Answer:
x=6
Step-by-step explanation:
81^x = 27 ^(x+2)
81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation
3^4^x = 3^3^(x+2)
When we have a power to a power we can multiply the exponents
a ^b^c = a^(b*c)
3^(4x) = 3^(3*(x+2))
Since the bases are the same, the exponents have to be the same
a^b = a^c means b=c
4x = 3(x+2)
Now we can solve for x
Distribute
4x = 3x+6
Subtract 3x from each side
4x-3x = 3x-3x+6
x = 6
Answer:
14 in^3.
Step-by-step explanation:
The volume = volume of the bottom prism + volume of the top pyramid
= area of base * height of the prism + 1/3 * area of base * height of the pyramid
= 2 * 1.5 * 4 + 1/3 * (2*1.5) * 2
= 3*4 + 1/3 * 6
= 14 in^3.
Let's use the variable x to represent the length of the first and second pieces.
If the third piece has twice the length of the first and second, its length is 2x.
If the fourth piece has half the length of the first and second, its length is 0.5*x.
Adding all four pieces and equating to 54 inches, we have:
So the length of each piece is:
12 inches, 12 inches, 24 inches and 6 inches.
Distribute
2z-1=z+8-2z
add like terms
2z-1=-z+8
add z to both sides
3z-1=8
add 1 to both sides
3z=9
divide both sides by 3
z=3
Answer:
x = -5
y = 2
Step-by-step explanation:
x = – 2y – 1
= -x - 2y - 1
-x - 2y = 1
x = – 5y + 5
= -x - 5y + 5
-x - 5y = -5
-x - 2y = 1
-x - 5y = -5
___________--
3y = 6
y = 6/3
<u>y = 2</u>
-x - 2y = 1
-x - 2(2) = 1
-x - 4 = 1
-x = 1 + 4
-x = 5
<u>x = -5</u>