How can you use the Distributive Property to check your work when factoring?

1. Once an expression has been factored, use the Distributive Property to expand the expression. The factored expression should be the original expression.

2. Once an expression has been factored, use the Distributive Property to factor the expression. The factored expression should be the original expression.

3. Once an expression has been factored, use the Distributive Property to factor the expression. The expanded expression should be the original expression.

4. Once an expression has been factored, use the Distributive Property to expand the expression. The expanded expression should be the original expression.

Answer:

Step-by-step explanation: try 14

Answer:

NO

Step-by-step explanation:

it's starts at the origin but is not a straight line.

Answer:

D (Alicia did 5 more jumping jacks per minute than Melissa.)

Step-by-step explanation:

Alicia's rate is 30 jumping jacks per minute. You can use the formula m=(y2-y1)/(x2-x1) to find the slope/rate. The two points in the table you can use are (1,30) and (2,60). You can plug those coordinates into the slope formula. (60-30)/(2-1)=30/1= 30 jumping jacks per minute.  To find the rate of change/slope for Melissa, you can use the same formula m=(y2-y1)/(x2-x1). The two points you could plug in are (0,0), and (4,100). (100-0)/(4-0)=100/4=25. Melissa does 25 jumping jacks per minute.

Step-by-step explanation:

the motorcyclist starts x hours after the bus.

it takes the motorcyclist 1.5 hours to meet the bus the first time, 6 hours to reach B, rest 1 hour and go another 2 hours before the bus arrives at B.

so, the bus needs

x + 9 hours to reach B.

x + 1.5 hours for 150 km (for the first meeting with the motorcyclist).

the speed of the bus is 600/(x + 9) km/h or 150/(x + 1.5) km/h.

so,

600/(x + 9) = 150/(x + 1.5)

4/(x + 9) = 1/(x + 1.5)

4(x + 1.5)/(x + 9) = 1

4(x + 1.5) = x + 9

4x + 6 = x + 9

3x + 6 = 9

3x = 3

x = 1

the motorcyclist starts 1 hour after the bus.

the speed of the bus is

600/(x + 9) = 600/(1 + 9) = 600/10 = 60 km/h

when the motorcyclist is starting its return trip, he is 7 hours after his start, and the bus is 7+x = 7+1 = 8 hours after its start, that means at

8×60 = 480 km of its total trip of 600 km.

120 km are still left for the bus to go.

from that point on both travel the same time y going with their speeds until they meet the second time.

the motorcyclist travels 100y km building up distance from B, while the bus travels 60y km reducing the 120 km distance from B.

when they meet the second time, the distance from B for the motorcyclist is the same as the remaining distance for the bus.

so,

100y = 120 - 60y

160y = 120

y = 120/160 = 3/4 = 0.75 hours

so, they meet at

100 × 0.75 = 75 km from B.

Answer:

  Large gear: 2 revolutions, 24 teeth

  Small gear: 3 revolutions, 24 teeth

Step-by-step explanation:

You want the number of teeth that have touched when a 12-tooth gear and an 8-tooth gear turn until they have the same relative position as when they started.

The least common multiple (LCM) of 8 and 12 is the smallest integer that is a positive integer multiple of both these numbers. That value is ...

  24 = 8·3 = 12·2

It is often found quickly by making use of your knowledge of multiplication tables.

The LCM can be found by looking at the unique factors of the numbers, taking each to the highest of the powers:

  8 = 2³

  12 = 2² × 3

Among the factors 2 and 3, the highest powers are 2³ and 3¹, so ...

  2³ × 3¹ = 24

is the LCM.

The LCM is also the product of the numbers, divided by their greatest common factor (GCF):

  LCM(8, 12) = 8·12/4 = 24

__

Additional comment

The problem statement is telling you to look for the same number in the two right columns of the table. That number is 24. It goes in the blanks at the bottom.

