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denis-greek [22]
2 years ago
8

Simplify sqrt(45/7y)

Mathematics
1 answer:
Alex_Xolod [135]2 years ago
7 0
8.2y that the cayse 45 is 7 byt 8.2
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Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and ro
Helga [31]

Answer:

Part 1) The shape is a trapezoid

Part 2) The perimeter is 25(4+\sqrt{2})\ units   or approximately  135.4\ units

Part 3) The area is 937.5\ units^2

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

The shape is a trapezoid

see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

P=AB+BC+CD+AD

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Find the distance AB

we have

A(-28,2),B(-21,-22)

substitute in the formula

d=\sqrt{(-22-2)^{2}+(-21+28)^{2}}

d=\sqrt{(-24)^{2}+(7)^{2}}

d=\sqrt{625}

d_A_B=25\ units

Find the distance BC

we have

B(-21,-22),C(27,-8)

substitute in the formula

d=\sqrt{(-8+22)^{2}+(27+21)^{2}}

d=\sqrt{(14)^{2}+(48)^{2}}

d=\sqrt{2,500}

d_B_C=50\ units

Find the distance CD

we have

C(27,-8),D(-4,9)

substitute in the formula

d=\sqrt{(9+8)^{2}+(-4-27)^{2}}

d=\sqrt{(17)^{2}+(-31)^{2}}

d=\sqrt{1,250}

d_C_D=25\sqrt{2}\ units

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

d=\sqrt{(9-2)^{2}+(-4+28)^{2}}

d=\sqrt{(7)^{2}+(24)^{2}}

d=\sqrt{625}

d_A_D=25\ units

Find the perimeter

P=25+50+25\sqrt{2}+25

P=(100+25\sqrt{2})\ units

simplify

P=25(4+\sqrt{2})\ units ----> exact value

P=135.4\ units

therefore

The perimeter is 25(4+\sqrt{2})\ units   or approximately  135.4\ units

step 3

Find the area

The area of trapezoid is equal to

A=\frac{1}{2}[BC+AD]AB

substitute the given values

A=\frac{1}{2}[50+25]25=937.5\ units^2

4 0
3 years ago
Which is an equivalent form of the expression 1800(1.2)^-t
ololo11 [35]

Answer:

1800(5/6)^t

Step-by-step explanation:

I don't see any answer choices, but this would be another form if it is listed. The negative exponent means that you get the reciprocal of the fraction (in this case 1.2). This turns 1.2 into (1/1.2), which is equivalent to 5/6.

7 0
1 year ago
Sung is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Alexus [3.1K]

Answer:

Step-by-step explanation:

Use the equation

89 < 75 + 0.7*M                Subtract 75 from both sides

89 - 75 < 0.7M                  Combine

14 < 0.7 M                          Divide both sides by 0.7

14/0.7 < M

20 < M

If M goes over 20 then the flat rate is cheaper.

8 0
2 years ago
HELP NOW PLEASE!!!!!!!!!!!!
musickatia [10]

Answer:

Negative numbers are used in navigation and directions determination

7 0
3 years ago
A rectangular billboard image is 5 ft wide and 4 ft high. If the available billboard space is 25 ft by 15 ft, what are the dimen
Lapatulllka [165]

Answer:

18¾ ft × 15 ft

Step-by-step explanation:

The dimensions of the billboard are 25 ft by 15 ft.

The dimensions of the image are 5 ft by 4 ft  

Case 1.<em> Expand the length of the image to 25 ft. </em>

We have multiplied the length by five, so we must multiply the width by five.

w = 5 × 4 = 20 ft. That's too big. The image will overflow the billboard

by 5 ft.


<em>Case 2. </em><em>Expand the width of the image to 15 ft. </em>

We have multiplied the width by 15/4, so we must multiply the length by 15/4.

l = 15/4 × 5 = 75/4 = . That will fit, with 6¼ ft left over.

The expanded image will be 18¾ ft × 15 ft.

In the image below, the big rectangle represents the billboard, and the red rectangle represents the original image.

The pink rectangle represents the dilation of the original image to a width of 15 ft.

5 0
3 years ago
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