159 - 90 = 69

Next, divide the remainder with 10%

Note that 10% = 0.10

69/0.10 = 690

$690 is your answer

hope this helps

<D = 360 - (80 + 115 + 100)

<D = 360 - 295

<D = 65

Answer

<D = 65°

In general, any equation like [tex] ax=b [/tex] (assuming [tex] a \neq 0[/tex]) is solved by

[tex] x= \dfrac{b}{a} [/tex]

So, in your case, the solution is

[tex] x = \dfrac{\frac{1}{5}}{\frac{3}{4}} [/tex]

Dividing by a fraction means to multiply by the inverse of that fraction:

[tex] \dfrac{\frac{1}{5}}{\frac{3}{4}} = \dfrac{1}{5} \cdot \dfrac{4}{3} = \dfrac{4}{15} [/tex]

(- 5, - 6 )

for x- coordinate x + 5 = 0 ⇒ x = - 5

given f(x) ± c , the value of c translates the graph vertically up/down by ± c

here c = - 6 , thus graph is shifted down by - 6

thus the vertex = (- 5, - 6)

it SHOULD be a function, it looks like it at least. All domains are not duplicated so its a function

The slope-point form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

The slope-intercept form of a line:

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

1.

[tex]m=6,\ (4,\ 1)\to x_0=4,\ y_0=1[/tex]

Substitute

[tex]y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}[/tex]

2.

[tex]m=-5,\ (6,\ -3)[/tex]

Substitute

[tex]y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}[/tex]

3.

[tex]m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}[/tex]

4.

[tex]m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}[/tex]

Answer:

Option D

Step-by-step explanation:

From the graph we find that the graph runs only in the I quadrant.

Hence x,y are positive only

Next is y intercept = 2500 and y increases continuously after that.

This implies y >=2500

Hence range is C>2500

Domain is the no of jars of peanut butter.

Hence j>0

In other words, 2500 is the fixed cost even when there is no production and cost cannot be less than 2500 at any time.

Production can be any number of jars from 0 onwards.

Hence option D

The salesman needs to sell $5000 worth of products or services to earn a $1000 commission, calculated by dividing the desired commission by the percentage of commission he retains from sales.

To find out how much a salesman needs to sell to earn $1000 as a commission, we need to consider that he keeps 20% of his sales as commission. Since 20% is the part of the sales that corresponds to the commission, we can set up the following equation: 0.20 x sales = $1000.

To solve for sales, we divide both sides of the equation by 0.20:

sales = $1000 / 0.20

sales = $5000

Therefore, the salesman must sell $5000 worth of products or services to earn a $1000 commission.

Answer:

The equation [tex]35x+93\frac{3}{4} =190[/tex] gives average time spent on 35 rehearsals.

Step-by-step explanation:

We are supposed to find that what question does the equation [tex]35x+93\frac{3}{4} =190[/tex] finds answer of.

We can see that 35x represents time spent on 35 rehearsals and [tex]93\frac{3}{4}[/tex] is time spent on other responsibilities related to play. The sum of these times equals to total time spent on preparing the play.

Now let us solve our equation step by step.

[tex]35x+\frac{375}{4} =190[/tex]

After subtracting [tex]93\frac{3}{4}[/tex] hours from 190 hours we will get time spent on 35 rehearsals.

[tex]35x =190-\frac{375}{4}[/tex]

[tex]35x =\frac{760-375}{4}[/tex]

[tex]35x =\frac{385}{4}[/tex]

Time spent on 35 rehearsals is 96.25 hours and we are told that each rehearsal took different amount of time. Dividing 96.25 by 35 we will get average time spent on each rehearsal.

[tex]x =\frac{96.25}{35}=2.75[/tex]  

Therefore, equation [tex]35x+93\frac{3}{4} =190[/tex] finds average time spent on 35 rehearsals.

Answer:

What was the average length of each rehearsal?

Step-by-step explanation:

Khan Academy

Hello!

When multiply binomials together, we should use the FOIL method.

The FOIL method is an acronym for First, Outer, Inner, and Last.

First, let's set up the expression.

(7x - 1)(3x - 2)

Now, we can multiply in accordance with the FOIL method.

First: 7x · 3x = 21x²

Outer: 7x · -2 = -14x

Inner: -1 · 3x = -3x

Last: -1 · -2 = 2

Now, we simplify the inner terms.

