Answer:
See picture attached
Step-by-step explanation:
<h3>
Answer: False</h3>
==============================================
Explanation:
I'm assuming you meant to type out
(y-2)^2 = y^2-6y+4
This equation is not true for all real numbers because the left hand side expands out like so
(y-2)^2
(y-2)(y-2)
x(y-2) .... let x = y-2
xy-2x
y(x)-2(x)
y(y-2)-2(y-2) ... replace x with y-2
y^2-2y-2y+4
y^2-4y+4
So if the claim was (y-2)^2 = y^2-4y+4, then the claim would be true. However, the right hand side we're given doesn't match up with y^2-4y+4
--------------------------
Another approach is to pick some y value such as y = 2 to find that
(y-2)^2 = y^2-6y+4
(2-2)^2 = 2^2 - 6(2) + 4 .... plug in y = 2
0^2 = 2^2 - 6(2) + 4
0 = 4 - 6(2) + 4
0 = 4 - 12 + 4
0 = -4
We get a false statement. This is one counterexample showing the given equation is not true for all values of y.
Answer:
(a) The system of the equations
has no solution.
(b) The system of the equations
has many solutions 
Step-by-step explanation:
(a) To find the solutions of the following system of equations
you must:
Multiply
by 2:

Subtract the equations

0 = -3 is false, therefore the system of the equations has no solution.
(b) To find the solutions of the system
you must:
Isolate x for 

Substitute
into the second equation

The system has many solutions.
Isolate y for 

Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
The simplification form of the provided expression is 2x²y⁴ option first is correct.
<h3>What is an expression?</h3>
It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
![= \rm \sqrt[3]{8x^6y^{12}}](https://tex.z-dn.net/?f=%3D%20%5Crm%20%5Csqrt%5B3%5D%7B8x%5E6y%5E%7B12%7D%7D)
![\rm =\sqrt[3]{8}\sqrt[3]{x^6}\sqrt[3]{y^{12}}](https://tex.z-dn.net/?f=%5Crm%20%3D%5Csqrt%5B3%5D%7B8%7D%5Csqrt%5B3%5D%7Bx%5E6%7D%5Csqrt%5B3%5D%7By%5E%7B12%7D%7D)
![\rm \rm = \rm 2\sqrt[3]{x^6}\sqrt[3]{y^{12}}](https://tex.z-dn.net/?f=%5Crm%20%5Crm%20%3D%20%5Crm%202%5Csqrt%5B3%5D%7Bx%5E6%7D%5Csqrt%5B3%5D%7By%5E%7B12%7D%7D)
![\rm =2x^2\sqrt[3]{y^{12}}](https://tex.z-dn.net/?f=%5Crm%20%3D2x%5E2%5Csqrt%5B3%5D%7By%5E%7B12%7D%7D)

Thus, the simplification form of the provided expression is 2x²y⁴ option first is correct.
Learn more about the expression here:
brainly.com/question/14083225
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