7. Multiply the binomials: (x - 9)(x + 2)
a. x^2 - 7x - 18
b. x^2 - 11x - 18
c. x^2 - 7x + 18
d. x^2 + 7x - 18

[tex]a)\\\dfrac{2}{3}\div\dfrac{1}{4}=\dfrac{2}{3}\cdot\dfrac{4}{1}=\dfrac{8}{3}=2\dfrac{2}{3}\\\\b)\\\dfrac{7}{5}\cdot8=\dfrac{56}{5}=11\dfrac{1}{5}\\\\c)\\\dfrac{2}{5}-\dfrac{1}{3}\\\text{common denominator is (5)(3) = 15}\\\\\dfrac{2\cdot3}{5\cdot3}-\dfrac{1\cdot5}{3\cdot5}=\dfrac{6}{15}-\dfrac{5}{15}=\dfrac{1}{15}\\\\d)\\\dfrac{3}{10}+2\dfrac{7}{12}\\\text{common denominator is 60}\\\\\dfrac{3\cdot6}{10\cdot6}+2\dfrac{7\cdot5}{12\cdot5}=\dfrac{18}{60}+2\dfrac{35}{60}=2\dfrac{53}{60}[/tex]

I believe this is the answer

7/16

Answer:

7/16

Step-by-step explanation:

Well the biggest number that is divisible by 35 and 80 is 5

Answer:

The cost of a hamburger is 2.25

The cost of fries is 1.75

Step-by-step explanation:

Let h = cost of hamburgers

let f= cost of fries

4h + 3f = 14.25

3h+5f = 15.50

I will solve these by elimination

Multiply the 1st equation by 3

3(4h + 3f )= (14.25)3

12h +9f = 42.75

Multiply the 2nd equation by -4

-4(3h+5f )= -4(15.50)

-12h - 20f = -62

Add the modified equations together

12h +9f = 42.75

-12h - 20f = -62

----------------------------

-11 f = -19.25

Divide each side by -11

-11f/-11 = -19.25/-11

f = 1.75

Now we need to find the cost of the hamburger

3h+5f = 15.50

Substitute the cost of the fries in

3h + 5(1.75) = 15.50

3h +8.75 + 15.50

Subtract 8.75 from each side

3h = 15.5-8.75

3h =6.75

Divide by 3

3h/3 =6.75/3

h = 2.25

The expressions 8x + 40 and 8(x + 5) are equivalent because both expressions have the same value at x = 6 and x = 10

The expressions are given as:

8x + 40 and 8(x + 5)

When x = 6, we have:

8x + 40 = 8 * 6 + 40

8x + 40 = 88

8(x + 5) = 8(6 + 5)

8(x + 5) = 88

When x = 10, we have:

8x + 40 = 8 * 10 + 40

8x + 40 = 120

8(x + 5) = 8(10 + 5)

8(x + 5) = 120

Notice that both expressions have the same value at x = 6 and x = 10

Hence, the expressions 8x + 40 and 8(x + 5) are equivalent

Read more about equivalent expressions at:

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Answer:
Sample Response: If both expressions have the same value after substituting and simplifying for x = 6 and x = 10, then they are equivalent. Substitute 6 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 88. Now, substitute 10 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 120. Therefore, the expressions are equivalent.

Step-by-step explanation: trust ‍

Answer:

x=12 makes (X-12)/(x-8) equal to zero

x=8 makes (X-12)/(x-8)  undefined

Step-by-step explanation:

(x-12)/(x-8) = 0

The  first step is to multiply each side by x-8

 (x-8) *(x-12)/(x-8) = 0 * (x-8)

This cancels the denominator.  x≠ 8 because the denominator would equal 0 and then it becomes undefined.

x-12 = 0

Add 12 to each side

x-12+12 = 0+12

x = 12

I

Answer:

1,722

Step-by-step explanation:

Answer:

1,722 remainder 3 is the correct answer. I didn't do the problem by hand, but for multiple choice answers, you can always just use a calculator to find the answer and the remainder will be given

Answer:

500 total pages. 190 pages with no pictures.

