Math8.U6L11Test.Spring24 (Copy) Answers
1. (in this order) inverse, multiplication, dividing by 5, cube root, one, -3
2. Step 1: Subtract 4 from both sides, Step 2: Take the square root of both sides, Step 3: Simplify - you get two rational solutions
3. The length is √40 units; find the sum of the vertical and horizontal distances squared and then take the square root.
4. The green path is 2 miles shorter than the yellow path.
5. 6^2 + b^2 = 24^2 ; 23.24 ft
6. x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance
7. 5, 12, and 13
8. Right triangles have side lengths that always follow a^2 + b^2 =c^2, Right triangles must have the side across from the 90 degree angle as the longest side., and Right triangles have interior angles that add to equal 180 degrees.
9. The four yellow triangles are congruent in both large squares and the large squares are congruent, so c^2 = a^2 + b^2
10. 42.7m
11. (in this order) Taking the square root of 81, Taking the square root of 81 and then multiply by 4, Taking the cube root of 125, and squaring has 2 factors of the base and cubing has 3 factors of the base
12. 289 and 324
13. True; the area of the green square + the area of the purple square = the area of the red square
14. You would use the inverse operation of square root; there would be two solutions for x; x = 3/11 and x = - 3/11
15. (in this order) Pythagorean Theorem, 5 cm, a leg, hypotenuse, 13 cm
16. Step 1: Set up the equation 5^2 + h^2 = 13^2, Step 2: Square 5 and 13 to get 25 + h^2 = 169, Step 3: Subtract 25 from both sides to get h^2 = 144, Step 4: Take the square root of both sides h = 12 cm
17. Each additional day is associated with an additional 17.5 grams of mass.