Answer: $\bold{9)\ \sin \theta=\dfrac{1}{3}\qquad 10)\ \sin \theta = \dfrac{4}{5}\qquad 11)\ \cos \theta = \dfrac{\sqrt{11}}{6}\qquad 12)\ \tan \theta = \dfrac{17\sqrt2}{26}}$

Step-by-step explanation:

Pythagorean Theorem is: a² + b² = c² , where "c" is the hypotenuse

$9)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{12}\quad \rightarrow \large\boxed{\dfrac{1}{3}}$

Note: 4² + (8√2)² = hypotenuse² → hypotenuse = 12

$10)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{16}{20}\quad \rightarrow \large\boxed{\dfrac{4}{5}}$

Note: 12² + opposite² = 20² → opposite = 16

$11)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{\sqrt{11}}{6}\quad =\large\boxed{\dfrac{\sqrt{11}}{6}}$

Note: adjacent² + 5² = 6² → adjacent = √11

$12)\ \tan \theta=\dfrac{\text{side opposite of}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{17}{13\sqrt2}\quad =\large\boxed{\dfrac{17\sqrt2}{26}}$

Note: adjacent² + 7² = (13√2)² → adjacent = 17

5 0

3 years ago

You have a coupon for an additional 25% off the price of any sale item at a store. The store has put a watercolor kit on sale fo

telo118 [61]

Final price=original price*(100%- discount 1)(100%-discount 2)
original price=$40
discount 1=25%⇒ 100 - discount 1=100%-25%=75%=75/100=0.75
discount 2=15%⇒ 100 - discount 2=100%-12%=85%=85/100=0.85

original price=$40(0.75)(0.85)=$25.5

Answer: $25.5

4 0

3 years ago

Simplify : 5y-2y+4=10

Mnenie [13.5K]

Answer:

See below.

Step-by-step explanation:

5y - 2y + 4 = 10

5y - 2y = 6

3y = 6

y = 2

Check:

5y - 2y + 4 = 10

5(2) - 2(2) + 4 = 10

10 - 4 + 4 = 10

6 + 4 = 10

10 = 10

The value of y = 2

7 0

3 years ago

Read 2 more answers

Pls give me the answer! Thanks!

Mademuasel [1]

Answer:

Step-by-step explanation:

7 x 6 = 42 + 9 = 51 + 54 = 105 + 75= 180

6 0

2 years ago

Read 2 more answers