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2 years ago

Simplify: -3(y + 2)^2– 5 + 6y What is the simplified product in standard form?

Mathematics

2 answers:

Ymorist [56]2 years ago

7 0

-3(y²+4y+4) - 5 +6y

-3y² - 12y - 12 -5 + 6y

-3y² -6y -17

-(3y²+6y+17)

VMariaS [17]2 years ago

4 0

Answer:

-3y^2 - 6y - 17

Step-by-step explanation:

-3(y + 2)^2 - 5 + 6y =

Expand the square of the binomial.

= -3(y + 2)(y + 2) - 5 + 6y

Use FOIL to multiply the binomials.

= -3(y^2 + 2y + 2y + 4) - 5 + 6y

Combine like terms inside the parentheses.

= -3(y^2 + 4y + 4) - 5 + 6y

Distribute the -3.

= -3y^2 - 12y - 12 - 5 + 6y

Combine like terms.

= -3y^2 - 6y - 17

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Answer:

y = 100 - 2.5 x is the equation that represents her total profit from

the project

Step-by-step explanation:

The given is:

1. An electrician earns 100 dollars for a project installing light fixtures

2. She must pay for the light fixtures herself and they cost 2 dollars

and 50 cents each

3. x represent the number of light fixtures and y represent her

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Her profit is the amount of money she has left over after paying for

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∵ The cost of each light fixtures is 2 dollars and 50 cents

- Let us change the cents to dollar

∵ $1 = 100 cents

∴ 50 cents = dollar

∴ 2 dollars and 50 cents = $2.5

∵ Her profit = The money she earns - The money she pays

∴ The cost of each light fixtures = $2.5

∵ She installs x light fixtures

∴ She pays 2.5 x dollar

∵ She earns $ 100 for installing x light fixtures

∵ Her profit is $y

∴ y = 100 - 2.5 x

y = 100 - 2.5 x is the equation that represents her total profit from

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Step-by-step explanation:

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2 years ago

The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

Thepotemich [5.8K]

<span>Use the distance formula to find the length of each side and then add the lengths.

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LenaWriter [7]

Answer:

Step-by-step explanation:

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Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares estimation.

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In order to conduct this test we are assuming the following conditions:

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c) We assume that the Y values are independent and the distribution of Y is normal

The significance level is provided and on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

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$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The confidence interval for the slope would be given by this formula:

$\hat \beta_1 + t_{n-2, \alpha/2} \frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

And using the last formula we got that the confidence interval for the slope coefficient is given by:

$-0.88 < \beta_1$

IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:

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Answer:

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