Answer:
Rearrange the equations that result from use of the Pythagorean theorem.
Step-by-step explanation:
Transversal AB crossing parallel lines AD and BC makes supplementary interior same-side angles A and B. Since A = 90°, B must be 90°. The Pythagorean theorem then applies in the right triangles ABC and ABD.
We can use that theorem to write two expressions for AB^2:
BD^2 -AD^2 = AB^2 = AC^2 -BC^2
The middle expression, AB^2, isn't needed beyond this point. Adding (AD^2 -AC^2) to both sides of the equation gives the desired result:
BD^2 -AC^2 = AD^2 -BC^2
Answer:
Option B
Step-by-step explanation:
Surface area of a triangular prism = Area of the triangular sides + Area of the rectangular sides
Area of the triangular sides = 2(Area of the triangular base)
= ![2[\frac{1}{2}(\text{Base})(\text{Height})]](https://tex.z-dn.net/?f=2%5B%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7BBase%7D%29%28%5Ctext%7BHeight%7D%29%5D)
= 10 × 12
= 120 ft²
Area of the rectangular sides = (Perimeter of the triangular side)(Height of the prism)
= (10 + 13 + 13)(15)
= 36 × 15
= 540 ft²
Surface area of the prism = 120 + 540
= 660 square feet
Option B will be the answer.
Answer:
Step-by-step explanation:
A. Alyssa did not get an A on the math test but rather a B- due to only getting 16 out of the 20 problems right. This can be found out by dividing the amount correct over the total amount of problems.
B. In order for Alyssa to get an A or 90% on her math test she would have had to get two more questions right to have a score of 18 out of 20.
C. In order to figure this question out you have to think that with every incorrect answer that Jessie answered she got three correct along with the one incorrect. By going with that information it can be figured that Jessie's score is 15 correct answers and 5 incorrect information if you go by the ratio 3:1 then go up tell the sides equal up to a total of 20 after being added. So Jessie's score again was 15 out of 20.
