A point P(3,4)is reflected in the x-axis, then rotated by 90 degrees clockwise about the origin.What are the coordinates of the image of P?

Answers

Answer 1

Answer:

Answer:

(-4, -3)

Step-by-step explanation:

When a point is reflected in the x-axis, the x-coordinate does not change, and the y-coordinate becomes negative:

(x, y) → (x, -y)

Therefore, if point P(3, 4) is reflected in the x-axis, then:

P' = (3, -4)

When a point is rotated90° clockwise about the origin, it produces a point that has the coordinates (y, -x):

(x, y) → (y, -x)

Therefore, if point P'(3, -4) is rotated 90° clockwise about the origin, then:

P'' = (-4, -3)

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Awaste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 19y * d ^ 3 of debris. Find the dimensions of the dumpster that will minimize its surface area.

Answers

Answer:

1.92 yd x 3.83 yd x 2.58 yd

Step-by-step explanation:

We have given a rectangular base, that its twice as long as it is wide.

It must hold 19 yd³ of debris.

Lets minimize the surface area, subject to the restriction of volume (19 yd³)

The surface is given by:

$S=2(w*h+w*2w+2wh)=2(3wh+2w^2)$

The volume restriction is:

$V=w*2w*h=2w^2h=19\n\nh=(9.5)/(w^2)$

replacing h in the surface equation, we have:

$S=2(3wh+2w^2)=6w((9.5)/(w^2))+4w^2=57w^(-1)+4w^2$

Derivate the above equation and set it to zero

$dS/dw=57(-1)w^(-2) + 8w=0\n\n57w^(-2)=8w\n\nw^3=57/8=7.125\n\nw=\sqrt[3]{7.124} =1.92$

The height will be:

$h=9.5/w^2=9.5/(1.92^2)=9.5/2.69=2.58$

Therefore,The dimensions that minimize the surface are:

Wide: 1.92 yd

Long: 3.83 yd

Height: 2.58 yd

Which fraction is equivalent to 4/10 6/8 2/5 3/5

Answers

Answer:

2/5 is equal to 4/10

Step-by-step explanation:

Answer:

2/5 is equivalent when you divide both numbers by 2

There is an "X" drawn on a sheet of paper. One of the smaller angles created is 57 degrees. What are the other 3 angle measures? What are the two typed of angle pairs we need to use?

Answers

in total the answer has to be 180 degrees so the other 2 angels would be any 2 numbers that when you add them and 57 together you get 180

According to the EPA, about 40 million U.S. tons of hazardous waste is produced each year. If individual household waste makes up 1.6 million tons of this waste, what percent of the total hazardous amount produced is household waste? A. 0.04% B. 0.03% C. 0.25% D. 2.5% E. 4%

Answers

Answer:

C.0.25%

Step-by-step explanation:

40/1.6=25

Then convert to percentage value by moving the decimal 2 places to the left.

25 turns into 0.25.

Factor
3x ^2 +20x+12

Answers

$3x^2+20x+12=3x^2+18x+2x+12\n\n=3x(x+6)+2(x+6)=(x+6)(3x+2)$

Five cakes cost 4.00 how much do 7 cost

Answers

The cost of 7 cakes will be equal to 5.6.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the cost of 5 cakes is 4. The cost of 7 cakes will be calculated as,

5 cakes = 4

1 cake = 4 / 5

7 cakes = ( 4 x 7 ) / 5

7 cakes = 5.6

To know more about an expression follow

brainly.com/question/936813

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you need to divide 5/4 and youll get the price for 1 cake (1.25) then just add 2 more times to 5 (6.5) is the total

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