True or false: “If a positive integer is divisible by both 2 and 3, then it is divisible by 12.”

Factor the equation please help

LiRa [457]

Answer:

For A

${ \rm{6 {x}^{2}(x + 1) - 2x(x + 1) }}$

• The equation above has a common bracket "(x + 1)". So, let's first factorise out that bracket:

$\dashrightarrow \: { \rm{(x + 1) \{6 {x}^{2} - 2x \} }}$

• now in the second bracket, the common factor is x and 2.

$\dashrightarrow \: { \rm{(x + 1) \{2x(3x - 1) \}}}$

• Final answer;

${ \boxed{ \boxed{ \rm{ \dashrightarrow \: 2x(x + 1)(3x - 1) \: \: }}}}$

For B

${ \rm{3(x - 1)(x + 2) + ( {x}^{2} - x)(x + 2) }}$

• In the equation, the common bracket is (x + 2).

So let's first factorise it out:

$\dashrightarrow \: { \rm{(x + 2) \{3(x - 1) + ( {x}^{2} - x) \}}} \\ \\ { \rm{(x + 2) \{3(x - 1) + x(x - 1) \}}}$

• In the second major bracket, the common bracket is (x - 1). so factorise it out:

${ \rm{(x + 2) (x - 1) \{3 + x \}}}$

• Final answer:

${ \boxed{ \boxed{ \rm{ \dashrightarrow \: (x + 2)(x + 3)(x - 1) \: \: }}}}$

8 0

2 years ago

4^-2 x 7^-2 equivalent expression

Savatey [412]

Answer:

Not sure exactly which equivalent expression you are looking for but my goal would be to write it without the negative exponent.

$\frac{1}{28^2}$

Step-by-step explanation:

They have the same exponent and it is multiplication.

There is a law of exponent that says $(a \cdot b)^x=a^x \cdot b^x$ .

So we have $4^{-2} \cdot 7^{-2}$ equals $(4 \cdot 7)^{-2}$ .

Let's simplify (4*7)^(-2).

Since 4*7=28, we can say $(4*7)^{-2}=(28)^{-2}$ .

Some people really hate that negative exponent. All that - in the exponent means is reciprocal. So $28^{-2}=\frac{1}{28^2}$ .

8 0

3 years ago

A kite has a perimeter of 70 centimeters. One of the shorter sides measures 16 centimeters. What are the lengths of the other th

Sveta_85 [38]

A kite has 2 short sides and 2 long sides. The 2 short sides are equal. The 2 long sides are also equal. This means that the other short side is 16cm. And the remaining longer sides can be found like this:
let's pretend *y* is the long side
2*y = 70 - 16 - 16. (two of the long sides = 70 - short side - another short side)
so use algebra to find y.
2*y = 38
y = 19 so the long sides are both 19cm each
Your final answer: 16cm, 19cm, 19cm

5 0

3 years ago

Read 2 more answers

Ms. McCormick keeps a rectangular recycling bin for used paper in her classroom. The area of the bottom of the bin is 400 square

aniked [119]

According to the dimensions given, the volume of paper in the recycling bin is of 6800 cubic inches.

<h3>What is the volume of a rectangular prism?</h3>

It is given by the multiplication of the base area by the height, that is:

$V = S_bh$