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3 years ago

Can the expression be factored furthered? show your work.(x2 + 4) (x2 -4)

Mathematics

2 answers:

lukranit [14]3 years ago

8 0

$(x^2 + 4) (x^2 -4) =\\
(x^2+4)(x-2)(x+2)$

torisob [31]3 years ago

5 0

Yes.The second factor is the difference of 2 squares,
so the second factor alone becomes

(x² - 4) = (x + 2) (x - 2)

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If g(x)=11x+3 find g(x+7) and g(x)+g(7).

Liono4ka [1.6K]

Answer:

g(x + 7) = 11x + 80

g(x) + g(7) = 11x + 83

Step-by-step explanation:

g(x + 7) = 11(x + 7) + 3 = 11x + 77 + 3 = 11x + 80

g(x) + g(7) = 11x + 3 + 11(7) + 3 = 11x + 3 + 77 + 3 = 11x + 83

8 0

2 years ago

A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the leng

chubhunter [2.5K]

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

<h3>How to determine the maximum length of each prism?</h3>

The surface area of the hexagonal prism is calculated using:

A = 6al + 3 $\sqrt$ 3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3 $\sqrt$ 3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48 $\sqrt$ 3]

Divide both sides by 0.04

275 = 24l + 48 $\sqrt$ 3

Subtract 48 $\sqrt$ 3 from both sides

24l = 275 - 48 $\sqrt$ 3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm

Read more about surface areas at:

brainly.com/question/6613758

6 0

1 year ago

What is 2 3/8 in a improper fraction?

FromTheMoon [43]

Answer:

See below a shorter way to convert 2 3 8 to an improper fraction. Step 1: Multiply the whole number part (2) by the denominator (8). Step 2: Add the product from Step 1 (16) to the numerator (3). Step 3: Write that result (19) above the denominator.

Step-by-step explanation:

hope this helps you if it does plz mark brainiest

4 0

2 years ago

Read 2 more answers

Use the picture for the question and the answer choices:)

Orlov [11]

Parenthesis first 5-2=3.

7^2=49

-3*3=-9

49-9=40.

A is your answer.

8 0

2 years ago

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating

Natali [406]

Answer:

a) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

b) Test statistic t=-1.565

P-value = 0.0612

NOTE: the sample size is n=65.

c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

d) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

Test statistic t=-1.565

Critical value tc=-1.669

t>tc --> Do not reject H0

Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Then, the null and alternative hypothesis are:

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

The significance level is 0.05.

The sample has a size n=65.

The sample mean is M=30.15.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565$

The degrees of freedom for this sample size are:

$df=n-1=65-1=64$

This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

<u>Critical value approach</u>

<u></u>

At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.

As the test statistic is greater than the critical value, it falls in the acceptance region.

The null hypothesis failed to be rejected.

6 0

2 years ago