Factor each of the following. Remember: It is the reverse of the distributive property and your first step is to find the greatest common factor of all terms.

Answers

Answer 1

To factor using the reverse of the distributive property, find what common factor the numbers have and what common factor the variables have.

10.

-8x - 16

8 is a factor of both -8 and 16.
The first term has x, but the second term does not, so there is no common variable. The only common factor is 8, or -8.

Factor out a -8:

-8x - 16 = -8(x + 2)

To see if the factorization is correct, multiply the answer using the distributive property. If you get the original expression, then the factorization is correct.

11.

w^2 - 4w

The first term only has a factor of 1. The second term has a 4. There is no common factor between 1 and 4 except for 1, so there is no number you can factor out. The first term has w^2. The second term has w. Both terms have a common factor of w. We can factor out w from both terms.

w^2 - 4w = w(w - 4)

12.

4s + 10rs

4 and 10 have a common factor of 2.
s and rs have a common factor of s.
2 times s is 2s, so the common factor is 2s.
We now factor out 2s

4s + 10rs = 2s(2 + 5r)

Related Questions

Which equation demonstrates the distributive property? A) 20 + 36 = 56 B) 20 x 36 = 36 x 20 C) 20 + 36 = 4(5 + 9) Eliminate D) (5 + 9)4 = 4(5 + 9)

Answers

distributive property
answer
C) 20 + 36 = 4(5 + 9)

the answer is Cc20+36=4(5+9)

the sum of two consecutive even integers is -298. What are the integers?

Answers

Answer: -148, -150

n + n + 2 = -298

2n = -300

n = -150

5. At a local store you find the following prices listed: Tape 2 rolls for $1.28 Notepads 3 pads for .87 Highlighters 1 for 1.59 Pens 2 for 1.98 How much would you pay for one roll of tape, two note pads, two highlighters, and two pens? A. $5.72 B. $6.38 C. $4.50 D. $8.07

Answers

To find the cost of one roll of tape, we divide the given price by 2 because the given price is for twice the number of rolls that we want.
$1.28/2 = $0.64
----------------
To find the cost of two note pads, we first divide the given price by 3 because we want to know how much one note pad costs.
$0.87/3 = $0.29
Each note pad is 29 cents. Since we want to note pads, we double this amount.
$0.29*2 = $0.58
----------------

One highlighter costs $1.59. We want two of them, so we double this amount.
$1.59*2 = $3.18
----------------
We want two boxes of ink catridges, and we are told that two boxes cost $1.98.
----------------
Let's total the amounts:
$0.64 + $0.58 + $3.18 + $1.98 = $6.38
We would pay $6.38 for these seven items.

the answer to the question above is $6.38

My number has 2 hundreds. The tens digit is 9 more than the ones digit

Answers

The number is 290. What is in the ones place

2/5 ab

What are the factors of the expression?

Drag all of the factors of the expression into the box.

please help me :D

the points are 50

Answers

2/5, a, and b is the answer

the answer is 2/5, a, b

Pizza World has a specialty cheese pizza that can be cut into 10 slices, and they have a specialty pepperoni pizza that can be cut into 16 slices. If Pizza World serves combos of one slice of cheese and one slice of pepperoni pizza with no slices left over, what is the smallest number of combos that Pizza World can prepare?

Answers

16/10=1.6 so the smallest number of combos would be 1.

The smallest number of combos that Pizza World can prepare with one slice of cheese and one slice of pepperoni pizza with no slices left over is 80.

The student is asking how many combos of one slice of cheese and one slice of pepperoni pizza Pizza World can prepare with no slices left over given that a cheese pizza has 10 slices and a pepperoni pizza 16 slices. This question is looking for the least common multiple (LCM) of two numbers, which is the smallest number that is a multiple of both numbers. To find the LCM of 10 and 16, we list the multiples of each number until we find a common multiple. The multiples of 10 are 10, 20, 30, 40, 50, 60, ... and the multiples of 16 are 16, 32, 48, 64, 80, .... The smallest common multiple of 10 and 16 is 80. Therefore, we can prepare 80 combos using 8 cheese pizzas (because 8 x 10 = 80) and 5 pepperoni pizzas (because 5 x 16 = 80).

Read the proposition and the implication shown below. "If the lights are off, there is no one inside." Which statement is a contrapositive to the proposition and logically equivalent to it?

Answers

The contrapositive switches the hypothesis and the conclusion and negates both in this form:
Statement: If A, then B
Contrapositive: If not B, then not A.

In this case, the statement is:
"If the lights are off, there is no one inside."
Contrapositive:
If there is someone inside, the lights are on.

