Answer: The HL Theorem can be used to prove ABR ≅ RCA because both triangles share the same hypotenuse and a leg. The HL theorem states that If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
1. The 2nd number line represents the inequality.
Explanation:
In words, the inequality reads "negative six is less than x, which is less than or equal to two". On the number line, the open circle at negative six means that -6 is not a solution to the inequality: -6 < x. The point at positive two means that positive two is a solution to the inequality: x ≤ 2. Therefore, all numbers greater than -6 and less than or equal to +2 are solutions to the inequality. This is shown on the second number line.
2. False
Explanation:
In words, the inequality reads "x is less than negative five". This means that all numbers less than -5 are solutions to the inequality. Positive four is not less than negative five, so it is not a solution to the inequality.
3. x > 2
Explanation:
To solve the inequality, we have to move all the terms that do not contain x to one side. This inequality is simple because it only requires one step: subtraction.
Solve for x: x + 3 > 5
1. Subtract 3 from both sides to get x by itself:
x + 3 - 3 > 5 - 3
2. Simplify
x > 2
Answer:
![\large\boxed{2.\ ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B2.%5C%20ab%5E%7B-3x%7D%3Da%5Cleft%28%5Cdfrac%7B1%7D%7Bb%7D%5Cright%29%5E%7B3x%7D%3Da%5Cleft%5B%5Cleft%28%5Cdfrac%7B1%7D%7Bb%7D%5Cright%29%5E3%5Cright%5D%5Ex%7D)
Step-by-step explanation:
![Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\------------\\\\(4)^{-3x^2}=\left[(4)^{-1}\right]^{3x^2}=\left(\dfrac{1}{4}\right)^{3x^2}](https://tex.z-dn.net/?f=Use%3A%5C%20a%5E%7B-n%7D%3D%5Cleft%28%5Cdfrac%7B1%7D%7Ba%7D%5Cright%29%5En%5C%5C------------%5C%5C%5C%5C%284%29%5E%7B-3x%5E2%7D%3D%5Cleft%5B%284%29%5E%7B-1%7D%5Cright%5D%5E%7B3x%5E2%7D%3D%5Cleft%28%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%5E%7B3x%5E2%7D)
![Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\ and\ (a^n)^m=a^{nm}\\--------------------\\\\ab^{-3x}=a\cdot b^{-3x}=a\left[(b)^{-1}\right]^{3x}=a\left(\dfrac{1}{b}\right)^{3x}\\\\ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x](https://tex.z-dn.net/?f=Use%3A%5C%20a%5E%7B-n%7D%3D%5Cleft%28%5Cdfrac%7B1%7D%7Ba%7D%5Cright%29%5En%5C%20and%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C--------------------%5C%5C%5C%5Cab%5E%7B-3x%7D%3Da%5Ccdot%20b%5E%7B-3x%7D%3Da%5Cleft%5B%28b%29%5E%7B-1%7D%5Cright%5D%5E%7B3x%7D%3Da%5Cleft%28%5Cdfrac%7B1%7D%7Bb%7D%5Cright%29%5E%7B3x%7D%5C%5C%5C%5Cab%5E%7B-3x%7D%3Da%5Cleft%28%5Cdfrac%7B1%7D%7Bb%7D%5Cright%29%5E%7B3x%7D%3Da%5Cleft%5B%5Cleft%28%5Cdfrac%7B1%7D%7Bb%7D%5Cright%29%5E3%5Cright%5D%5Ex)
Answer:
Step-by-step explanation:
<h2>E X P L A N A T I O N</h2>
Answer:
8/15
Step-by-step explanation:
tangent = opposite/adjacent,
so tan(A) = 8/15
