All categories

4 years ago

Apply the distributive property to factor out the greatest common factor

Mathematics

1 answer:

Solnce55 [7]4 years ago

5 0

Hey there!

If we want to understand this problem, we have to understand the keywords. We want to know what the words mean so we can use the definition and solve the problem.

The distributive property is a property in math for multiplication and it's defined as:

a(b+c) = ab + ac

Next, a factor is a number that when multiplied by another gives the specified or needed number. For example, two is a factor of four because two times two is four.

We want the greatest common factor of both. So, we can list the factors of both 16 and 36 and find the greatest common one. Remember, according to our formula, this GCF would be the a in a(b+c). It would be the number that goes into both.

16 - 1, 2, 4, 8, 16
36- 1, 2, 3, 4, 6, 9

It looks as if the greatest common factor is 4. Therefore, we know our a value is 4. We have:

4(b+c) = 16+36

We know a(b+c) = ab + ac.

Therefore, we want to plug in the values of b and c the number of times 4 goes into 16 and 36. That means we have:

4(4+9) = 16 + 36
16 + 36 = 16 + 36

We're right! :)

Hope this helps!

You might be interested in

The cost to purchase a golf ball is $5 at Marty’s Sports Goods. To purchase a golf ball at Golf Club you must be a member. The m

LenKa [72]

It would be 10 for it tovbe the same price as at the golf club

6 0

3 years ago

if fifty cents is divided equally among three friends there will be some cents left how many cents will be left

HACTEHA [7]

Greetings!

This can be solved by dividing 50 by 3 (the amount of friends, you're spiting the money with.)

50/3=16.6667

We have to round down in order to get a whole number: 16

16*3=48
50-48=2

If 50 cents is divided equally among three friends, each would get 16 cents and there would be 2 cents left over.

Hope this helps.
-Benjamin

5 0

4 years ago

The sum of four consecutive terms of an arithmetic progression is 32 and the ratio of product of the first and the last term to

OverLord2011 [107]

The four consecutive terms are 2,6,10,14.

Explanation:

Let the four consecutive terms of an arithmetic progression be (a - 3d), (a - d),(a + d), (a + 3d)

It is given that the sum of four consecutive terms is 32.

Thus, adding all the four consecutive terms, we have,

$\begin{array}{r}{a-3 d+a-d+a+d+a+3 d=32} \\{4 a=32} \\{a=8}\end{array}$

Thus, the value of a is 8.

It is also given that the ratio of the product of first and last term to the product of the two middle terms is 7:15. Thud, we have,

$\frac{(a-3d)(a+3d)}{(a-d)(a+d)} =\frac{7}{15}$

Simplifying the terms, we have,

$\begin{aligned} \frac{a^{2}-9 d^{2}}{a^{2}-d^{2}} &=\frac{7}{15} \\ 15\left(a^{2}-9 d^{2}\right) &=7\left(a^{2}-d^{2}\right) \\ 15 a^{2}-135 d^{2} &=7 a^{2}-7 d^{2} \\ 8 a^{2} &=128 d^{2} \end{aligned}$

Now, substituting a = 8, we have,

$\begin{aligned} 8(64) &=128 d^{2} \\ 512 &=128 d^{2} \\ 4 &=d^{2} \\ 2 &=d \end{aligned}$

Thus, the value of d is 2.

Now, we shall substitute the value of a and d in the terms (a - 3d), (a - d),(a + d), (a + 3d), we get, the four consecutive terms.

Thus, the four consecutive terms are 2,6,10,14.

8 0

3 years ago

Select all values of x that make the inequality true: (6x<24)

Stolb23 [73]

9514 1404 393

Answer:

A, B

Step-by-step explanation:

Divide both sides by 6 to see what those values should be:

x < 4

Of course all negative numbers are less than 4, so choices A and B are correct. The given positive numbers are not less than 4, so the remaining choices are not correct.

8 0

3 years ago

Xác suất xảy ra môt sự kiện là 0.3. Xác suất để sự kiện đó không xảy ra là?

hodyreva [135]

Câu trả lời:

0,7

Giải thích từng bước:

Xác suất để một sự kiện xảy ra = 0,3

Cho sự kiện = A

P (A) = 0,3

Xác suất mà sự kiện không xảy ra có thể thu được bằng cách sử dụng quy tắc bổ sung;

P (A ') = 1 - P (A)

Vì thế,

P (A ') = 1 - 0,3 = 0,7

3 0

3 years ago