Final answer:

The contrapositive of the proposition 'If the lights are off, then there is no one inside' is 'If there is someone inside, then the lights are not off'. Contrapositives are formed by negating and interchanging the hypothesis and conclusion of a conditional statement, and is a key concept in mathematics.

Explanation:

In logic, the contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. So, the contrapositive of the given proposition 'If the lights are off, then there is no one inside' would be 'If there is someone inside, then the lights are not off'.

This implies that, in the context of this statement, if we know that there is someone inside, we can deduce that the lights must not be off as per the contrapositive. Thus, contrapositives are a helpful way to understand conditional statements from another perspective, and are an integral concept in logic and mathematics.

Learn more about Contrapositive here:

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Factor out the coefficient of the variable.
The expression 38d+34 factored is

Answers

Final answer:

The highest common factor of 38 and 34 is 2. Dividing both coefficients by 2 gives us 19d and 17. Therefore, the factored expression of 38d + 34 is 2(19d + 17).

Explanation:

Factoring out the coefficient of a variable in the expression 38d + 34 involves finding a number that divides both coefficients exactly. The highest common factor (HCF) of 38 and 34 is 2. So, we divide 38 and 34 by 2 to get 19d and 17 respectively.

Therefore, the expression, when factored out, becomes 2(19d + 17). This means that the expression 38d + 34 can thus be factored into 2 times the expression (19d + 17).

Learn more about Factoring coefficients here:

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A ticket agency charges 9.5% fee on all tickets sold .if a ticket cost 40$ what is the fee

Answers

$3.80

you have to multiply the 9.5% fee by $40 and you will get how much the fee will be

Find 9.5% of $40 and then add the result to 40
0.095x40=3.8
40+3.8=43.8
So it costs $43.80

The length of a rectangle is 8 more than the width. The area is 825 square inches. Find the length and width of the rectangle

Answers

Let width be x then

Length is x+8

Therefore area which is given by L*W will be

Area=x*(x=8)

But area =825 sq inches

x*(x+8)=825

x^2+8x-825=0

we use quadratic formula to solve this

and get our x=25 therefore

our width is 25

and length is 33

can someone tell me the scientific notation for this?

Answers

Count out the number of zeros. While there a lot of zeros, luckily they are grouped with the commas to make it simpler on the eyes.

There are 4 groups of three zeros per group giving 4*3 = 12 zeros plus the 0 just after the 6. So in total 12+1 = 13 zeros

If we placed the decimal point just after the 6 we'd have 6.0

To get 6.0 back to the original number 60,000,000,000,000 we need to move the decimal point 13 times to the right. We move it 1 time per zero.

So 13 is the exponent. The value 6.0 or simply 6 is the coefficient.

Overall, this means
[tex]60,000,000,000,000 = 6 \times 10^{13}[/tex]

the final answer is therefore
[tex]6 \times 10^{13}[/tex]
(six times ten to the thirteenth power)

Side Note: The number 60,000,000,000,000 written in English is "sixty trillion"

Fanga ran 28 miles per in 4 hours She ran at a rate of how many miles per hour

Answers

7 mph. 28 divided by 4 is 7. Or 7 miles in one hour

The answer for this problem is 7

what is the value of w in the equation w-5.5=-3.4

Answers

Add -5.5 to both sides to make the equation:

w=2.1

Hope this helps!

w-5.5 = -3.4

add 5.5 to each side

w = -3.4 + 5.5 = 5.5-3.4 = 2.1

w = 2.1

Which best describe the meaning of this function notation ? Cost(weight

A. The weight is greater than the cost.
B. The weight depends on the cost
C.The cost depends on the weight
D.The cost is multiplied by the weight

Answers

I think in a logical sense it would be C because usually depending on how big or small the item is then the cost will vary to that amount of grams or tons is in that item you're purchasing. So I would go with C but I'm not completely sure.

Hope this helps :)

Solve 5(y - 4) = 7(2y + 1)

Answers

5y-20=14y+7

5y-20+20=14y+7+20

5y-14y=14y + 27 -14y

9y=27
Divide both by -9
Y=-3

5(y-4)=7(2y+1) use the distributive property: 5y-20=14y+7 then isolate one variable: 5y-20(-7)=14y+7(-7) which is: 5y-13=14y next subtract 5y from 14y which gives you: -13=9y the last step is to divide each side by 9, isolating y. your answer will be y=-1.4

A and b thank you on 92

Answers

a. Each student will get 8/10 of the pizza or .8 of the pizza.
Not sure how you would go about b though.

Can someone help me pls ?

