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Triss [41]
3 years ago
11

In the figure, side AB is given by the expression 5x+5x+3, and side BC is 3x+92x−4. The simplified expression for the area of re

ctangle ABCD is ________ and the restriction on x is_____
Mathematics
1 answer:
kherson [118]3 years ago
3 0
We are asked to solve for the simplified expression of rectangle ABCD and the restriction on x. The solution is shown below:
L = 3X + 92X -4 = 95X -4
W =5X + 5X +3 =10X +3

The formula is Area = L*W
Area = (95x-4) * (10x +3)
Area = 950x² + 285x - 40x -12
 Area = 950x² + 245x -12
 x should be greater than zero    
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c. Debbie and Jan are both in the 28% tax bracket. Since the interest is deductible, how much would Debbie and Jan each save in
alisha [4.7K]

Step-by-step explanation:

Let's assume Debbie paid $1700 in interest, while Jan paid $9000.

Debbie Saves = $1700* 0.28

Jan Saves = $9000 * 0.28

Debbie Saves $476 in taxes

Jan Saves $2520 in taxes

7 0
3 years ago
A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is
Ainat [17]

Answer:

15.2~mph

Step-by-step explanation:

Let the time flown by the flying carpet be t. Then, we have that (2.4)/t=(1.4)/t+2*4.

We multiply both sides of the equation by t to get 2.4=1.4+8t.

We subtract 1.4 from both sides to get 1=8t.

We divide both sides of the equation by t=1/8.

We know that the speed of the flying carpet in still wind is the average of the rates of the speed of the flying carpet with the wind and against the wind.

The speed with wind is (2.4)/(1/8)=19.2mph.

The speed against wind is (1.4)/(1/8)=11.2mph.

The speed in still wind is (19.2+11.2)/2=(30.4)/2=15.2.

Therefore, the answer is \boxed{15.2~mph} and we're done!

4 0
3 years ago
Rectangle ABCD has vertex coordinates A(1, -2), B(4, -2), C(4,-4), and D(1,
hram777 [196]
The coordinates of C is, (3,-1)
A is the. Answer
4 0
3 years ago
Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four
gregori [183]

Answer and step-by-step explanation:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = -5x + 750

Next we divide both sides by 2:

2y/2 = -5x/2 + 750/2

y = -2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width.  In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x(-2.5x+375)

A = -2.5x² + 375x

This is a quadratic equation, with values a = -2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex.  First we find the axis of symmetry, using the equation

x = -b/2a

x = -375/2(-2.5) = -375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = -2.5x² + 375x

A = -2.5(75)² + 375(75) = -2.5(5625) + 28125 = -14062.5 + 28125 = 14062.5

6 0
3 years ago
What is the slope of the line that passes through the points (-2, -11) and (-9, 17)?
Vinil7 [7]

rise/run

17--11/-9--2

=28/-7

=-4

Done!

6 0
3 years ago
Read 2 more answers
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