You are wrong.
1, 2, 3 and 4 are correct.
5. 75%
6 is also correct
7. 100%
8. 50%
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A 
Answer:
1000
Step-by-step explanation:
x = 1, y = -1, and z = 2
Problem: 2x^2+3x-9
For a polynomial of the form, ax^2+bx+c rewrite the middle term as the sum of two terms whose product a·c=2·-9=-18 and whose sum is b=3.
Factor 3 out of 3x
2x^2+3(x)-9
Rewrite 3 as -3 plus 6.
2x^2+(-3+6)x-9
Apply the distributive property
2x^2(-3x+6x)-9
Remove the parentheses
2x^2-3x+6x-9
Factor out the greatest common factor from each group
Group the first two terms and the last two terms
(2x^2-3x) (6x-9)
Factor out the greatest common factor in each group.
x(2x-3)+3(2x-3)
Factor the polynomial by factoring out the greatest common factor, 2x-3
(x+3) (2x-3). So, the quotient is 2x-3
Patrick will be able to paint the home on his own after a ten-hour effort.
This is further explained below.
<h3>How much time will it take for Patrick to paint the house by himself?</h3>
Generally, the equation for time is mathematically given as
1/(t+4) + 1/(t+9) = 1/t
Therefore
[1/(t+4)] (t+4)(t+9)(t) + [1/(t+9)](t+4)(t+9)(t) = (1/t)(t+4)(t+9)(t)
(t² + 9t) + (t² + 4t) = t² + 13t + 36
Place the equation on the left side of the page and make it equal to 0. Use the additive inverse property as follows:
t² + t² - t² + 9t + 4t - 13t - 36 = 0
2t² - t² + 13t - 13t - 36 = 0
t² - 36 = 0
Calculate the product of the difference of two squares using the formula t2 - 36 = 0.
Both the total and the difference between the two terms constitute the factors.
(t + 6) (t - 6) = 0
t + 6 = 0
t = -6
t - 6 = 0
t = 6
Choose the positive value for time, t = 6 hours.
It will take 10 hours for Patrick to paint the house alone.
Patrick will be able to paint the home on his own after a ten-hour effort.
Read more about time
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