Use the distributive property to rewrite each expression in its equivalent form.

1. 4(x + 3)

2. -7(4 - y)

3. 6(3x + 5y -4)

4. 9a-3/3

Rewrite each linear expression by factoring out the greatest common factor.

5. 64x + 24

6. -5y -35
HELPP I NEED TO SUMBIT SOON

Answers

Answer 1
The distributive property states: a(b+c)=a•b+a•c. In other words, the terms inside the parentheses are multiplied by the factor outside the parentheses; remember that a(b)=a•b

1.) 4x+12

2.) -28+7y

3.) 18x+30y-24

4.) For number 4, is the question 9(a-3/3) or a different expression? If it’s the first one, then it equals 9a-9.

5.) To factor out the GCF, we need to find the greatest factor that divides into both 64 and 24. We will find that 8 is the largest factor of 24 and 64. Therefore, all terms are divided by 8, and 8 remains out in front. We are essentially “undoing” distribution. We need to factor out a number that will make the multiples of 64 and 24.

(64+24)/8

5.) Answer: 8(8x+3)

Notice that if we distribute, we end up with 64x+24, so we simply revers distribution. Since distribution is multiplication, and division reverse multiplication into a simplified form, we divided each term by the GCF of 8.

6.) Factor out a GCF that divides into -5y and -35. The GCF is 5, since 5 divides evenly into both terms.

(-5y-35)/5

5(-y-7) is the answer.

Also notice that even though both terms were divided by 5, we kept the 5 out in front to distribute. This is because the goal of factoring is to break the expression down into a simplified, equivalent form.

Related Questions

GUYS HELP 4-10! ASAP IF YOU CAN EXPLAIN STEP MY STEP SO I CAN UNDERSTAND NEED MY GRADES UP! PLEASE HELP Please help. I need to get my grades up so the help would really mean a lot!

Answers

Step-by-step explanation:

so, the best way to help you is to help you understand how to solve such problems yourself.

let me know if you still don't understand something :

4.

this you can solve just by common sense.

let's see if you understand it with smaller numbers :

1 ball costs $3. how much will 2 balls cost ? well, twice as much : 2×3 = $6.

how much will 3 balls cost ? hmmm ? three times as much : 3×3 = $9.

and so on.

so, how much will 10 balls cost ? right, ten times a much : 10×3 = $30.

now,

8 eggs for 3 cups of flour.

how many eggs for 30 cups of flour ? you notice that 30 is 10 times 3, right ?

yes, ten times a many eggs : 10×8 = 80 eggs.

5.

3 quarters simply means 3/4.

if we want to know how much 3/4 of something is, we have to multiply that something by 3/4.

so, for 60 students :

60 × 3/4 = 180/4 = 45 students bring a lunch from home.

6.

similar to 4.

5 books in 2 days.

how many books in 8 days ?

you notice that 8 is 4 times 2 ?

so, yes, 4 times as many books : 4×5 = 20 books.

7.

now we are getting into areas, where we need more thinking and apply formal mathematics.

10 pounds jam requires 5 pounds apples.

8 pounds jam require x pounds apples.

the easiest way is to use ratios :

jam to apples = 10/5 = 2/1 = 2

8 pounds jam to x pounds apples must follow the same ratio, as we are using the same recipe.

8/x = 2

8 = 2x

x = 4

so, to get 8 pounds of jam we need 4 pounds of apples.

8.

it seems they were very, very hungry ...

Jenny ate 6 1/4 pizzas.

Dolly ate 5 1/4 pizzas.

6 1/4 = (6×4 + 1)/4 = 25/4

5 1/4 = (5×4 + 1)/4 = 21/4

so, Jenny ate 25/4 / 21/4 = 25/21 = 1.19047619... times more pizza.

or in other words she ate

25/4 - 21/4 = 4/4 = 1 more pizza.

