Let s and g represents the numbers of suits and gowns produced.
The number of zippers used is 2s+g.
The number of buttons used is 5s+8g.
In order to use all of the available zippers and buttons, we must have ...
- 2s + g = 171
- 5s + 8g = 576
Cramer's rule tells you the solution to the system
Is given by
- x = (bf-ey)/(bd-ea)
- y = (cd-fa)/(bd-ea)
Using this rule on the equations for zippers and buttons, we have
... s = (1·576 -8·171)/(1·5 -8·2) = -792/-11 = 72
... g = (171·5 -2·576)/-11 = -297/-11 = 27
72 suits and 27 gowns can be made from available zippers and buttons.
Option A
The solution is 
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
3x + 6y = 1 ------ eqn 1
x - 4y = 1 ------ eqn 2
We have to find solution to system of equations
We can use substitution method
From eqn 2,
x = 1 + 4y -------- eqn 3
Substitute eqn 3 in eqn 1
3(1 + 4y) + 6y = 1
3 + 12y + 6y = 1
18y = 1 - 3
18y = -2
Divide both sides by 18

Substitute the above value of y in eqn 3

Thus solution is 
The answer is a = 3/4 = 0.75
First get rid of the paranthesis,

Then set the denominators equal:

Then remove the denominators and solve:

Eliminate -12a^2 by adding 12a^2 to both sides:

Take the fourth root of them or take the square root twice:
![\sqrt[4]{256 {a}^{4} } = \sqrt[4]{81} \\ 4a = 3](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B256%20%7Ba%7D%5E%7B4%7D%20%7D%20%20%3D%20%20%5Csqrt%5B4%5D%7B81%7D%20%20%20%5C%5C%20%204a%20%3D%203)
Divide both sides by 4:
3(2x^2 + 4) - 4(x - 6)
= 6x^2 + 12 - 4x + 24
= 6x^2 - 4x + 36
therefore first answer is correct
Answer:
∠C=90°
∠A=67°
∠B=23°
Step-by-step explanation:
For angle C:
Thales' Theorem states that an angle inscribed across a circle's diameter is always a right angle.
Therefore, since AB is the diameter(hypotenuse) then angle C is the right angle. (90°)
For Angle A:
The measure of arc BC= 134 degrees. We can just use a formula for an inscribed triangle. ∠A = 1/2 (mBC)
∠A= (1/2)134
∠A= 77°
For angle B:
All triangle angles all add up to 180. We can just subtract angles A and C from 180°:
∠B = 180-(90+67)
∠B = 23°