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3 years ago

Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and blank

Mathematics

2 answers:

prisoha [69]3 years ago

8 0

Answer:

12 is the answer.

Step-by-step explanation:

The best way to get the roots of the equation is to factorize the equation but when the factors are not possible then we should apply the quadratic equations formula to get the value of x.

Now we will try to factorize

x² - 8x -48 = 0

Now we multiply coefficient of highest degree term and constant term

48×1 = 48 which may be factored in 12×4. 8×6, 24×2.

Now we will choose 12×4 out of three because the 12-4 = 8 which is the coefficient of x.

Now its simple.

x²-12x + 4x -48 = 0

x(x -12) + 4(x-12) = 0

(x +4)(x-12) = 0

Therefore roots are x + 4 = 0

x = -4

and x - 12 = 0

x = 12

So the answer is 12.

Likurg_2 [28]3 years ago

3 0

Answer:

12 is the answer.

Step-by-step explanation:

We have given an equation.

x²-8x-48 = 0

We have given one root of equation. We have to find the other root of equation.

We use method of factoring to solve this.

Splitting the middle term, we have

x²-12x+4x-48 = 0

Making groups, we have

x(x-12)+4(x-12) = 0

Taking (x-12) common, we have

(x-12)(x+4) = 0

Applying Zero-Product Property, we have

x-12 = 0 or x+4 = 0

x = 12 or x = -4.

Hence, the roots of the given equation are -4 and 12.

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EXAMPLE

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Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

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The top line reads:

Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

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Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

Let

p= the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:

Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

Write the equation.

18=12p

Multiply both sides by 2.

⋅

2⋅18=2⋅12p

Simplify.

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$36.”

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3 years ago

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3 years ago

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Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

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3 years ago

Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and *blank*

Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and blank