9.

so, he wins 5 of every 15, that is a ratio of 5/15 = 1/3.

he had 75 matches. 1/3 of 75 matches (see also 5.) means

75 × 1/3 = 75/3 = 25.

he won 25 matches.

10.

Mrs. Paul is 145 cm tall.

the daughter is 1/5 of that. see 5. and 9. :

1/5 of 145 means

145 × 1/5 = 145/5 = 29 cm

her daughter is 29 cm tall (a baby).

What is the difference between -21 and -8?

Answers

Answer:

-13

Step-by-step explanation:

(-21) - (-8) = -13

-21 - -8 = -13

Because of the two subtract signs next to each other before the number 8, they change to an addition sign.

From -21, move right 8 places along the number line because it is add 8.

-21  -20  -19  -18  -17  -16  -15  -14  -13

And you get to -13

Therefore, -21 + 8 = -13

Systems by elimination
2x - y = 2
-8x + 4y = −8

Answers

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by elimination.

2x−y=2;−8x+4y=−8

Multiply the first equation by 4,and multiply the second equation by 1.

4(2x−y=2)

1(−8x+4y=−8)

Becomes:

8x−4y=8

−8x+4y=−8

Add these equations to eliminate x:

0=0

What’s the next number in the pattern, and what is the formula to find the next 2 numbers in the pattern?
7, 28, 63, 112.. 175..

Answers

Answer: 7, 28, 63, 112, 175, 252, 343, ...

Step-by-step explanation:

7, 28, 63, 112, 175

7*1, 7*4, 7*9, 7*16, 7*25, ...

7*1², 7*2², 7*3^2, 7*4², 7*5²

Hence, 7n², n=1, 2, 3, 4, ...

7*6²=

7*6*6=

252

7*7²=

7*7*7=

343

Thus,

7, 28, 63, 112, 175, 252, 343, ...

Answer:

good luck brooooooooooo

Multiply. 6/7 ⋅ 4/15

A. 8/35
B. 14/45
C. 5/11
D. I don't know

Answers

Answer:

A

Step-by-step explanation:

Multply = 24/105

Divide by 3

8/35

it'd be 8/35
6•4 = 24
7•15 = 105
simplify and you get 8/35 :)

HELPP DUE TODAY
Geometry bisectors

Answers

Answer:

Step-by-step explanation:

Bisects means that ∠RED will be divided in two parts by segment EB. This means that ∠REB = ∠BED. So,

5x-3 + 5x-3 = 8x+16

10x-6 = 8x+16

2x = 22

x = 11

Keep in mind that 11 is NOT the angle of ∠BED. You will plug it back into ∠REB to get

5(11)-3 = 52

Therefore, ∠BED = 52°

52 is going to be your correct answer.

Write the fraction 12/28 in simplest form.

Answers

Answer:

3/7

Step-by-step explanation:

12/28=3*4/4*7=3/7

i need help please thanks​

Answers

Answer:

the answer is the answer of the answer okay answer

Step-by-step explanation:

the answer is the answer of the answer okay aanswer

how many different letter arrangements can be obtained from the letters of the word statistically, using all the letters?

Answers

Different letter arrangements that can be obtained from the letters of the word statistically, using all the letters= 6,48,64,800

Given,

Total number of arrangements obtained = 6,48,64,800

Given words = STATISTICALLY

Total word count = 13

Here we have repeated alphabets as -

"S"s = 2

"T"s = 3

"A"s = 2

"I"s = 2

"L" = 2

Total permutations we have here = 13! / 2!2!2!2!3!

= 6,22,70,20,800 / 96

= 6,48,64,800

What is Permutation?

A permutation of a set in mathematics is, broadly speaking, the rearranging of its components if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

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The inventor of a new game believes that the variable cost for producing the game is $0.50 per unit and the fixed costs are $4,300. the inventor sells each game for $1.89. let x be the number of games produced. (a) the total cost for a business is the sum of the variable cost and the fixed costs. write the total cost c (in dollars) as a function of the number of games produced. c = (b) write the average cost (in dollars) per unit c = c x as a function of x. c =

Answers

The total cost is represented as C = $0.50x + $4300  and the average cost as avgC = $0.50 + $4300/x

We have been given that,

The variable cost for producing the game = $0.50 per unit

The fixed cost for producing the game = $4300

Let the total cost be denoted by C.

