Given : cos(θ)= -4/5 | sin x = -12/13
Evaluate: cos(θ + x)

cos (θ + x) is 16/65

Step-by-step explanation:

Given cos θ = -4/5, find sin θ.

cos θ = adjacent side/hypotenuse = -4/5

The opposite side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Opposite side² = Hypotenuse² - Adjacent Side²

                             = 5² - (-4)² = 25 - 16 = 9

∴ Opposite Side = 3

⇒ sin θ = opposite side/hypotenuse = 3/5

Given sin x = -12/13, find cos x.

sin x = opposite side/hypotenuse = -12/13

The adjacent side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Adjacent side² = Hypotenuse² - Adjacent Side²

                             = 13² - (-12)² = 169 - 144 = 25

∴ Adjacent Side = 5

⇒ cos x = adjacent side/hypotenuse = 5/13

Find cos (θ + x).

cos (θ + x) = cos θ cos x - sin θ sin x

                 = -4/5 × 5/13 - 3/5 × -12/13

                 = -20/65 + 36/65 = 16/65

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

step-by-step explanation:

a rhombus is a parallelogram enjoying his symmetry.