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3 years ago

Which of the following represents the factorization of the binomial below?

Mathematics

1 answer:

Serggg [28]3 years ago

4 0

Answer:

Step-by-step explanation:

x² - 81 ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

Here a = x and b = 9, thus

x² - 81 = (x + 9)(x - 9) → D

You might be interested in

Which is a complete list of factors of each term in the expression 15 + 20 x?

BigorU [14]

Answer:

15: 1, 3, 5, 15

20x: 1, 2, 4, 5, 10, 20, x

Step-by-step explanation:

When finding divisors of a number, it is often convenient to start with the <em>prime</em> factors. Those may be raised to some power.

For the numbers here, the prime factors are ...

15 = 3·5

20 = 2²·5

One of the reasons this is useful is that each of these prime factors has an exponent. The number of divisors is the product of these exponents incremented by 1. That is, the number of divisors will be ...

for 15: (1+1)(1+1) = 4

for 20: (2+1)(1+1) = 6

Knowing this can help you make sure you have found all of the divisors. This number includes 1 and the number itself.

Then the divisors are ...

15 ⇒ 1, 3, 5, 15 . . . . . . . . . . . 4 divisors

20 ⇒ 1, 2, 4, 5, 10, 20 . . . . . 6 divisors

For the variables, it is a little hard to tell what is intended. At least, a list of the individual variables is required. Hence x is added to the list for 20x.

The "complete" list of factors is ...

15: 1, 3, 5, 15
20x: 1, 2, 4, 5, 10, 20, x

_____

<em>Further comment on variable factors</em>

If the variables were to be included in the divisor list the way the prime factors are, then we would first start by listing the prime factors:

{2, 2, 5, x}

Then we would form the possible subsets:

{ }, {2}, {5}, {x}, {2, 2}, {2, 5}, {2, x}, {5, x}, {2, 2, 5}, {2, 2, x}, {2, 5, x}, {2, 2, 5, x}

and finally, form the products of the contents of these subsets:

1, 2, 5, x, 4, 10, 2x, 5x, 10, 4x, 10x, 20x

Apparently, the answer choices for this question do not recognize 2x as a factor of the second term. The treatment for numbers is obviously different from the treatment for variables, but it is hard to tell what the rules for variables are from the answer choices here. (Consult your teacher and/or text.)

3 0

3 years ago

What kind of fraction is 8/3

Wewaii [24]

improper you need to simplify which would become 2 and 2/3

3 0

3 years ago

Write in factored form:

Katyanochek1 [597]

Answer:

( 3x + 5 ) ( x - 4 )

Step-by-step explanation:

1.) Factors of 20 = (1,20) (2,10) and (4,5)

2.) ( 3x + 5 ) ( x - 4 )

3.) 3x - 12x + 5x - 20 = 0

4.) 3x^2 + 7x - 20 = 0

4 0

3 years ago

A car park has 20 vehicles 12 of them are cars.what fraction of the vehicles are cars?

svetlana [45]

3/5 of the vehicles are cars.
hope this helped.

3 0

2 years ago

A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res

AveGali [126]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 15 \ months$

The sample size is n = 25

The sample mean is $\= x = 17 \ months$

The standard deviation is $s = 5.5 \ months$

Let assume the level of significance of this test is $\alpha = 0.05$

The null hypothesis is $H_o : \mu = 15$

The alternative hypothesis is $H_a : \mu > 17$

Generally the degree of freedom is mathematically represented as

$df = n -1$

=> $df = 25 -1$

=> $df = 24$

Generally the test statistics is mathematically represented as

$t = \frac{\= x- \mu }{\frac{s}{\sqrt{n} } }$

=> $t = \frac{ 17 - 15 }{\frac{5.5}{\sqrt{25} } }$

=> $t = 1.8182$

Generally from the student t distribution table the probability of obtaining $t = 1.8182$ to the right of the curve at a degree of freedom of $df = 24$ is

$p-value = P(t > 0.18182 ) = 0.4286$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.

7 0

2 years ago