Question 1(multiple choice worth 2 points)
find a ⋅ b.
a = 10i + 9j, b = 4i + 3j
< 40, 27>
< 14, 12>
67
-13
question 2(multiple choice worth 2 points)
find a ⋅ b.
a = < 2, 4> , b = < 2, 5>
< 4, 9>
24
< 4, 20>
16
question 3(multiple choice worth 2 points)
determine whether the vectors u and v are parallel, orthogonal, or neither.
u = < 6, -2> , v = < 2, 6>
neither
orthogonal
parallel
question 4(multiple choice worth 2 points)
find the angle between the given vectors to the nearest tenth of a degree.
u = < 8, 7> , v = < 9, 7>
-8.3°
1.7°
3.3°
13.3°
question 5 (essay worth 2 points)
evaluate the expression:
v ⋅ w
given the vectors:
r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

answer: do we write it

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

answer: i feel you honey.

step-by-step explanation:

-1/3(x+1)^5

i’m pretty sure this is correct