Step-by-step explanation:

310 is 0.62 of the total pages. 310 divided bye 0.62 is 500.

500 minus 310 is 190 pages with no pictures.

Hope this helps!

Answer:

I BELIEVE ITS B

Step-by-step explanation:

Answer: 452.16

Step-by-step explanation:

The x-intercepts of the equation represent the points where the height of the toss is equal to 0. The bocce ball lands on the ground at a horizontal distance of 0 feet and 4 feet.

The x-intercepts of the graph of the equation represent the points where the height of the toss is equal to 0.

In other words, these points represent the horizontal distance where the bocce ball lands on the ground.

o find the x-intercepts, we set y=0 and solve the equation:

0=-x^2+4x

x(x-4)=0

Therefore, the x-intercepts are x=0 and x=4.

This means that the bocce ball lands on the ground at a horizontal distance of 0 feet and 4 feet.

Prime numbers less than 20 in numerical order are 2, 3, 5, 7, 11, 13, 17, and 19. Note that 2 is the only even prime number.

Bryan's statement that all prime numbers are odd numbers is not entirely correct. By definition, prime numbers are numbers that have only two distinct positive divisors: 1 and the number itself. Therefore, the number 2 is considered a prime number, despite being even. Listing all the prime numbers less than 20, we have:

Note that apart from 2, all other prime numbers are indeed odd numbers.

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The inverse of the function x + 2y + 3 = 0 is found by first expressing the function explicitly as y = -½x - 1½ and then swapping x and y to solve for the new y, yielding the inverse function y = -2x - 3.

To find the inverse of a function, we typically swap the roles of x and y, and then solve for y. Given the function x + 2y + 3 = 0, we first write the function explicitly as y in terms of x:

y = -½x - ³2

Now let's find the inverse:

This new function y = -2x - 3 is the inverse of the original function.

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Answer: similar

Step-by-step explanation:

Answer:

Answer is similar

Step-by-step explanation:

Answer:

12.5 per kilometers

Step-by-step explanation:

to find speed is going to be distance divided by time so 62.5/5

so her speed is going to be 12.5

Amanda's average speed while riding her bicycle is found by dividing the total distance of 62.5 kilometers by the total time of 5 hours, resulting in an average speed of 12.5 kilometers per hour.

To calculate her speed, we use the formula for speed, which is speed = distance ÷ time. Applying the given values, we have speed = 62.5 kilometers ÷ 5 hours.

Therefore, Amanda's average speed is 12.5 kilometers per hour. This calculation involves dividing the total distance traveled by the total time taken, resulting in the average speed over the journey.

[tex]a-one\ side\ of\ rectangle\\a+3-other\ side\ of\ rectangle\\2a+2(a+3)=2a+2a+6=4a+6-the\ perimeter\\46\ in-the\ perimeter\\\\\text{The equation:}\\\\4a+6=46\qquad\text{subtract 6 from both sides}\\\\4a=40\qquad\text{divide both sides by 4}\\\\a=10\\\\a+3=10+3=13\\\\\text{Dimensions of the rectangle:}\ 10\ in\ \times\ 13\ in.\\\\\text{The area of the rectangle:}\\\\\boxed{A=10\cdot13=130\ in^2}[/tex]

Answer:

D

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y) → (- y, x)

A translation of 3 units up → + 3 in the y- direction, that is add 3 to the y- coordinate, hence

(x, y) → (- y, x) → (- y, x+ 3) → D

Answer:

48

because 4 * 12 is 48

Answer:

48

Step-by-step explanation:

12 x 0.25 = 48

Answer:

C

Step-by-step explanation:

t² - 8t - 7 - (t² + 5t - 6)

= t² - 8t - 7 - t² - 5t + 6 ( collect like terms )

= - 13t - 1 → C

Answer: C) −13t - 1

Step-by-step explanation: usatestprep approved

Answer:

Bernie, Chrissy, Dina and Frank

Step-by-step explanation:

if all 73 tickers are sold, the theatre makes $438 so each ticket is worth $438/73

this equals to $6.00 for one ticket

this means that Bernie, Chrissy, Dina and Frank have enough money to see the movie

Answer:

Bernie, Chrissy, Dina, and Frank are able to go.

