In order to easily picture out the operation involving fractions, let's write it in an algebraic equation. So, the above description is written as
20x⁶/15y⁵ × 5y²/6x⁴
The first thing to do is to simplify the easiest terms: the constants. Just multiply all the constants on the numerator and all the constants on the denominator independently. The simplified constant becomes
(20*5)/(15*6) = 10/9
So, the equation to be solved now is
10x⁶y²/9y⁵ x⁴
So, I also multiplied all the variables in the numerator and denominator independently, just like the constants. Then, you apply the laws of exponents. When you divide terms with exponents of the same value of the base, you subtract the exponent on the numerator minus the denominator. It goes like this:
10/9 * x⁶⁻⁴*y²⁻⁵ = 10/9*x²y⁻³
Now, when the exponent as written to the power of a negative exponent, just simply take its reciprocal to make it positive. So, the final answer is
10x²/9y³ or that is letter D.
Answer:
B. Similar - AA
Step-by-step explanation:
Two angles in ∆ABC are congruent to two corresponding angles in ∆DEF. Thus, it follows that the third pair of angles of both triangles would also be congruent.
Therefore, the three sides of ∆ABC and corresponding sides of ∆DEF will be proportional to each other.
This satisfies the AA Similarity Criterion. Therefore, ∆ABC ~ ∆DEF by AA.
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Answer:
D.) $12n + $8u = 112 ;u = 4 + n
Step-by-step explanation:
Given that :
Cost per new books (n) = $12
Cost per used book (u) = $8
Total revenue earned = $112
store sold 4 more used books than new books
Hence,
Total revenue should be :
Revenue from new books + Revenue from used book = total revenue
Revenue from new books = $12 * n = $12n
Revenue from used books = $8 * n = $8n
$12n + $8u = 112
Number of books sold :
Number of used books sold = 4 + number of new books sold
u = 4 + n
Answer:
5
Step-by-step explanation:
For the point to be a solution to the equation, it has to lie on the line 5x -2y= 30 and therefore must satisfy the equation.
5x -2y= 30
When x=8,
5(8) -2y= 30
40 -2y= 30
40 -30= 2y (bring constant to 1 side)
2y= 10 (simplify)
y= 10 ÷2
y=5
Thus the missing value is 5.