21x² - 14x - 3x + 2

21x² - 17x + 2

Therefore, the area of the rectangle is 21x² - 17x + 2.

The area of the rectangle is (21x² - 17x + 2) units².

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Given the length of the rectangle is (7x-1) units, while its breadth is (3x-2) units. Therefore, the area of the rectangle is,

Area of rectangle = (7x-1) units × (3x-2) units

= 21x² - 14x - 3x + 2

= 21x² - 17x + 2 units²

Hence, the area of the rectangle is (21x² - 17x + 2) units².

Learn more about Rectangle:

https://brainly.com/question/15019502

#SPJ2

The multiples of 8 are: 0, 8, 16, 24, 32, 40, 48, ...

The multiples of 10 are: 0, 10, 20, 30, 40, 50, ...

LCM(8, 10) = 40

LCM(x²y², x²y³) = x²y³

Therefore

The LCM of 8x²y² and 10x²y³ is Option A: 40x²y³.

Identify the LCM of the numerical coefficients.

For 8 and 10, the LCM =40.

Determine the highest power of each variable present in the terms,

For x2 from both terms, the highest power is [tex]x^2[/tex].

For y2 and y3, the highest power is [tex]y^3.[/tex]

Therefore, the LCM of [tex]8x^2y^2[/tex] and [tex]10x^2y^3[/tex]is [tex]40x^2y^3[/tex].

The correct answer is Option A: [tex]40x^2y^3.[/tex]

Answer:

(x - 2) is not a factor of f(x)  = 3x^5 - 7x^3 -  11x^2 + 2

Step-by-step explanation:

According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).

So first we will divide f(x) by (x - 2) using long division to get:

(3x^5 - 7x^3 -  11x^2 + 2) / (x - 2)

= 3x^4 + (6x^4 - 7x^3 - 11x^2 + 2) / (x-2)

= 3x^4 + 6x^3 + (5x^3-11x^2+2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)

= [tex]\frac{-2 + 3x^{5} - 7x^{3} - 11x^{2} + 2x}{x - 2} - 2[/tex]

Therefore the remainder is -2.

Now check x = 2 for 3x^5 - 7x^3 -  11x^2 + 2:

3(2)^5 - 7(2)^3 -  11(2)^2 + 2 = -2

The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.

So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .

Answer:

Answers to the Complex Zeroes of a Polynomial Function Quiz Part 1 (I tried to signify each question)

Step-by-step explanation:

1. C, f(x) is a polynomial function. The degree is 5... -7

2. A, f(x)=7x^9-3x^2-6

3. C,D

4. Written

5. Rational Zero Theorem, B

6. Written

7. B, -5,-2, 3

8. A, (4 + 6i, -2 -11i)

9. D, (2,3, plus minus sqrt 5i)

Answer:

Using the calculator angle whose cos  is 0.9511 is  18 degrees

Sine of the complementary angle = 0.9511 also

Step-by-step explanation:

The sine of the complementary angle( which is 90-18 = 72 degrees) is same value  0.9511

Answer: 18 degrees and 0.9511

Step-by-step explanation:

18°; 0.9511

Cos-1(0.9511) = 18°

The complement of 18° is 72°. The sine of 72° is the cos of 18°, which is 0.9511.

Answer:

y3 - 4 y2 + 2 y - 5

Step-by-step explanation:

The correct expansion of (y + 1)(y² + 2y + 3) is y³ + 3y² + 5y + 3, achieved through the FOIL method and combining like terms.

The correct expansion of (y + 1)(y² + 2y + 3) is obtained by multiplying each term in the first polynomial by each term in the second polynomial and then simplifying the result. This process is known as FOIL (First, Outer, Inner, Last), which is an acronym that stands for multiplying the first terms, the outside terms, the inside terms, and the last terms of each binomial.

To expand (y + 1)(y² + 2y + 3), we perform the following steps:

Now, add up all the products: y³ + 2y² + y² + 2y + 3.

Combine like terms to simplify: y³ + (2y² + y²) + (2y) + 3

The final answer is y³ + 3y² + 5y + 3.

the answer is b f(x)=-4/x-5

Total number of pizzas Juan ordered [tex]20[/tex]

Since, [tex]45\%[/tex] of pizzas have [tex]8[/tex] slices.

