Let's use the variable x to represent the number.
3x+12-5x=22
Combine like terms
-2x+12=22
Subtract 12 from both sides
-2x=10
Divide both sides by -2
x=-5
Final answer: The number is -5
144 miles on 4.5 gallons
Solution: 144mi 4.5 32mi
------------ divided by = -------------
4.5gal 4.5 1 gal
Answer:
x=2
Step-by-step explanation:
(x+2)(x-6)= y
0 = x+2 0 = x-6
The zeros of the functions are at -2 and 6 using the zero product property
We know a parabola is symmetric so the vertex is 1/2 way between the zeros
(-2+6)/2 = 4/2 =2
The x coordinate of the vertex is at 2
<h3>
Answer: sin(2x)</h3>
In other words, you'll type "sin" without quotes in the green box.
Also, you'll type "2" in the gray box, which also won't have quotes.
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Explanation:
We'll use the first hint. Note the pattern of sin cos +- cos sin which matches (somewhat) with the original expression.
Specifically, we'll use this identity
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
In this case, A = 3x and B = x
So,
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
sin(A)cos(B) - cos(A)sin(B) = sin(A - B)
sin(3x)cos(x) - cos(3x)sin(x) = sin(3x - x)
sin(3x)cos(x) - cos(3x)sin(x) = sin(2x)