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nexus9112 [7]
3 years ago
10

In each part, a and b represent the length of a leg of a right triangle, and c represents the length of its hypotenuse. Find the

missing length, given the other two lengths.

Mathematics
1 answer:
Pie3 years ago
4 0

Answer:

c=13 and a=20

Step-by-step explanation:

Here you need to use the Pythagoras theorem :

c²=a² + b²

c = √a² + b²

c = √(12)²+(5)²

c= √144+25

c = √169

c = 13

2) c²=a²+b²

    b= √c²-b²

    b= √(29)²-(21)²

    b = √400

    b = 20

In 2 you change your formula just so that it can be easier and just calculate your length straight forward but you can also just do it in the original equation

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adelina 88 [10]

Answer:

Step-by-step explanation:

3 0
3 years ago
The area of parallelogram WXYZ is approximately 45 square units.
neonofarm [45]

Answer:

Option (4)

Step-by-step explanation:

Area of a triangle = \frac{1}{2} (a.b.\text{Sin}\theta)

Where a and b are the sides of a triangle and θ is the angle between the sides a and b.

By this rule,

Area of ΔWZY = \frac{1}{2}(\text{WZ}).(\text{YZ}).\text{Sin}(115)

45 = \frac{1}{2}(\text{YZ}).(10).\text{Sin}(115)

9 = (YZ).Sin(115)°

YZ = \frac{9}{\text{Sin}(115)}

YZ = 9.93

Perimeter of parallelogram WXYZ = WX + XY + YZ + WZ

                                                         = 9.93 + 10 + 9.93 + 10

                                                         = 39.86

                                                         ≈ 40 units

Therefore, perimeter of the parallelogram is 40 units.

Option (4) is the answer.

4 0
3 years ago
An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn
Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43  inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24,  this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative  value ( -49.7)  so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0
2 years ago
What is the answer? please help
amid [387]

Answer:

<h2><em>(</em><em>4</em><em>,</em><em>5</em><em>)</em></h2>

<em>sol</em><em>ution</em><em>,</em>

<em>A</em><em>(</em><em>2</em><em>,</em><em>7</em><em>)</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>></em><em> </em><em>(</em><em>X1,</em><em>y1</em><em>)</em>

<em>B</em><em>(</em><em>6</em><em>,</em><em>3</em><em>)</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>-</em><em>></em><em>(</em><em>x2</em><em>,</em><em>y2</em><em>)</em>

<em>now</em><em>,</em>

<em>ab = ( \frac{x1 + x1}{2}  \: , \frac{y1 + y2}{2} ) \\  =  (\frac{2 + 6}{2}  \: , \frac{7 + 3}{2} ) \\  = ( \frac{8}{2}  \:,  \frac{10}{2} ) \\  = (4 ,\: 5)</em>

<em>hope</em><em> </em><em>this</em><em> </em><em>helps</em><em>.</em><em>.</em><em>.</em>

<em>Good</em><em> </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em><em>.</em>

7 0
3 years ago
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Alex_Xolod [135]

Answer:

+35 per month

Step-by-step explanation:

8 0
3 years ago
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