Therefore, number of pizzas with [tex]8[/tex] slices are: [tex]45\%\times(20)[/tex]

                                                                                          [tex]=\frac{45}{100} \times(20)[/tex]

                                                                                          [tex]=\frac{45}{10} \times(2)[/tex]

                                                                                          [tex]=\frac{90}{10}[/tex]

                                                                                          [tex]=9[/tex] pizzas

Also, since, [tex]55\%[/tex] of pizzas have [tex]12[/tex] slices.

Therefore, number of pizzas with [tex]12[/tex] slices are: [tex]55\%\times(20)[/tex]

                                                                                          [tex]=\frac{55}{100} \times(20)[/tex]

                                                                                          [tex]=\frac{55}{10} \times(2)[/tex]

                                                                                          [tex]=\frac{110}{10}[/tex]

                                                                                          [tex]=11[/tex] pizzas

Now, there are [tex]9[/tex] pizzas with [tex]8[/tex] slices and [tex]11[/tex] pizzas with [tex]12[/tex] slices.

Therefore, total number of slices of pizza are: [tex]=(9)(8)+(11)(12)[/tex]

                                                                            [tex]=72+132[/tex]

                                                                            [tex]=204[/tex] slices

Answer:

I hope this helped! <3

Step-by-step explanation:

Number of pizzas with 8 slices:  9

Number of pizzas with 12 slices:  11

45% of the pizzas have 8 slices each. In total, there are  72  slices in these pizzas.

55% of the pizzas have 12 slices each. In total, there are  132  slices in these pizzas.

Altogether, there is a total of 204  slices of pizza.

7.5y - z/9 + 50 + 2y

Okay, so it would be best to organize and simplify this expression: 9.5y -z/9 + 50

Alright, now let's eliminate some answers.

True or false: The constant is 7.5. This is false. 7.5 is a coefficient, 50 is a constant.

True or false: The coefficients are 7.5 and -9. This is false. Sure, 7.5 is a coefficient, but -9 is not. Actually, z/9 is also equal to (1/9)z, so technically 1/9 is the coefficient.

True or false: The variables are x and y. This is false. Where is x? Nonexistent.

True or false: The like terms are 7.5y and 2y. This is true. When we simplified the equation, we first combined like terms. 7.5y and 2y are like terms and therefore able to be combined. That's how we got 9.5y.

The answer, I believe, is D. Hope this helps!

The volume of a cylinder is given by the multiplication of the base area and the height.

The base is a circle, so its area is given by

[tex] A = \pi r^2 = 144\pi [/tex]

If we then multiply this by the height, we have

[tex] V = A\cdot h = 144\pi \cdot 16 = 2304\pi[/tex]

Answer:

Yesenia has qty 1 of 10s and qty 7 of 1s

Misty has qty 6 of 10s and qty 8 of 1s

Step-by-step explanation:

Note that there are two different types of blocks: 1s and 10s.  Let x represent the number of 10s and y represent the number of 1s.

                   Value of the blocks                         Number of blocks

Yesenia:           1x + 7y                                                   8

Misty:                                                                                                

Total:                8x + 5y                                                 22

Start with the number of blocks that Misty has: 22 - 8 = 14

Next, how many 1s can be added to Yesenia's to make 5? 15 - 7 = 8

How many blocks are left over from Misty's 14? 14 - 8 = 6

********************************************************************************************

Fill in the information:

                   Value of the blocks                         Number of blocks

Yesenia:           1x + 7y                                                  8

Misty:                6x + 8y                                              14                  

Total:                8x + 5y                                                 22

Answer:

Each of them get 365.

Explanation:

Total income =  1820

Total expense = 360

Total profit = Total income - Total expense = 1820 - 360 = 1460

Number of persons sharing the profit = 4

Profit got by each person = Total profit/ number of persons sharing profit

                           = 1460/4 = 365

So each of them get 365.

The formula that can be used to describe the sequence is:

               [tex]f(x)=-3\cdot (\dfrac{-1}{5})^{x-1}[/tex]

We are given a sequence of numbers as:

[tex]-3\ ,\ \dfrac{3}{5}\ ,\ \dfrac{-3}{25}\ ,\ \dfrac{3}{125}\ ,\ \dfrac{-3}{625}[/tex]

Hence, we could observe that the series is a series with alternating sign such that the power of 5 is increasing in the denominator and there is no change in the numerator i.e. the power of 3 remain unchanged.

