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3 years ago

Identifying Additive Inverses

Mathematics

1 answer:

mestny [16]3 years ago

4 0

Answer:

he additive inverse of:

a) $-6x^2-x-2$ is : $6x^2+x+2$

b) $6x^2-x+2$ is : $-6x^2+x-2$

c) $6x^2+x-2$ is : $-6x^2-x+2$

d) $6x^2+x+2$ is : $-6x^2-x-2$

Step-by-step explanation:

You need to consider that the additive inverse of a polynomial is that polynomial that consists of the opposite of each term of the polynomial given.

Then, the additive inverse of:

a) $-6x^2-x-2$ is : $6x^2+x+2$

b) $6x^2-x+2$ is : $-6x^2+x-2$

c) $6x^2+x-2$ is : $-6x^2-x+2$

d) $6x^2+x+2$ is : $-6x^2-x-2$

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Elis [28]

Answer:

D) y=5x+20

Step-by-step explanation:

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2 years ago

Using the curve of best fit, what would be the output (y) when the input (x) is 7?

IrinaVladis [17]

Answer:

y = 260

Step-by-step explanation:

locate x = 7 on the x- axis, go vertically up to meet the graph at (7, 260 )

when input is 7 then output y = 260

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2 years ago

2<br> .<br> 2<br> 12n = 42<br> NEED HELP ASAP⬆️

Anni [7]

Answer:

—————

n + 8

Step-by-step explanation:

Step by Step Solution:

More Icon

STEP

Equation at the end of step 1

((12•(n3))-(24•(n2))) (12n-42)

—————————————————————•———————————————————

(((4•(n2))-22n)+28) ((6•(n3))+(24•3n2))

STEP

Equation at the end of step

((12•(n3))-(24•(n2))) (12n-42)

—————————————————————•——————————————————

(((4•(n2))-22n)+28) ((2•3n3)+(24•3n2))

STEP

12n - 42

Simplify ——————————

6n3 + 48n2

STEP

Pulling out like terms

4.1 Pull out like factors :

12n - 42 = 6 • (2n - 7)

STEP

Pulling out like terms

5.1 Pull out like factors :

6n3 + 48n2 = 6n2 • (n + 8)

Equation at the end of step

((12•(n3))-(24•(n2))) (2n-7)

—————————————————————•————————

(((4•(n2))-22n)+28) n2•(n+8)

STEP

Equation at the end of step

((12•(n3))-(24•(n2))) (2n-7)

—————————————————————•————————

((22n2-22n)+28) n2•(n+8)

STEP

Equation at the end of step

((12•(n3))-(23•3n2)) (2n-7)

————————————————————•————————

(4n2-22n+28) n2•(n+8)

STEP

Equation at the end of step

((22•3n3) - (23•3n2)) (2n - 7)

————————————————————— • ————————————

(4n2 - 22n + 28) n2 • (n + 8)

STEP

12n3 - 24n2

Simplify ——————————————

4n2 - 22n + 28

STEP

Pulling out like terms

10.1 Pull out like factors :

12n3 - 24n2 = 12n2 • (n - 2)

STEP

Pulling out like terms

11.1 Pull out like factors :

4n2 - 22n + 28 = 2 • (2n2 - 11n + 14)

Trying to factor by splitting the middle term

11.2 Factoring 2n2 - 11n + 14

The first term is, 2n2 its coefficient is 2 .

The middle term is, -11n its coefficient is -11 .

The last term, "the constant", is +14

Step-1 : Multiply the coefficient of the first term by the constant 2 • 14 = 28

Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is -11 .

-28 + -1 = -29

-14 + -2 = -16

-7 + -4 = -11 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -4

2n2 - 7n - 4n - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

n • (2n-7)

Add up the last 2 terms, pulling out common factors :

2 • (2n-7)

Step-5 : Add up the four terms of step 4 :

(n-2) • (2n-7)

Which is the desired factorization

Canceling Out :

11.3 Cancel out (n-2) which appears on both sides of the fraction line.

Equation at the end of step

6n2 (2n - 7)

—————— • ————————————

2n - 7 n2 • (n + 8)

STEP

Canceling Out

12.1 Cancel out (2n-7) which appears on both sides of the fraction line.

Canceling Out :

12.2 Canceling out n2 as it appears on both sides of the fraction line

Final result :

—————

n + 8

8 0

3 years ago

The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar busi

eimsori [14]

Answer:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=4.2$ represent the sample mean

$s=1.4$ represent the sample standard deviation

n=16 represent the sample selected

$\alpha=0.05$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 3.6, the system of hypothesis would be:

Null hypothesis: $\mu = 3.6$

Alternative hypothesis: $\mu \neq 3.6$

If we analyze the size for the sample is < 30 and we know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Critical values

On this case since we have a bilateral test we need to critical values. We need to use the t distribution with $df=n-1=16-1=15$ degrees of freedom. The value for $\alpha=0.05$ and $\alpha/2=0.025$ so we need to find on the t distribution with 15 degrees of freedom two values that accumulates 0.025 of the ara on each tail. We can use the following excel codes:

"=T.INV(0.025,15)" "=T.INV(1-0.025,15)"

And we got $t_{crit}=\pm 2.131$

So the decision on this case would be:

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

Conclusion

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

3 0

3 years ago

Find the measures of the angles of the ∆ABC if m∠A : m∠B:m∠C=2:3:4

dsp73

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