15 > x = 9 I'm pretty sure
If two triangles are congruent the corresponding angles and sides are congruent.
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There are two prime numbers between 20 and 30: 23 and 29.
To find the percentage each number is of 125, you’d divide the number by 125 and move the decimal in the answer 2 places to the right to turn it to percentage notation (from decimal notation), so you’d solve 23/125 and 29/125.
23/125= .184
Moving the decimal two places to the right makes this 18.4%
29/125= .232
Moving the decimal two places to the right makes this 23.2%
X has two possible values of which you are to pick/use only one: 18.4 and 23.2
To find our scale factor, let's determine the length of AB, and compare it to the length of A'B'.
The length of AB is the distance from (9,4) to (5,-4).
Let's apply the distance formula:
AB = √ ((9-5)² + (4+4)²)
AB = √ (4² + 8²)
AB = √(16 + 64)
AB = √ (80)
AB = 4 √5
The length of AB is 4 √5.
Now for A'B':
A'B' = √ ((6-5)² + (3+4)²)
A'B' = √( 1 + 49)
A'B' = √ 50
A'B' = 5 √2
To find our scale factor k:
A'B' = k AB
5 √2 = 4 √5 * k Divide both sides by 4√5
5 √2 / (4 √5) = k To simplify, multiply the left side by (√5 / √5)
(5 *√5 * √2) / (4 *5) = k the 5's in the numerator and denominator cancel
√5 * √2 / 4 = k
√10 / 4 = k
To confirm, make sure AB * k = A'B', using the values that we've calculated.
