The equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x
<h3>How to evaluate the expression?</h3>
The expression is given as:
(8x)^-2/3 * (27x)^-1/3
Evaluate the exponent 8^-2/3
(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * (27x)^-1/3
Evaluate the exponent (27x)^-1/3
(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * 1/3(x)^-1/3
Multiply 1/4 and 1/3
(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^-2/3 * (x)^-1/3
Evaluate the exponent
(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-2/3 -1/3)
This gives
(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-1)
So, we have
(8x)^-2/3 * (27x)^-1/3 = 1/12x
Hence, the equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x
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Answer:
12°, 78°, 90°
Step-by-step explanation:
let the third angle be x then the second angle is 7x - 6
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
x + 7x - 6 + 90 = 180, that is
8x + 84 = 180 ( subtract 84 from both sides )
8x = 96 ( divide both sides by 8 )
x = 12
Thus second angle = 12° and third = 7(12) - 6 = 84 - 6 = 78°
The 3 angles are 12°, 78° and 90°
Answer: The cost per game is $5.5
Step-by-step explanation:
Zhang Lei spent $20.00 during his last outing at the bowling alley. There is a one time shoe rental fee of $3.50. He spent the rest of the money on bowling a number of games.
This means that amount paid for x number of games = 20 - 3.5 = $16.5
If it took Zhang Lei 45 minutes to bowl each game and he spent 2 hours and 15 minutes bowling, total time spent in minutes is 120+ 15 = 135 minutes. Therefore, the number of games is played is 135/45 = 3
If the total number of games played cost 16.5, therefore, the cost per game will be 16.5/3 = $5.5
=Y2-10Y
We move all terms to the left:
-(Y2-10Y)=0
We add all the numbers together, and all the variables
-(+Y^2-10Y)=0
We get rid of parentheses
-Y^2+10Y=0
We add all the numbers together, and all the variables
-1Y^2+10Y=0
a = -1; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-1)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
Y1=−b−Δ√2aY2=−b+Δ√2a
Δ‾‾√=100‾‾‾‾√=10
Y1=−b−Δ√2a=−(10)−102∗−1=−20−2=+10
Y2=−b+Δ√2a=−(10)+102∗−1=0−2=0
10 is the least common denominator