Hence,third and last option are discarded.

Also, in first option each of the terms of the digit will be negative and not alternating and hence option (1) is also discarded.

    Hence, the function that represent this sequence is:

        [tex]f(x)=-3\cdot (\dfrac{-1}{5})^{x-1}[/tex]

Answer:

Worth of Tim's house in 2018 = 146410 $

Explanation:

Worth of house in 2014 =  $100000

Raise in worth per year = 10 % = 0.1

Worth of house in 2015 = 100000 + 0.1 * 100000 = 110000 $

Worth of house in 2016 = 110000 + 0.1 * 110000 = 121000 $

Worth of house in 2017 = 121000 + 0.1 * 121000 = 133100 $

Worth of house in 2018 = 133100 + 0.1 * 133100 = 146410 $

So, worth of Tim's house in 2018 = 146410 $

Easy Method;

   No of years considering = 4

   Initial worth = $100000

   Rate of increase = 0.1

   Final worth  [tex]=100000(1+0.1)^4=146410$[/tex]

Worth of Tim's house in 2018 = 146410 $

The value of Tim's house at the start of 2018 will be $ 146,410.

Given that at the start of 2014 Tim's house is worth $ 100000, and the value of the house increase by 10% every year, to determine the value of his house at the start of 2018 the following calculation must be performed:

Therefore, the value of Tim's house at the start of 2018 will be $ 146,410.

Learn more in https://brainly.com/question/25243351

Final answer:

The expression that results from using the distributive property on 2(5 + r) is 10 + 2r.

Explanation:

The expression that results from using the distributive property on 2(5 + r) is 10 + 2r.

The distributive property allows us to multiply a number or variable by each term inside parentheses.

In this case, we multiply 2 by both 5 and r.

Multiplying a number by 10 simply means to add a 0 at the end of the number, or to shift the decimal separator one unit to the right. So, for example,

[tex] 3 \cdot 10 = 30,\ -152 \cdot 10 = -1520,\ 25.467 \cdot 10 = 254.67 [/tex]

So, in your case, you have to add a 0 at the end of 6000, obtaining

[tex] 6000 \cdot 10 = 60000 [/tex]

The toy company must sell more than 40 dolls to make a profit, taking into account the production cost of $20 per doll, a fixed promotion cost of $400, and a selling price of $30 per doll. The inequality that represents this problem is x > 40, where x is the number of dolls sold.

To determine how many dolls a toy company must sell to make a profit, we consider the cost of making each doll, the promotion cost, and the selling price per doll.

The company spends $20 to make each doll and has a fixed promotion cost of $400.

Each doll sells for $30.

The inequality representing the situation is:

30x - (20x + 400) > 0

Where x is the number of dolls sold. To find the breakeven point:

Calculate total cost: Total cost is the sum of the production cost for each doll and the promotion cost. If x is the number of dolls, then the total cost is 20x + 400.

Calculate total revenue: This is the selling price multiplied by the number of dolls, or 30x.

Set total revenue greater than total cost to find the breakeven point: 30x > 20x + 400.

Subtract 20x from both sides: 10x > 400.

Divide both sides by 10: x > 40.

The company must sell more than 40 dolls to make a profit. Thus, the inequality that represents this problem is x > 40.

Final answer:

The toy company must sell more than 40 dolls to make a profit. The cost of producing each doll is $20, and they are sold for $30 each, with a fixed promotional cost of $400. The inequality representing the situation is 30x > 20x + 400, where x is the number of dolls sold.

Explanation:

The question asks about the number of dolls a toy company must sell to make a profit. To calculate this, we must establish the costs and revenues involved in the production and sale of the dolls. The cost per doll is $20 and there is an additional fixed promotional cost of $400. Each doll is sold for $30.

Let's denote the number of dolls sold as x. The total cost for x dolls would be $20x (variable cost) plus $400 (fixed cost). The total revenue from selling x dolls would be $30x. To make a profit, the total revenue must be greater than the total costs.

Using this information, we can write the inequality for profit as follows:

Total Revenue > Total Cost
$30x > $20x + $400

To find the breakeven point where the company begins to make a profit, we must solve for x:

$10x > $400
x > 40

So, the company needs to sell more than 40 dolls to start making a profit.