Answer:a.3 is the coefficient

b.3minutes

c.27inches

Step-by-step explanation:

a. In d=3t equation, d and t are variables. 3 is the coefficient for 't'.

b. In d=3t , d is 9inches.

so 9 = 3t

or t = 9/3 =3minutes

c. In d= 3t, t is 9minutes.

So d= 3*9 = 27inches.

Answer:   b.3minutes  c.27inches

Step-by-step explanation:

Answer:

Answers below

Step-by-step explanation:

B. is [tex]1 \frac{2}{5} *3=4 \frac{1}{5}[/tex]

C. 75 -:- 2[tex]\frac{1}{5}= 30[/tex]

D. 27-:-6=4.5(or 4 and 1/2)

Answer:

15 sides

Step-by-step explanation:

As we know the full angles of a polygon is 360°

And

Each side has angle 24°

So,

n = 360/24

n = 15 sides

I hope my answer helps you.

Answer:

Its the second one

Step-by-step explanation:

5 3-digit numbers that have three equal digits.

we need to apply the principle of inclusion-exclusion to account for the fact that some 3-digit numbers may be counted multiple times.

any 3-digit number that has three equal digits will be counted twice once as a 3-digit number with two equal digits and one different digit, and once as a 3-digit number with three equal digits.

There are 5 choices for the digit that is repeated, and 1 way to arrange the digits, so there are 5 3-digit numbers that have three equal digits.

Therefore, we need to subtract 5 from the total number of 3-digit numbers that have two equal digits and one different digit.

60 number are 3-digit numbers that have two equal digits and one different digit.

Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter.

The given digits are,

1, 2, 3, 4, 5.

Since, to find the 3 digits numbers which are written by using given digits, and have two equal digits and one different digit,

Here order of arrangement matters.

Use permutation formula,

From 5 digits, 3 are chosen,

Ways of arrangement = ⁵P₃  

= 5! / (5-3)!

= 5! / 2!

= 5 x 4 x 3 x 2! / 2!

= 60

There are total 60 different ways, in which numbers can be arranged.

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Answer:

 57/10 or 5 7/10

Step-by-step explanation:

Simplify the following:

3 + 1/5 + 7/2 - 1

Put 3 + 1/5 + 7/2 - 1 over the common denominator 10. 3 + 1/5 + 7/2 - 1 = (10×3)/10 + 2/10 + (5×7)/10 - 10/10:

(10×3)/10 + 2/10 + (5×7)/10 - 10/10

10×3 = 30:

30/10 + 2/10 + (5×7)/10 - 10/10

5×7 = 35:

30/10 + 2/10 + 35/10 - 10/10

30/10 + 2/10 + 35/10 - 10/10 = (30 + 2 + 35 - 10)/10:

(30 + 2 + 35 - 10)/10

| 3 | 5

| 3 | 0

+ | | 2

| 6 | 7:

(67 - 10)/10

| 6 | 7

- | 1 | 0

| 5 | 7:

Answer:  57/10 or 5 7/10

[tex]6(x-2)=-18[/tex]

Distribute:

[tex](6)(x)+(6)(-2)=-18[/tex]

[tex]6x-12=-18[/tex]

Add 12 to both sides:

[tex]6x-12+12=-18+12[/tex]

[tex]6x=-6[/tex]

Divide both sides by 6:

[tex]\dfrac{6x}{6} =\dfrac{-6}{6}[/tex]

[tex]\fbox{x = -1}[/tex]

Answer:

Slope = -2

y-intercept = (0, 4)

Step-by-step explanation:

The equation is written in slope-intercept form, y = mx + b, where "m = slope" and "b = y-intercept". Thus, we have to identify what part of the equation is part of each element in slope-intercept form:

Slope-intercept form

y = mx + b

Equation:

y = -2x + 4

m = -2

b = 4

Thus, the slope is -2 and the y-intercept is (0, 4)

Answer:0.24

Step-by-step explanation:

Answer:

0.24

Step-by-step explanation:

⅘% of 30

⅘ = 0.8

0.8% of 30

eg: 0.8 = x     30 = y

[tex]\frac{x*y}{100}[/tex] (this is the formula for calculating the percentage of a number)

[tex]\frac{0.8*30}{100}[/tex] = 0.24

Answer:

72

Step-by-step explanation:

First, we will multiply the number of posts (7) by the posts' width (6) to get 42.