Step-by-step explanation:

The question is not entirely clear. I take it that 73 tickets will bring in 438 dollars. If that is so, each ticket is selling for the solution of this proportion.

x / 1 = 438/73       Just do the division on the right

x = 6.00 dollars.

So Amanda will not be able to go.

Even will not be able to go.

Everyone else can.

Answer:

F  $185

G 12 weeks

Step-by-step explanation:

Assuming your equation is correct

y = -35x +500

We want to let x=9

y = -35(9) +500

y = -315+500

y =185

Jason will have $185  after 9 weeks

If he has 80 dollars left we put that in for y and solve for x

80 = -35x +500

Subtract 500 from each side

80-500 = -35x +500-500

-420 = -35x

Divide each side by -35

-420/-35 = -35x/-35

12 = x

After 12 weeks he will have 80 dollars left

Answer:

5 Hours

Step-by-step explanation:

Given :- 2 hours can be earned each day if she eats all of her vegetables and does all of her chores.

Saved hours at the start of the week = 3 hours

Hours earned in 4 days = 2 hours × 4

                                       = 8 hours

Hours used in 4 days = 6 hours

Hours left after 4 days = Saved hours at the start of the week + Hours earned in 4 days - Hours used in 4 days

Hours left after 4 days = 3 + 8 - 6

                                       = 5 hours

Answer:

Use the slope formula.

Step-by-step explanation:

Input your x and y values to this:

(x - x1)/(y-y1) = m

About Slope: Rise

                      Run

Hi!!! If you still need more help, ASK!!! :) Hope this info helps you!!! :)

The total amount you would pay at the physical store after all discounts, taxes, and fees have been applied is [tex]{128.36} \)[/tex].

Let's go through the calculations again to find the final cost at the physical store after all discounts, taxes, and fees.

Physical Store Pricing:

- Batteries: 2 packs at $5.99/pack

- Stereo: 1 system at $100.00

- CDs: 3 CDs at $7.95 each

Discounts and Taxes in the Physical Store:

1. 10% Off Coupon: This coupon applies to the total purchase amount before tax.

2. Sales Tax: 5% sales tax applies to the total purchase amount after applying discounts.

Calculation Steps:

Step 1: Calculate the total cost of items before discounts and tax:

- Batteries: 2 packs × $5.99/pack = $11.98

- Stereo: $100.00

- CDs: 3 CDs × $7.95/CD = $23.85

Total before discounts: $11.98 + $100.00 + $23.85 = $135.83

Step 2: Apply the 10% off coupon:

- 10% of $135.83 = $13.583

- Total after 10% off: $135.83 - $13.583 = $122.247

Rounded to two decimal places: $122.25

Step 3: Apply the 5% sales tax:

- 5% sales tax on $122.25:

[tex]\[0.05 \times 122.25 = 6.1125\][/tex]

Rounded to two decimal places: $6.11

Step 4: Calculate the final cost at the physical store:

- Total cost after tax: $122.25 + $6.11 = $128.36

The complete question is

You are buying batteries, a stereo, and some CDs from the I.B. Electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. You are trying to decide whether to shop at the physical store or the online store. Using the pricing information below, how much would you pay at the physical store after all discounts, taxes, and shipping fees have been applied?

Item          Quantity        Physical Store           Online Store

Batteries    2 packs            $5.99/pack                $4.99/pack

Stereo        1 system           $100.00/system        $90.00/system

CDs            3 CDs               $7.95/CD                    $8.95/CD

Answer: The car would need 0.3 gallons of fuel to travel 20km.

Step-by-step explanation: 40mile x 1.6km = 64km

                                           1 gallon     1 mile    1 gallon

20km ÷ 64km = 0.3125

Answer:

In 0.3 gallon of fuel, the car will travel 20 km.

