Equations and Inequalities: Tutorial
Each year, the junior class at East High School sells discount cards as a fundraiser. Each $20 discount card is valid for a year
and provides discounts at many area businesses.
This year's juniors are analyzing the revenue, or earnings, from past years and this year. If n represents the number of cards
that students sold last year, match each algebraic expression to what it represents.
Drag the tiles to the correct boxes. Not all tiles will be used.
Tiles
20n
n + 200
20n + 200
20(n + 200)
200n
Pairs
revenue from last year
number of cards sold this year if students sell 200 more cards than last year
revenue this year if students sell 200 more cards than last year

Answer:

min: (-2;-6) & (1; 3/4); max: (0;2).

Step-by-step explanation:

1) f`(x)=3x³+3x²-6x;

2) f`(x)=0, ⇒ 3x³+3x²-6x=0;

3) 3x³+3x²-6x=0; ⇒ x(x²+x-2)=0; ⇒ x(x-1)(x+2)=0; ⇒ x₁=0; x₂=1; x₃=-2;

other steps are provided in the attachment.

Answer:

2.70$

Step-by-step explanation:

Answer:

The answer is 11,316,108

Step-by-step explanation:

[tex]58^{4} - 388[/tex]

(58)(58)(58)(58) - 388

11,316,496 - 388

= 11,316,108

Answer:

24 miles

Step-by-step explanation:

50 minutes = 8 miles

100 miles = 16 miles

150 minutes = 24 miles

Answer:

Jason can travel 24 miles in 150 minutes.

Step-by-step explanation:

8= miles. 50&150= mins

8=50.

Your trying to find how many miles Jason can travel in 150 mins. So your going to divide the new amount of minutes to the old amount.

150÷50= 3.

So since 50 can go into 150 3 full times that means you will multiply the original amount of miles by 3 to get your new amount.

3×8= 24

So, if Jason can travel 8 miles in 50 mins (8=50) Then, he can travel 24 miles in 150 mins (24=150)

Hope this wasn't too confusing,

Hope this helps!

Answer:

1. Loss ₹50

2. - 60

3. 50 km towards North

4. 1000

5. - 30

6. - 15° C

The polynomial division problem can be concluded finished if; their is no remainder or the Divisor is larger than the remainder.

According to the question:

In polynomials, the division of a polynomial NY the Divisor gIves a quotient and a remainder.

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Answer:

rate of change from 8 to 32

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x + y = 6

y = -2x + 6

Comparing this with y = 1/2x - 7

Multiplying the 2 slopes:

-2 * 1/2

= -2/2

= -1

- this means that the 2 lines are perpendicular.

Answer:

A. 8

Step-by-step explanation:

We are given the functions:

[tex]f(x)=\sqrt{x}\\\\g(x)=7x+b[/tex]

    We are told that on a standard (x, y) coordinate plane that y = f(g(x)) passes through the point (4, 6). In order to solve for b, we need to figure out what f(g(x)) is equal to.

    As with a regular function like the two above, f(g(x)) means you are substituting x with g(x) in function f. The problem gave us the two functions, so I will demonstrate what I mean.

[tex]f(g(x))=\sqrt{(7x+b)}[/tex]

    The problem again tells us that y = f(g(x)) goes through (4, 6). Substitute those values for their respective variables and solve for b.

[tex]y=f(g(x))\\\\y=\sqrt{(7x+b)}\\\\6=\sqrt{(7(4)+b)}\\\\6=\sqrt{(28+b)}\\\\(6)^2=(\sqrt{(28+b)})^2\\\\36=28+b\\\\36-28=28+b-28\\\\8=b[/tex]

Therefore, the value of b is equal to 8.

Answer:

Father is 80 years old and the son is 30

Step-by-step explanation:

Let father be x and son be y:

x-5 = 3(y-5)

x = 3y-10 ------ eq1

x+y = 110

x = 110 -y -------- eq2

Now if we combine the 2 equations we get:

3y + y = 110+10

y=30 (sons age)

Substituting in equation 2 we get:

x = 110 - 30

x = 80

Therefore, the fathers age is 80 and the sons age is 30.

yes it does belong on pizza

Answer:

$7

Step-by-step explanation: Five step plan

1. How much is each hamburger?

Variables

Price paid : $50

Change: $22

No. of hamburgers: 4

2. Price for all hamburgers. 50-22 = 28

3. y(price of each hamburger) = 28/4

4. y = 7

5. The price of each hamburger is 7

Answer:

137 i am sorry if incorrect

Step-by-step explanation:

Answer:

1500-8000

Step-by-step explanation:

It depends what type of truck and what its carrying

Based on the information given, the length will be 68 yards while the value of the width will be 52 yards.

The calculation will go thus:

Perimeter = 2l + 2w

240 = 2(w + 16) + 2w

240 = 2w + 32 + 2w

240 = 4w + 32

4w = 240 - 32

4w = 208

w = 208/4 = 52

Therefore, the length will be:

= w + 16 = 52 + 16 = 68

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Answer:

183

Step-by-step explanation:

percentage=actual/base

B=A/P

B=43.9/0.24

B= 182.9=183

The value of x rounded to the nearest whole number is 183.

In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. To find the % of a number, divide it by its value, then multiply the result by 100. Percentage is a relative value that denotes one tenth of any quantity. As one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

As per the given data:

Number = 43.9

The given number is 24% of x.