And let x be the number of games produced.

a) Total cost = variable cost + fixed cost

          C = $0.50x + $4300

b) Average cost = total cost/number of games produced

                        = C/x

                        = ($0.50x + $4300)/x

                        = $0.50 + $4300/x

Hence the total cost is C = $0.50x + $4300 and the average cost is $0.50 + $4300/x

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s it true that for any integer n ≤ 2, φ(n) has a primitive root? if so, prove it. if not, give an explicit counterexample

Answers

No, it is not it true that for any integer n ≤ 2, φ(n) has a primitive root

What is primitive root?

In modular arithmetic, a number g is called a primitive root modulo n if every number  coprime to n is congruent to a power of  modulo . Mathematically, g is a primitive root modulo n if and only if for any integer  a such that gcd(a, n)=1 , there exists an integer k such that:

.[tex]g^{k}[/tex]≡ a (mod n)

Now,

Existence of Primitive root modulo n exists if and only if:

n is 1, 2, 4, orn is power of an odd prime number , orn is twice power of an odd prime number .

So,

if n be a positive integer. A primitive root mod n is an integer g such that every integer relatively prime to n is congruent to a power of g mod n.

For example,

As ϕ(11)=10, the order of 2(mod11) must divide 10.  

So we check 22≡4(mod11) and 25≡10(mod11).

Since neither of these are 1, and

we know 2ϕ(11)=210≡1(mod11) by Euler's Theorem,

ord112=ϕ(11), making 2 a primitive root modulo 11.

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Find FH

FH = {Blank}

Answers

Answer:

22

Step-by-step explanation:

By the segment addition postulate, FH=8+14=22.

The equation will be,

→ FH = FG + GH

Then the value of FH will be,

→ FH = 8 + 14

→ [ FH = 22 ]

Hence, the value of FH is 22.

It took Jane 3.5 hours to write 1 paper. At this rate, how long would it take Jane to write all 8 of her papers due this semester?

Answers

3.5 * 8 = 28 hours. 3.5hr=1 paper, 7hr=2 papers…..

Puzzle #4
1: Find the slope:
3: Find the slope:
(2,-6), (-4, -3)
2: Find the slope:
X
Y
-1
-12
1
-8
-4
0
35
5
4: Find the slope:
answer choices
B:
A:
C:
m=-2 m=0 m = 2
D:
m = -4
G:
m=
undefined
E: IF:
m =-
2
m = 4
I
H: -I:
m =
2
m =
Type the 4-
letter code into
the answer
box. All CAPS,
no spaces.
Does anyone know the code to puzzle 4???? Please

Answers

Answer:

1/-2

Step-by-step explanation:

Slope(m) = y2- y1/x2-x1

= -3-(-6)/-4-2

=+3/-6

=1/-2

helpppp plssssssssss

Answers

Answer:

x=2

Step-by-step explanation:

11-2x=5x-3

the first step, move the 3 over

14-2x=5x

In the second step moves 2x over

14=7x

finally, we just isolate the x from 7 by dividing 7

14/7=7x/7

simplify

2=x or x=2

Answer:

x=2

Step-by-step explanation:

*Shown two ways to solve.

11-2x=5x-3

 +2x +2x

11=7x-3

+3    +3

14=7x

Divide by 7.

2=x

11-2x=5x-3

-11          -11

-2x=5x-14

-5x -5x

-7x=-14

Divide by -7.

x=2

Check to see if you're right.

11-2(2)=5(2)-3

11-4=10-3

7=7

Yep, it's correct.

Hope this helps.

please im begging you help me

Answers

Answer: Translation means you move a shape without rotating or flipping it and reflection is a mirror image of the shape. In the current example, the shape is translated right and down a noncalculable amount.