Answers

8: 25/5=5 5x10=50 100-50=50
10: 3x5=15 2x5=10 15-10=5
12: 56/7=8 42/7=6 8x6=48

Remember: PEMDAS

Parentheses (please)
Exponets (excuse)
Multiply (my)
Divide (dear)
Add (aunt)
Subtract (sally)

From left to right as if reading a book

PLZZZ HELP. LOOK IN THE PICTURE BELOW TO ANSWER MY QUESTION.

Answers

Greetings!

To add or subtract fractions, we need find a common denominator:

Simplify.
[tex]3/8-(-3/2)[/tex]
[tex]3/8+3/2[/tex]
Find the LCM.
[tex]3/8+12/8[/tex]
The Answer Is:
[tex]15/8[/tex]

Hope this helps.
-Benjamin

3/8 - -3/2= 3/8+ 3/2. The LCD of the two fractions is 8, so converting 3/2 to eighths gives you: 3/8+12/8=15/8 ANSWER: 15/8 good luck and have a nice benevolentpuppy day!

163water bottles in 9 cases=

Answers

you would do 163 ÷ 9 and you will get your answer

Find the y-intercept of the line:

2x + 4y = 8

Question 5 options:

a) (2,4)
b) (0,2)
c) (4,0)
d) (4,2)

Answers

(0,8)

Glad I could help!!!

an item is purchased for a wholesale price of $48 and will be sold at a 55 percent markup. which expression should be used to find the amount of the markup

Answers

48 times 1.55 equals 74.4.

Answer:

$48(0.55)

Step-by-step explanation:

what is 1.18 repeating as a fraction

Answers

1.181818181818181818 repeating is 117/99

Solve the system of equations: 12x + 6y = 60 and 3y = -6x + 30

a) (10,0)
b) (0,10)
c) Infinite Solutions
d) No solutions

Answers

Hello there!

12x + 6y = 60
3y = -6x + 30

Ok so we need to solve 12x + 6y = 60 for x

Let's start by adding -6y to both sides

12x + 6y - 6y = 60 - 6y

12x = -6y + 60

Since we are looking for x, we need to divide both sides by 12

12x/12 = (-6y + 60)/12

x = -1/2 y + 5

We are not done yet, now we need to substitute -1/2 y + 5 for x in 3y = -6x + 30

3y= -6x + 30

3y = -6(-1/2 y + 5)+ 30

3y = 3y

Finally subtracting 3y from both sides

3y - 3y = 3y - 3y

0 = 0

Thus, Infinite Solutions

Rebecca ran 12 1/4 miles in 2 1/2 hours. What was your average speed in miles per hour

Answers

Divide your miles by hour hours:
12.25/2.5 = 4.9
Her average speed was 4.9 miles per hour

(1-x)y"-4xy'+5y=cosx

Answers

y"(1-x) - 4ry' + 5y - cos(x)= 0

determine if this triangle is acute, obtuse, right, or impossible

Answers

make a graph and plot the numbers

Acute would be the answer!

Amber has a 4/5 pound bag of colored sand, she uses 1/2 of the bag for an art protect. How much sand does she uses for the protect?

Answers

Okay. So, Amber used 1/2 of the 4/5 bag for the art project. Let’s do 4/5 / 2. 4/5 * 1/2 is 4/10 or 2/5 in simplest form. Amber uses 2/5 of a pound of sand for her art project.

How do u solve- if 3 onions way 0.75 pounds how much do 10 Onions weigh.

Answers

divide .75 by 3

.75/3

that will give u the weight of one onion
which is:

.25

now multiply .25 by 10 and this will give you the weight of 10 onions

.25(10)

2.5lbs

a gym membership costs $30 to join and $ 12 each month. write and use an algebraic expression to find the cost of the gym membership fo 6 months

Answers

Gym membership = G

G = 12x+30
G = 12(6)+30
G = 72+30
G = 102

30+12m

30+12(6)

30+ 72

102

The cost of the gym membership for 6 months is $102.

Hope this helps!

the music for Alyssa's dance routine last exactly 4 min. when she dances her routine, she starts with her music and finishes 12 seconds before the music ends. what percent of the time the music is playing is Alyssa dancing.

Answers

If her music lasts 4 minutes, her music is 60*4=240 seconds since there are 60 seconds in a minute. Next, since her dance is 12 seconds less than the music, her dance is 240-12=228 seconds long. To finish this up, we have 228/240. I challenge you to figure out the percentage on your own!

As an example, we have 123/463, which is around 0.266. Multiplying that by 100, we end up with around 26.6 percent as the percent 123 is of 463

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