Percentage = (value / total) × 100

By substituting the given data:

24 = (43.9 / x) × 100

x = (4390/24)

x = 182.91

after rounding off to the nearest whole number

x = 183

Hence, the value of x rounded to the nearest whole number is 183.

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Step-by-step explanation:

it is a linear function, if the increases in y are constant from point (ordered pair of x and y) to point reissue to the increase in x.

the first table (top left) increases x constantly by 1.

but y increases first by 2 and then by 3 and then again by 3.

this is not constant, so it does not follow the pattern of x.

in technical terms : the slope of the function is not the same for every point of the function.

in other words : it is not a straight line all the way.

so, it is not a linear function.

the second table (top right) increases x constantly by 2.

and y increases constantly by 2.

this is constant also in relation to x.

in technical terms : the slope of the function is the same for every point of the function.

in other words : it is a straight line all the way.

so, it is a linear function.

the third table (bottom left) increases x constantly by 1.

but y increases first by 4 and then by 1 and then again by 1.

this is not constant, so it does not follow the pattern of x.

in technical terms : the slope of the function is not the same for every point of the function.

in other words : it is not a straight line all the way.

so, it is not a linear function.

the fourth table (bottom right) increases x constantly by 2.

but y increases first by 2 and then by 3 and then again by 3.

this is not constant, so it does not follow the pattern of x.

in technical terms : the slope of the function is not the same for every point of the function.

in other words : it is not a straight line all the way.

so, it is not a linear function.

Answer: $15.90/hr

Step-by-step explanation:

We need to add 6% to her $15/hr current pay.  This can be calculated with:

$15/hr *(1+0.06) = $15.90/hr

The "(1+0.06)" represents a) 1  the current salary, and b) the 6% raise.

Answer:

D, y+8=2(x_4)

Step-by-step explanation:

Answer:

43/8 or 5 and 3/8

Step-by-step explanation:

This is because if you find the lcd, its 24. 36/6, or 6, in 24 is 144/24.

5/8 is 15/24.

144/24-15/24 is 129/144, which simplified is 43/8, or 5 and 3/8

Answer:

3

Step-by-step explanation:

so we know that this question is asking for the y value when x is equal to -1, so according to the graph its 3

[tex]5(m -3 ) = 40 \\ = > 5m - 15 = 40 \\ = > 5m = 40 + 15 \\ = > 5m = 55 \\ = > m = 11[/tex]

Therefore, m = 11

5m = 5 × 11 = 55

5m is 55, m is 11.

Hope it helps.

Do comment if you have any query.

Answer:

m=11

5m=55

Step-by-step explanation:

To find the answer to this question, isolate m. Do this by using the properties of equality.

First, distribute the 5 to the terms within the parentheses

Then, add 15 to both sides

Next, divide both sides by 5

This gives you the solution to both questions. If you want to check the answer, simply plug the variable back in. This gives you, 5(11-3)=40. Once solved this equals 40=40. Therefore, 11 is correct.

Answer:

Well, the answer is: it depends on what was printed in the problem. The principal square root symbol never has a negative output, so if the test maker printed that symbol, it’s restrictions have to be respected: all square roots then are positive.

Step-by-step explanation:

a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16. Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √(x), where the symbol √( ) is called the radical sign or radix.

Answer/Step-by-step explanation:

The square root could be positive or negative because multiplying two negative numbers gives a positive number. The principal square root is the nonnegative number that when multiplied by itself equals a. The square root obtained using a calculator is the principal square root.

~fractions

[tex] \large \tt( \frac{ 5 }{ 7 } ) ^ { 3 } ( \frac{ 4 }{ 5 } ) ^ { 3 }[/tex]

[tex] \large \tt = \frac{125}{343}\times \left(\frac{64}{125}\right) [/tex]

[tex] \large \tt = \frac{125\times 64}{343\times 125} [/tex]

[tex] \large \tt = \boxed{\frac{64}{343} } \: ✓[/tex]

~ nice to help you ^^

Answer:

m<H= 80*

m<P= 80*

m<I= 33*

M<Q= 33*

M<J=67*

M<R=67*

Step-by-step explanation:

Given States that ️ HIJ = ️ PQR

<H=<P

2x=x+40

2x-x=x-x+40

x=40

<I=<Q

<J=<R

ALL TRIANGLES MEASURE 180*

Y= the measure of <R and <J

2x+33+y=180

2(40)+33+y=180

80+33+y=180

113+y=180

113-113+y=180-113

y=67

Answer:

See answer below

Step-by-step explanation:

If ΔHIJ ≅ ΔPQR ,then you know six  congruent parts:

 ∠H ≅ ∠P ; ∠I ≅ ∠Q;  ∠J ≅ ∠R    and HI ≅ PQ; HJ ≅ PQ ; IJ ≅ QR

   ∠H ≅ ∠P         ∠I ≅ ∠Q

2x = x + 40°          ∠I = 35°

x = 40°

So ∠H = 2x = 2(40) = 80°                        Δ HIJ = 180°

    ∠P = x + 40 = 40 + 40 = 80°               ∠H + ∠I  + ∠J = 180°

    ∠Q = 35°                                                  80° + 35° + ∠J = 180°

    ∠ I = 35°                                                   115° + ∠J = 180°

    ∠ J = 65°                                                          ∠J = 65°

    ∠R = 65°                                                      ∠J ≅ ∠R

Answer:

3.5 hours

Step-by-step explanation:

8.75/2.5=3.5

Answer:

3.5 miles

Step-by-step explanation: