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rosijanka [135]
3 years ago
15

Factor this trinomial 4x^2-6x-10 If you can please try to show me how to do it.

Mathematics
1 answer:
lilavasa [31]3 years ago
8 0

Answer:

=2(2x-5)(x+1)

Step-by-step explanation:

So we have the trinomial:

4x^2-6x-10

First, factor out a 2:

=2(2x^2-3x-5)

Now, factor within the parentheses.

To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b

(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.

-5 and 2 works. Therefore:

=2(2x^2-3x-5)

Replace -3x with 2x and -5x:

=2(2x^2+2x-5x-5)

Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:

=2(2x(x+1)-5(x+1))

Grouping:

=2(2x-5)(x+1)

And we're done!

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National data indicates that​ 35% of households own a desktop computer. In a random sample of 570​ households, 40% owned a deskt
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Answer:

Yes, this provide enough evidence to show a difference in the proportion of households that own a​ desktop.

Step-by-step explanation:

We are given that National data indicates that​ 35% of households own a desktop computer.

In a random sample of 570​ households, 40% owned a desktop computer.

<em><u>Let p = population proportion of households who own a desktop computer</u></em>

SO, Null Hypothesis, H_0 : p = 25%   {means that 35% of households own a desktop computer}

Alternate Hypothesis, H_A : p \neq 25%   {means that % of households who own a desktop computer is different from 35%}

The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;

                                  T.S.  = \frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }  ~ N(0,1)

where, \hat p = sample proportion of 570​ households who owned a desktop computer = 40%

            n = sample of households = 570

So, <u><em>test statistics</em></u>  =  \frac{0.40-0.35}{{\sqrt{\frac{0.40(1-0.40)}{570} } } } }

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<em>Since, in the question we are not given with the level of significance at which to test out hypothesis so we assume it to be 5%. Now at 5% significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics doesn't lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.</em>

Therefore, we conclude that % of households who own a desktop computer is different from 35%.

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Step-by-step explanation:

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