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olga55 [171]
3 years ago
6

Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates

of the vertices.
R(1, -3), S(4, -1), T(2, 2), U(-4, -2)

Click on the graphic to complete the answer.
Mathematics
1 answer:
Mrac [35]3 years ago
3 0
Slope RS: 2/3
Slope ST: -3/2
Slope TU: 4/6 = 2/3
Slope UR: -1/5

Sides RS and TU have the same slope, so they are parallel.
The slope of side ST is the negative reciprocal of the slopes of sides RS and TU, so side ST is perpendicular to sides RS and TU.
Side UR is not parallel or perpendicular to any other side.

The quadrilateral is a trapezoid.
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Solve the equation 3(x - 7) = 42
Effectus [21]

Answer:

x=21.

Step-by-step explanation:

First you distribute 3 to the parenthesis. You should get 3x-21=42 at this point. Then you add 21 to 42 to get 63. Here you should be at 3x=63. Divide 63 by 3 to get x=3

6 0
3 years ago
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The answer please for my online class
Eddi Din [679]

Answer:

B. -500

Step-by-step explanation:

\dfrac{(2a^4)^2}{a^0a^5} =

= \dfrac{2^2a^8}{a^5}

= 4a^3

= 4(-5)^3

= 4(-125)

= -500

3 0
2 years ago
a rectangular box with two sqaure opposite ends is to hold 8000 cubic inches. find the dimensions of the cheapest box if tge rec
AveGali [126]

Answer:

the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in

Step-by-step explanation:

since the box has a volume V

V= x*y*z = b=8000 in³

since y=z (square face)

V= x*y² = b=8000 in³

and the cost function is

cost = cost of the square faces *  area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides

C = a* 2*y² +  a* 2*x*y + 15*a* 2*x*y =  2*a* y² +  32*a*x*y

to find the optimum we can use Lagrange multipliers , then we have 3  simultaneous equations:

x*y*z = b

Cx - λ*Vx = 0 → 32*a*y -  λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ

Cy - λ*Vy = 0  → (4*a*y + 32*a*x) - λ*2*x*y = 0

4*a*32/λ  + 32*a*x - λ*2*x*32*a/λ = 0

128*a² /λ +  32*a*x - 64*a*x = 0

32*a*x = 128*a² /λ

x  = 4*a/λ

x*y² = b

4*a/λ * (32*a/λ)² = b

(a/λ)³ *4096 =  8000 m³

(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in

then

x  = 4*a/λ = 4*5/4 in = 5 in

y=32*a/λ = 32*5/4 in = 40 in

then the box has dimensions 5 in x 40 in x 40 in

3 0
3 years ago
Hi answeeeer and no links
ololo11 [35]
Paper he needs = total surface area

So to break it down into 2D shapes, that prism has 2 2D triangles, and 3 2D rectangles of different sizes.

The triangles are the same size, since you have 2, just multiply 2 by the formula for the area of a triangle: 1/2(base)(height) which is 2x1/2(5)(12) = 60

Next you'll need the area of all the rectangles: length x width. which would be (5 x 5) + (13 x 5) + (12 x 5) = 150

So the total amount of wrapping paper he'd need is 150mi^2
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Which ordered pair is the reflection of (5,-8) across the x axis and the y axis?
Lerok [7]
The ordered pair would be (-5,8)
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