Rewrite the Expressions using Distributive Property
(2+3)6

Answers

30

six times three is equal to 18.
six times two is equal to 12.
18+12=30

Answer:

Step-by-step explanation:

If you distribute 6 to the  numbers inside the parenthesis, it means that you multiply both number by 6
2 x 6 = 12
3 x 6 = 18
the expression can be rewritten like the following:

12 + 18 = 30

Rhiannon and Sophie both started saving for a new piano this month. Rhiannon will deposit $35.80 per week, but her bank account is currently overdrawn with a -$253.50 balance. Sophie also has a negative bank account balance of -$78.25 and will deposit $23.30 each week. How many weeks (w) will it take for the two bank accounts to have the same balance?​

Answers

It will take 14.02 weeks for both the accounts to have the same balance

Bank account balance of Rhiannon = -$253.50

Money deposited by Rhiannon in the bank account each week = $35.80

Bank account balance of Sophie = -$78.25

Money deposited by Sophie in the bank account each week = $23.30

Let the number of weeks it takes to have the same account balance be x, therefore formulating the algebric equation we get:

Bank balance of Rhiannon + Money deposited by her each week*No of weeks it will take for the balance to be equal = Bank balance of Sophie + Money deposited by her each week*No of weeks it will take for the balance to be equal

= -253.5 + 35.8(x)  = -78.25 + 23.3(x)

= -175.25 = -12.5(x)

x =  14.02 weeks

Therefore, it will take 14.02 weeks for both the accounts to have the same balance

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how many 20mm long wire pieces could be cut from a 1 meter long wire piece

Answers

Answer is 50 pieces of wire

Step by step

1 meter wire = 1000 mm wire

Divide 1000mm wire by 20mm length pieces = 50 pieces

You can cut 50 x 20mm pieces from 1 meter of wire

what is 5,435,778 expressed in scientific notation? a.5.435778 x 10 b.5.435778 x 10 c.5.435778 x 10 d.5.435778 x 10

Answers

5,435,778 in scientific notation will be 5.435778×10⁶.

Scientific notation is the way to represents huge numbers in simple form. This ease understanding and calculation of the numbers. When written in a scientific notation, the number is called coefficient, the number to which power is raised is called base and raised power is called exponent. For instance, in the given answer, 5.435778 is coefficient, 10 is base and 6 is exponent.

While converting the numbers into scientific notation, we need to remember following points -

If the number is greater than 1 or is a multiple of 10, the decimal will be placed on the Left Hand Side. Like in the number in question, decimal moved to left and we got positive exponent. If the number is less than 1, then decimal will be placed at Right Hand Side. In this case, the exponent will be negative. For instance, we will represent 0.005 as 5*10-³.

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The complete question is -

what is 5,435,778 expressed in scientific notation? a.5.435778 x 10⁷ b.5.435778 x 10³ c.5.435778 x 10⁶ d.5.435778 x 10⁵

Help?? The answer isn't -1026 btw i already guessed :(

Answers

Answer:

153

Step-by-step explanation:

12² - 3 [ 4([tex]\frac{1}{4}[/tex] - [tex]1^{8}[/tex] ) ] ← evaluate the inside part of the bracket

= 144 - 3 [ 4([tex]\frac{1}{4}[/tex] - 1) ]

= 144 - 3 [ 1 - 4 ]

= 144 - 3(- 3)

= 144 + 9

= 153  


Alyse bought 1/3lb of orange pekoe tea and 1/2lb of
English cinnamon tea. How many pounds of tea did
she buy?

Answers

According to the solving Alyse buy 5/6lb pounds fraction of tea.

What in math is a fraction?

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator as well as denominator of a complex fraction is a fraction.

How come a fraction is a number?

A numerator, which is located above the line, and a denominator make up fractions (which is below the line). You may find out how many equally sized pieces are divided into something by looking at the denominator. How many of these equal components are taken into account is indicated by the numerator.

