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Maksim231197 [3]

2 years ago

5

Which expression is equivalent to 2x² - x + ?

1 answer:

Delvig [45]2 years ago

6 0

Answer: $2\left(x-\frac{1}{4} \right)^{2}$

Step-by-step explanation:

$2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}$

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A total of $6000 was invested, part of it at 3% interest and the remainder at 8%. If the total yearly interest amounted to $380,

Nastasia [14]

$ 2000 is invested at 3 % interest and $ 4000 is invested at 8 % interest

<em><u>Solution:</u></em>

Given that, total of $6000 was invested

Let "x" be the amount invested at 3 % interest

Then, (6000 - x) is the amount invested at 8 % interest

Given that,

<em><u>The total yearly interest amounted to $380</u></em>

Then, we can frame a equation as:

$x \times 3 \% + (6000 - x) \times 8 \% = 380$

<em><u>Solve the above expression for "x"</u></em>

$x \times \frac{3}{100} + (6000-x) \times \frac{8}{100} = 380\\\\0.03x + (6000-x) \times 0.08 = 380\\\\0.03x + 480 - 0.08x = 380\\\\-0.05x = -100\\\\\text{Divide both sides by -0.05 }\\\\x = 2000$

Thus, $ 2000 is invested at 3 % interest

(6000 - x) = 6000 - 2000 = 4000

$ 4000 is invested at 8 % interest

4 0

4 years ago

What does 15=-3y+21x in slope intercept form

DENIUS [597]

<u>the slope would be 7</u> once you added 3y to both sides, and then subtracted the 15 from both sides and then divided all terms by 3

8 0

3 years ago

The canoe costs $96 for 8 hours. How much does it cost per hour?

vesna_86 [32]

Answer:

$12

Step-by-step explanation:

just divide 96÷8=12

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3 years ago

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3 years ago

The mean height of women in a country (ages 20minus29) is 64.2 inches. A random sample of 75 women in this age group is select

padilas [110]

Answer:

$z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440$

And we can find the probability using the complement rule and with the normal standard table like this:

$P(Z>2.440) =1-P(Z$

The probability that the mean height for the sample is greater than 65 inches is 0.007

Step-by-step explanation:

Let X the random variable that represent the women heights of a population, and we know the following parameters

$\mu=64.2$ and $\sigma=2.84$

We are interested on this probability

$P(X>65)$

Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we find the z score for 65 inches we got:

$z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440$

And we can find the probability using the complement rule and with the normal standard table like this:

$P(Z>2.440) =1-P(Z$

The probability that the mean height for the sample is greater than 65 inches is 0.007

7 0

3 years ago