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3 years ago

Consider the diagram below. Which of the following represent the values of x,y, and z to the nearest hundredth?

Mathematics

1 answer:

astraxan [27]3 years ago

7 0

See the attached figure to better understand the problem

we know that
in the triangle BCD
y²+5.66²=z²-------> y²=z²-5.66²------> equation 1

in the triangle ABC
y²+5.66²=x²-------> y²=x²-5.66²------> equation 2

equals 1 and 2

z²-5.66²=x²-5.66²--------> z²=x²---------> z=x

if z=x then
angle A=45°
angle D=45°

in the triangle ABD
cos 45=z/(5.66*2)-------> z=11.32*cos 45-----> 11.32*√2/2----> 8
z=8
x=8

y²=z²-5.66²------> 8²-5.66²-----> y²=31.96------> y=5.65

the answer is
the value of x is 8
the value of z is 8
the value of y=5.65

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A pentagonal prism has a height of 9 feet, and each base edge is 3 feet. Find the volume. Round your answer to the nearest hundr

OLga [1]

Height of the pentagon = 9 ft

Edge of base = 3 ft

$area of pentagon = \frac{s^{2}n}{4 tan\left ( \frac{180}{n} \right )}$

s is the length of any side = 3

n is the number of sides = 5

tan is the tangent function calculated in degrees

$\\ \\\\area of pentagon = \frac{3^{2}(5)}{4 tan\left ( \frac{180}{5} \right )}\\\\\\area of pentagon = \frac{9(5)}{4 tan\left ( 36 \right )}\\\\area of pentagon = \frac{45}{4 ( 0.7265 )}\\\\area of pentagon = \frac{45}{2.906}\\\\area of pentagon = 15.4852$

Volume of the pentagon = area of base (height )

Volume of the pentagon = 15.4852 (9)

Volume of the pentagon = 139.366

Volume of the pentagon = 139.37 cu.ft

5 0

3 years ago

Read 2 more answers

A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

morpeh [17]

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

$x^2 +(x+7)^2=(x+9)^2\\\\$

Expand the terms in brackets

$x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81$

collect like terms

$x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0$

solve for x in the quadratic equation by factorization

$x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8$

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

6 0

3 years ago

37-(y-19)=2y this is a problom from rsm

ankoles [38]

Answer:

y = 56/3

Step-by-step explanation:

Distribute:

37 - (y - 19) = 2y

37 - y + 19 = 2y

Add the numbers:

37 - y + 19 = 2y

56 - y = 2y

Rearrange the terms:

56 - y = 2y

-y + 56 = 2y

Solution:

y = 56/3

8 0

2 years ago

-2(-9m-2)-1=27+10m<br><br><br> it’s a multi-step equation!

Basile [38]

Answer:

m=3

Step-by-step explanation:

expand and move the terms around

18m+4-1=27+10m

8m=24

m=3

7 0

3 years ago

Find the product 12 times 2/3 <br> simplify. Your answer completely

Finger [1]

Answer:

2/3 X 12 =8

Step-by-step explanation:

-----. X 12 =2 x 12= 24 Which is 24/3 =8

7 0

2 years ago