A is the correct option.

Step-by-step explanation:

We have been given that in 1 gallon of fuel the car can travel 40 miles.

Now, 1 mile = 1.6 km.

Hence, in 1 gallon the car travel 40×1.6 = 64 km

Let the car will consume x gallons of fuel to travel 20 km.

Thus, we have the equation

[tex]\frac{1}{64}=\frac{x}{20}[/tex]

ON solving for x

[tex]x=\frac{20}{64}\\\\x=0.3[/tex]

Therefore, in 0.3 gallon of fuel, the car will travel 20 km.

A is the correct option.

Answer:

$16.32

Step-by-step explanation:

$1.32 Per Stick Times 32 = $44.80

$.59 Per Crayon Box Times 32 = $18.88

$44.80 + $18.88 = $63.68

$80 - $63.68 =     [$16.32]

[tex]0.8\times10^2\ \text{is 10,000 times greater than}\ 0.8\div10^2\\\\\dfrac{0.8\times10^2}{0.8\div10^2}=\dfrac{10^2}{1\div10^2}=\dfrac{10^2}{\frac{1}{10^2}}=10^2\times10^2=10^4=10,000[/tex]

Dividing 0.8 by 10² moves the decimal two places to the left, resulting in 0.008. Multiplying 0.8 by 10² moves the decimal two places to the right, resulting in 80. Thus, the two operations produce different magnitudes of the original number.

Understanding the Relationship Between 0.8 ÷ 10² and 0.8 × 10²:

In mathematics, it's essential to understand how operations involving powers of ten affect numbers. Let’s break down the operations:

0.8 ÷ 10²: When you divide a number by 10 raised to the power of 2 (which is 100), you move the decimal point two places to the left. So, 0.8 ÷ 100 = 0.008.

0.8 × 10²: When you multiply a number by 10 raised to the power of 2, you move the decimal point two places to the right. So, 0.8 × 100 = 80.

We can conclude that 0.8 ÷ 10² results in moving the decimal to the left, making the number smaller (0.008), while 0.8 × 10² results in moving the decimal to the right, making the number larger (80).

Answer:

There is ONE outlier in this problem. The outlier is 22.

Step-by-step explanation:

The outlier is 22 because for a number to be an outlier, it has to be much smaller or much larger than the other values in a set of data. 22 is very far away from the given numbers.

[tex]\text{Use:}\\\\a^n\cdot a^m=a^{n+m}\\\\(-6a^5b^4c^3)(5a^3b^2c)\\\\=(-6\cdot5)(a^5a^3)(b^4b^2)(c^3c^1)\\\\=-30a^{5+3}b^{4+2}c^{3+1}\\\\=\boxed{-30a^8b^6c^4}[/tex]

Event A Answer: [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

sum greater than 7 leaves are the following combinations for 8, 9, 10, 11, and 12:

8 = 26, 35, 44, 51, 62  (5 possibilities)

9 = 36, 45, 54, 63  (4 possibilities)

10 = 46, 55, 64  (3 possibilities)

11 = 56, 65  (2 possibilities)

12 = 66  (1 possibility)

This is a total of 15 possibilities out of 36 total: [tex]\frac{15}{36}[/tex] = [tex]\frac{5}{12}[/tex]

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

Event B Answer: [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

sum is an even number means both dice are odd or both dice are even.  That results in the following combinations:

11   13  15

22  24  26

31  33  35

42  44  46

51  53  55

62  64  66

This is a total of 18 possibilities out of 36 total: [tex]\frac{18}{36}[/tex] = [tex]\frac{1}{2}[/tex]

The answer is the top left corner choice

The first line of each box is the same, so we can move onto the second line. In the top left corner, the negative 1 is being distributed to every term in (5 - 3x) to have the signs flip and give us -5 + 3x. The other stuff stays the same.

Answer:

The top left corner

Step-by-step explanation:When you have to simplify an expression, distributing is a common way to begin, since it’s easier and it helps to get rid of that 1, which makes the process of simplifying easier