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3 years ago

Simplify fully 6x2 +x–1 4x2 – 1

Mathematics

1 answer:

AlexFokin [52]3 years ago

8 0

Answer:

3x−1

Step-by-step explanation:

1 Split the second term in 6{x}^{2}+x-16x

+x−1 into two terms.

\frac{6{x}^{2}+3x-2x-1}{4{x}^{2}-1}

−1

+3x−2x−1

2 Factor out common terms in the first two terms, then in the last two terms.

\frac{3x(2x+1)-(2x+1)}{4{x}^{2}-1}

−1

3x(2x+1)−(2x+1)

3 Factor out the common term 2x+12x+1.

\frac{(2x+1)(3x-1)}{4{x}^{2}-1}

−1

(2x+1)(3x−1)

4 Rewrite 4{x}^{2}-14x

−1 in the form {a}^{2}-{b}^{2}a

−b

, where a=2xa=2x and b=1b=1.

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

(2x)

−1

(2x+1)(3x−1)

5 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

−b

=(a+b)(a−b).

\frac{(2x+1)(3x-1)}{(2x+1)(2x-1)}

(2x+1)(2x−1)

(2x+1)(3x−1)

6 Cancel 2x+12x+1.

\frac{3x-1}{2x-1}

2x−1

3x−1

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3 years ago

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µd =

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Answer:

d: 2, 4, -6, 0, -1, -5, 0, 1

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{29}{8}=-0.625$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.378$

The next step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.625 -0}{\frac{3.378}{\sqrt{8}}}=-0.523$

And the correct option would be:

a. t = -0.523

Step-by-step explanation:

We assume the following notation:

x=test value after , y = test value before

x: 34 39 28 33 27 23 35 33

y: 32 35 34 33 28 28 35 32

The system of hypothesis for this case is given by:

Null hypothesis: $\mu_y- \mu_x = 0$

Alternative hypothesis: $\mu_y -\mu_x \neq 0$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: 2, 4, -6, 0, -1, -5, 0, 1

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{29}{8}=-0.625$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.378$

The next step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.625 -0}{\frac{3.378}{\sqrt{8}}}=-0.523$

And the correct option would be:

a. t = -0.523

5 0

4 years ago

Select the correct answer.

MissTica

Answer:

The graphs are missing, but we can find the inequality for this problem:

She has $60.

The price of a T-shirt is $10, the price of a sweatshirt is $14.

If T is the number of T-shirts she buys, and S is the number of sweatshirts that she buys, we have:

T + S ≥ 5 (because she wants to buy at least 5 items)

T*$10 + S*$14 < $60 (because she wants to spend under $60)

Those two inequalities define the number of T-shirts and sweatshirts that she can buy.

3 0

3 years ago

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