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OLga [1]
3 years ago
6

Rewrite the following expression 15+21 using the GCF and the distributive property

Mathematics
2 answers:
saul85 [17]3 years ago
7 0

Answer:

3(5+7)

Step-by-step explanation:

We are asked to rewrite 15+21 using the GCF and the distributive property.

We know that greatest common factor of 15 and 21 is 3.

15=3\times 5 and 21=3\times 7.

We can rewrite our given expression as:

3\times 5+3\times 7

Now, we will factor out 3 from our expression as:

3(5+7)

Therefore, after rewriting our given expression using the GCF and the distributive property we will get 3(5+7).

avanturin [10]3 years ago
3 0
First, we want to find the GCF of 15 and 21, which is 3. Now we do 15 divided by 3 and 21 divided by 3, which gives us 5 and 7. To rewrite the expression, we take the GCF and put it on the outside of the parenthesis. Inside the parenthesis, we put 5 + 7. So it'll look like this:

3(5 + 7)
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Find a power series representation for the function. (Give your power series representation centered at x=0 .) f(x)=15+x
Anna71 [15]

Answer:

f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}

Step-by-step explanation:

Given

f(x) = \frac{1}{5 + x}

Required

The power series centered at x = 0

We have:

f(x) = \frac{1}{5 + x}

Factor out 5 from the denominator

f(x) = \frac{1}{5(1 + \frac{x}{5})}

Rewrite as:

f(x) = \frac{\frac{1}{5}}{(1 + \frac{x}{5})}

Further, rewrite as:

f(x) = \frac{1}{5}(1 + \frac{x}{5})^{-1}

Expand the bracket

f(x) = \frac{1}{5}(1 - \frac{x}{5} + (\frac{x}{5})^2 - (\frac{x}{5})^3+..........)

Evaluate all exponents

f(x) = \frac{1}{5}(1 - \frac{x}{5} + \frac{x^2}{25} - \frac{x^3}{125}+......)

Open brackets

f(x) = \frac{1}{5} - \frac{x}{5^2} + \frac{x^2}{5^3} - \frac{x^3}{5^4}+......

Notice the pattern as:

f(x) = \frac{1}{5} - \frac{x}{5^2} + \frac{x^2}{5^3} - \frac{x^3}{5^4}+......\± \frac{x^n}{5^{n+1}}

So, the power series is:

f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}

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telo118 [61]

Answer:

(5x - 3y)(25x² +15xy + 9y²)

Step-by-step explanation:

125x³ - 27y³ is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

Given

125x³ - 27y³

= (5x)³ - (3y)³

= (5x - 3y)((5x)² + (5x)(3y) + (3y)²)

= (5x - 3y)(25x² + 15xy + 9y²)

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3 years ago
Which value of x makes the equation -5x-(-7-4x) =-2(3x-4 true?
Ludmilka [50]

Answer:

x = 1/5

Step-by-step explanation:

Step 1: Write equation

-5x - (-7 - 4x) = -2(3x - 4)

Step 2: Solve for <em>x</em>

  1. <u>Distribute:</u> -5x + 7 + 4x = -6x + 8
  2. <u>Combine like terms:</u> -x + 7 = -6x + 8
  3. <u>Add 6x to both sides:</u> 5x + 7 = 8
  4. <u>Subtract 7 on both sides:</u> 5x = 1
  5. <u>Divide by 5 on both sides:</u> x = 1/5

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

-5(1/5) - (-7 - 4(1/5)) = -2(3(1/5) - 4)

-1 - (-7 - 4/5) = -2(3/5 - 4)

-1 - (-39/5) = -2(-17/5)

-1 + 39/5 = 34/5

34/5 = 34/5

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