Trapezoid EFGH ~ trapezoid MNOP. Find the value of y.<br><br> answers in the picture

My father invests $5000 in a new bank that has an annual

jeka94

$6900

$5000+3.8%=$5190

$190x10=$1900

$5000+$1900=$6900

5 0

2 years ago

A café owner is designing a new menu and wants to include a decorative border around the outside of her food listings. Due to th

kipiarov [429]

The 13-in. by 9-in. rectangle where the food listings fit has an area of 13 in. * 9 in. = 117 in.^2

Adding 48 in.^2 for the border, the total area of the menu with the border will be 117 in.^2 + 48 in.^2 = 165 in.^2

The border has to have uniform width around the menu. We need to find the width of the border. Let the border be x inches wide. Then since you have a border at each of the 4 sides, the border will add 2x to the length of the rectangle and 2x to the width of the rectangle. The menu will have a length of 2x + 13 and a width of 2x + 9. The area of the larger rectangle must by 165 in.^2. The area of a rectangle is length times width, so we get our equation:

(2x + 13)(2x + 9) = 165

Multiply out the left side (use FOIL or any other method you know):

4x^2 + 18x + 26x + 117 = 165

4x^2 + 44x + 117 = 165

4x^2 + 44x - 48 = 0

Divide both sides by 4.

x^2 + 11x - 12 = 0

Factor the left side.

(x + 12)(x - 1) = 0

x + 12 = 0 or x - 1 = 0

x = -12 or x = 1

The solution x = -12 is not valid for our problem because the width of a border cannot be a negative number. Discard the negative solution.

The solution is x = 1.

Answer: The border is 1 inch wide.

Check. Add 2 inches to the length and width of the food listings rectangle to get 15 inches by 11 inches. A = 15 in. * 11 in.= 165 in.^2. Now subtract the area of the border, 48 in.^2, 165 in.^2 = 48 in.^2 = 117 in.^2, and you get the area of the 13-in. by 9-in. rectangle. This shows that our solution is correct.

6 0

3 years ago

Read 2 more answers

GIVING OUT BRAINLIST QUICK! NUMBER 6

Sunny_sXe [5.5K]

Answer:

40

Step-by-step explanation:

AREA=LW

L₁W₁=40

L₂W₂=160

x(L₁W₁)=L₂W₂

x(40)=160

x=40

7 0

3 years ago

Match the given angle pair to their relationship using the figure beloe

hoa [83]

Answer:

Vertical: 1

corresponding: 3

alternate interior: 2

alternate exterior: 4

6 0

2 years ago

The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked

Serggg [28]

Answer:

a) The 99% confidence interval would be given by (24.409;24.979)

b) n=464

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=47-1=46$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,46)".And we see that $t_{\alpha/2}=2.01$