According to the given fraction:

1/3lb of orange pekoe tea.

1/2lb of English cinnamon tea.

find the total pound of tea she buy:

So,

Adding these two fraction we get the total pounds:

= [tex]\frac{1}{3} + \frac{1}{2}[/tex]

= [tex]\frac{2 + 3}{6}[/tex]

= 5/6 lb

According to the solving Alyse buy 5/6lb pounds of tea.

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Pleasee help I need the answer rn

Answers

I'll give you the answer if you cas ap $2


Find the least common denominator (LCD) of 5/6 and
8/9

Answers

5/6 and 8/9 can be multiplied to be 15/18 and 16/18. so the lcd is 18

PLEASE HELPPPPPPPPPP

Answers

Answer:

20 1/16

Step-by-step explanation:

please give brilliantest pls

Answer:

You have the correct answer [tex]20 \frac{1}{16}[/tex]

Step-by-step explanation:

I am willing to give a brainliest to anybody, just please help !!!
During which game is she more effective serving?
How did you find this answer and please show your work?

Answers

Answer: The First game with 16/19 serves

Step-by-step explanation: Fraction also means division. So once you divide both fractions, you'll see that 16/19 > 13/16. That shows that she was more effective in the first game.

44 < 5x6 and 5x - 6 ≤ 54

Answers

Answer:

5x - 6 ≤ 54

5x-6+6 ≤ 54+6

5x ≤ 60

divide by 5

x ≤ 12

Step-by-step explanation:

Given [tex]f(x)=\frac{1}{x+5}[/tex], find the average rate of change of f(x) on the interval
[1,1+h]. Your answer will be an expression involving h.
Pls halp

Answers

The average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h

How to find the average rate of change of f(x) on the interval [1,1+h]?

The function is given as

f(x) = 1/(x + 5)

The interval is given as

[1, 1 + h]

Calculate f(1) as follows

So, we have

f(1) = 1/(1 + 5)

f(1) = 1/6

Calculate f(1 + h) as follows

So, we have

f(1 + h) = 1/(1 + h + 5)

f(1 + h) = 1/(h + 6)

The average rate of change of f(x) on the interval [1,1+h] is then calculated as

Rate = [f(1 + h) - f(1)]/[1 + h - 1]

This gives

Rate = [1/(h + 6) - 1/6]/h

Hence, the average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h

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CRAFT FAIR Kylie is going to try to sell two of her oil paintings at the local craft fair. She is hoping to earn at least $400.

a. Write the inequality that represents the constraint of the situation, where x is the price of the first oil painting, and y is the price of the second.

b. Graph the inequality that represents the constraint on the sale.

Answers

The inequality that represents the constraint of the situation is x+y ≥ 400.

Inequality is defined as the mathematical expression in which both sides are not equal .

In inequalities the two vales are compared by "≤" , "≥" , "≠"  .

For Example : 2x+3y≥4 is an example of inequality .

In the given question

Part (a)

Given Kylie sell first oil painting in $x

and second oil painting in $y.

Kylie is trying to earn at least $400.

the term at least means she can earn $400 or greater than $400, so ≥ sign will  be used,

According to the question

we get , x+y ≥ 400    

So , x+y ≥ 400, is the inequality that represents the constraint of the situation.

Part (b)

The Graph of the inequality x+y ≥ 400 that represents the constraint on the sale is shown below .

Therefore , the inequality that represents the constraint of the situation is x+y ≥ 400.

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Given that
3x8 7:2
Calculate the value of x.
Give your answer in its simplest form.
X =

Answers

The value of x in the equation is x = -8/30

What are linear equations?

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

How to determine the value of x?

The equation is given as

3x + 8 = 7.2

Subtract 8 from both sides of the equation

3x = -0.8

Divide both sides by 3

x = -0.8/3

Rewrite as

x = -8/30

Hence, the value of x in the equation is x = -8/30

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