Since there is a chain between each post, there are 6 chains.

Multiplying the number of chains (6) by the chains' length (5), we get 30.

The question asks us to find the total length of the fence, so we add 42 and 30 and get 72.

Hope this helps!

Answer: this might be wrong

c

Step-by-step explanation:

Sorry if this is wrong

Answer: c

Step-by-step explanation:

Answer:

sorry I have no clue I don't like mathe either the half of the reason I can't answer it

The expression of length in terms of width is L = 10W and the length of the pan when the width is 7 feet will be 70 feet.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Suppose, the length and width of the pan are L and W corresponding.

As per the given,

(a)

The length of the pan was ten times its width.

L = 10W

The above expression is the length of the pan in terms of width.

(b)

The lasagna measured 7 feet wide.

L = 10 x 7 = 70 feet

Hence "According to the formula L = 10W, the length of the pan will be 70 feet when the width is 7 feet.".

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Answer:2/3

Step-by-step explanation: the line is at the same distance at (-2,-10) as it is at (4,-6)

so from (-2,-10) to (4,-6) is 2 up and 3 over

meaning 2/3 = slope

Answer:

Step-by-step explanation:

20 + 30 + 30 then 792 + 260 get your answer for both and add the answers together

Answer:

Step-by-step explanation:

the answer is 23.4 ?

Answer:

x = 8

Step-by-step explanation:

1/2 x - 2x = -5 -7

(1-4)/2 x = -12

-3/2 x = -12

3/2 x = 12

x = 12 · 2/3

x = 4 · 2

x = 8

100

35/42 is about 83 percent 83 percent of 120 is roughly 100

The answer is 100 females

Answer:

its 4-6

Step-by-step explanation:

Answer: The answers are A, B, C.

Step-by-step explanation:

Answer: (q + 10) - r

Step-by-step explanation:

The linear function that represents the amount of baskets in the xth month of the year is given as follows:

The percentage of her collection that she needs to get rid of is of 3.85%.

Linear Function:-

The definition of a linear function is:

y = b + mx

In which the parameters of the equation are given as follows:

•b is the value of y when x=0

•m is the rate of change for each unit of x

Every month she adds 2 new baskets to her collection, hence the slope is of : m = 2

Then: y = b + 2x

From the March amount, when x = 3, y = 60, hence the intercept b is given as follows:

60 = b + 6

b = 54

Hence the equation is: y = 54 + 2x

At the end of the year (12 months) the amount of baskets that she will have is of:

y = 54 + 2 × 12 = 78

Hence, she has to get rid of 3 baskets, as 78 - 75 = 3, and the percentage is of:

p = 3/78 × 100% = 3.85%.

Answer:

Step-by-step explanation: The linear function that represents the number of baskets in the month of the year is given as follows:

The percentage of her collection that she needs to get rid of is of 3.85%.

The definition of a linear function is:

y = b + mx

In which the parameters of the equation are given as follows:

•b is the value of y when x=0

•m is the rate of change for each unit of x

Every month she adds 2 new baskets to her collection, hence the slope is: m = 2

Then: y = b + 2x

From the March amount, when x = 3, y = 60, hence the intercept b is given as follows:

60 = b + 6

b = 54

Hence the equation is: y = 54 + 2x

At the end of the year (12 months) the number of baskets that she will have is:

y = 54 + 2 × 12 = 78

Hence, she has to get rid of 3 baskets, as 78 - 75 = 3, and the percentage is of:

p = 3/78 × 100% = 3.85%.