The expression for 8 times x is just 8x
Answer:
Step-by-step explanation:
This is probably pretty late, but I'll do it anyway.
There are 8 parts all together.
3x + 5x = 32 Combine the terms on the left.
8x = 32 Divide by 8
8x = 32/8
x = 4
Therefore the red gifts are 3*4 = 12
The green gifts are <u> 5*4 = 20</u>
Total 32 Just as it should
10×10 as an exponent would be 10². Why? Because 10×10 equals 100 and do does 10².
So the Newfoundland dog weighs 100 pounds.
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
Use the Difference Identity: cos(A - B) = cosA · cosB + sinA · sinB
Use the Double Angle Identity: cos 2Ф = 1 - 2sin²Ф
<u>Proof LHS → RHS</u>
LHS: (cosA - cosB)² + (sinA - sinB)²
Expand: cos²A - 2cosA · cosB + <u>cos²B</u> + sin²A - 2sinA · sinB <u>+ sin²B</u>
Pythagorean Identity: 2 - 2cosA · cosB - 2sinA · sinB
Factor: 2(1 - (cosA · cosB + sinA · sinB))
Difference Identity: 2(1 - (cos(A - B))
Let Ф = (A-B)/2: 2(1 - cos2Ф)
Double Angle Identity: 2(1 - (1 - 2sin²Ф))
Simplify: 2(1 - 1 + 2sin²Ф)
= 4sin²Ф
Substitute (A-B)/2=Ф: 4sin²(A-B)/2
LHS = RHS: 4sin²(A-B)/2 = 4sin²(A-B)/2 