The length of the unknown sides of the triangles are as follows:
CD = 10√2
AC = 10√2
BC = 10
AB = 10
<h3>Triangle ACD</h3>
ΔACD is a right angle triangle. Therefore, Pythagoras theorem can be used to find the sides of the triangle.
where
c = hypotenuse side = AD = 20
a and b are the other 2 legs
lets use trigonometric ratio to find CD,
cos 45 = adjacent / hypotenuse
cos 45 = CD / 20
CD = 1 / √2 × 20
CD = 20 / √2 = 20√2 / 2 = 10√2
20² - (10√2)² = AC²
400 - 100(2) = AC²
AC² = 200
AC = √200 = 10√2
<h3>
Triangle ABC</h3>
ΔABC is a right angle triangle too. Therefore,
Using trigonometric ratio,
cos 45 = BC / 10√2
BC = 10√2 × cos 45
BC = 10√2 × 1 / √2
BC = 10√2 / √2 = 10
(10√2)² - 10² = AB²
200 - 100 = AB²
AB² = 100
AB = 10
learn more on triangles here: brainly.com/question/24304623?referrer=searchResults
The 3 lbs of candy is irrelevant, so we can discard that. All you need to do is divide 147 by 26, which is 5.65 pieces of candy. Each student will get 5 pieces, with a few left over.
Answer:
The original length was 41 inches and the original width was 16 inches
Step-by-step explanation:
Let
x ----> the original length of the piece of metal
y ----> the original width of the piece of metal
we know that
When squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box
The dimensions of the box are

The volume of the box is equal to


so

simplify
-----> equation A
Remember that
The piece of metal is 25 in longer than it is wide
so
----> equation B
substitute equation B in equation A

solve for y

Solve the quadratic equation by graphing
using a graphing tool
The solution is y=16
see the attached figure
Find the value of x

therefore
The original length was 41 inches and the original width was 16 inches
A) Width = 9/2, length = 10
Rectangle area = length(l)x width(w)
9/2 = 4.5
4.5(l) x 10(w) = 45ft
Answer:

Step-by-step explanation:
Given expression is:
![(\sqrt[8]{x^7} )^{6}](https://tex.z-dn.net/?f=%28%5Csqrt%5B8%5D%7Bx%5E7%7D%20%29%5E%7B6%7D)
First we will use the rule:
![\sqrt[n]{x} = x^{\frac{1}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D)
So for the given expression:
![\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bx%5E%7B7%7D%7D%3D%28x%5E%7B7%7D%20%29%5E%7B%5Cfrac%7B1%7D%7B8%7D%20%7D)
We will use tha property of multiplication on powers:


Applying the outer exponent now

