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stepladder [879]

2 years ago

8

A window in the shape of a rectangle as shown below has a width of x+5 and a length of x^2- 3x+7 express the area of the rectang

le as a single polynomial in simplest form

1 answer:

Ksju [112]2 years ago

6 0

Answer:

$x^3+x^2-5x+28$

Step-by-step explanation:

since a=lw, the area is (x^2-3x+7)(x+4)

1. distribute parentheses $\left(x^2-3x+7\right)\left(x+4\right)=x^2x+x^2\cdot \:4+\left(-3x\right)x+\left(-3x\right)\cdot \:4+7x+7\cdot \:4$

2. apply +(-a)=-a rule $x^2x+4x^2-3xx-3\cdot \:4x+7x+7\cdot \:4$

3. Simplify

Steps to simplify:

$x^2x=x^3$

$3xx=3x^2$

$3\cdot \:4x=12x$

$7\cdot \:4=28$

$x^3+4x^2-3x^2-12x+7x+28$

4. Add like terms $=x^3+4x^2-3x^2-5x+28$

5. Add like terms $=x^3+x^2-5x+28$

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Brainly which is the distance between (-3,4) and (7,13)

Veseljchak [2.6K]

Answer:

Root 181

Step-by-step explanation:

Using distance formula, we know that the answer will be the square root of 181. Unfortunately, this is not a perfect square, and it is prime, so that number will remain the same.

Distance Formula: $\sqrt{(13-4)^{2} + (7+3})^2} = \sqrt{181}$

Hope this helped!

5 0

3 years ago

A researcher tests five individuals who have seen paid political ads about a particular issue. These individuals take a multiple

devlian [24]

Answer:

$t=\frac{46-40}{\frac{5.148}{\sqrt{5}}}=2.606$

The degrees of freedom are given by:

$df=n-1=5-1=4$

The p value wuld be given by:

$p_v =2*P(t_{(4)}>2.606)=0.060$

For this case the p value is higher than the significance level so then we can conclude that the true mean is not significantly different from 40

The distribution with the critical values are in the figure attached

Step-by-step explanation:

Information given

48, 41, 40, 51, and 50

The sample mean and deviation can be calculated with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=46$ represent the mean height for the sample

$s=5.148$ represent the sample standard deviation

$n=5$ sample size

$\mu_o =40$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test

Hypothesis to test

We want to test if the true mean for this case is equal to 40, the system of hypothesis would be:

Null hypothesis: $\mu = 40$

Alternative hypothesis: $\mu \neq 40$

The statistic is given by:

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

Replacing we got:

$t=\frac{46-40}{\frac{5.148}{\sqrt{5}}}=2.606$

The degrees of freedom are given by:

$df=n-1=5-1=4$

The p value wuld be given by:

$p_v =2*P(t_{(4)}>2.606)=0.060$

For this case the p value is higher than the significance level so then we can conclude that the true mean is not significantly different from 40

The distribution with the critical values are in the figure attached

6 0

3 years ago

A professor obtains SAT scores and freshman GPA for a group of 15 college students with the hope that she can predict GPA using

kramer

The hypothesis test analyzes the null and alternative hypothesis of the

plausibility of a correlation between the SAT scores and GPA.

The hypothesis test that would be appropriate is <u>a hypothesis test that checks that the slope of the regression line is not zero</u>.

Reasons:

The data collected by the professor = The scores of the college students

The type of scores collected = SAT scores, and GPA scores

The test that would be appropriate for the example, is the test for the

existence of a significant linear relationship between the input variable

(the SAT scores) and the output variable (the GPA)

The test is known as <u>the test for the slope of the regression line</u>

The equation of the regression line is; Y = B₀ + B₁·X

Where;

Y = The value of the GPA score (The dependent variable)

X = The value of the SAT score (The independent variable)

The test aims to check that the value the slope of the regression line is

much different from zero, such that there exist a correlation.

Learn more about hypothesis test for linear regression here:

brainly.com/question/13938204

4 0

2 years ago

What is the equivalent expression in factored form of 15x^7y^2+4x^3

tensa zangetsu [6.8K]

Answer:

x^3(15x^4y^2+4)

Step-by-step explanation:

4 0

3 years ago

HELPPP ILL GIVE BRAINLIEST IF ITS RIGHT

Veseljchak [2.6K]

Answer:

Mixed Number: 4 191919/1,000,000

Fraction: 4191919/1,000,000

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers