Calculate cos theta to two decimal places.
a. 0.69
b. 1.38
c. -0.07
d. 0.77

A. 0.69

Step-by-step explanation:

We need to use cosine theorem:

c²=a²+b² - 2ab* cos(θ)

c=8, a=7, b=11

8² = 7²+11² - 2*7*11 *cos(θ)

64 = 49 + 121 - 154*cos(θ)

64 - 170 = - 154*cos(θ)

- 106/ (- 154) = cos(θ)

cos(θ) = 0.69

A. 0.69

Step-by-step explanation:

Using the cosine law

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

c² = a² + b² - 2ab cos C

8² = 7² + 11² - 2 × 7× 11 cos ∅

64 = 49 + 121 -154 × cos ∅

64 = 170 - 154 cos ∅

64 - 170 = -154 cos ∅

- 106 = -154 cos ∅

cos ∅ = -106/-154

cos ∅ = 0.6883116883 ≈ 0.69

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!