Answer:
Pythagorean theorem: a^2 + b^2 = c^2
1. we have to find a. b is 12 and c is 15 because the right angle is pointing towards 15 so that is the hypotenuse. then we simply plug the info in the equation we have above.
a^2 + 12^2 = 15^2
a^2 + 144 = 225
a^2 = 81 --> sqaure root to find the answer basically.
a = 9
- we put AD as a so AD = 9
final answer : 9
2. to find AC, simply add AD and DC.
9 + 16 = 25
final answer: AC = 25
3. ABC is not a right triangle because it does not have a right angle. the smaller triangles do, but that does not mean that ABC is a right triangle.
-- let me know if you need any further explanations.
Do the division
(5.685 * 10^26) / (3.302*10^23)
= 1.722 * 10^3
or 1722 times greater
Answer:
1. ΔXYZ is a right Δ with altitude YU.
Given
2. ΔXYZ ~ ΔYUZ
Right Triangle Altitude Similarity Theorem
3. VW || XY
Given
4. ∠VWZ ≅ ∠XYZ
Corresponding angles
5. ∠Z ≅ ∠Z
Reflexive property of congruence
6. ΔXYZ ~ ΔVWZ
AA Similarity postulate
7. ΔYUZ ~ ΔVWZ
Transitive property of similar triangles
Step-by-step explanation:
The first statement is given in the problem. Since we know the altitude of a right triangle, we can use the Right Triangle Altitude Similarity Theorem to say that the triangles formed by the altitude are similar to each other and the original triangle.
Next, we are given in the problem statement that the lines VW and XY are parallel. Therefore, ∠VWZ and ∠XYZ are corresponding angles, which makes them congruent. And since ∠Z is equal to itself (by reflexive property), we can use AA similarity to say ΔXYZ and ΔVWZ are similar.
Finally, combining statements 2 and 6, we can use transitive property to say that ΔYUZ and ΔVWZ are similar.
Answer: 20
<u>Step-by-step explanation:</u>
h(x) = |3x| - 1
h(7) = |3(7)| - 1
= |21| - 1
= 21 - 1
= 20
