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3 years ago

4. 9d - 5 = 4 What does d = 5. 6-3w=-27 what does w = 6. -4= q/8-19 what does q =

Mathematics

1 answer:

trapecia [35]3 years ago

6 0

Answer:

4) d = 1

5) w = 11

6) q = 120

Step-by-step explanation:

4) $9d - 5 = 4$

Adding 5 on both the sides ,

$= > 9d - 5 + 5 = 4 + 5$

$= > 9d = 9$

Dividing both the sides by 9 ,

$= > \frac{9d}{9} = \frac{9}{9}$

$= > d = 1$

5) $6 - 3w = - 27$

Substracting 6 from both the sides ,

$6 - 3w - 6 = - 27 - 6$

$= > - 3w = - 33$

Dividing both the sides by -3 ,

$= > \frac{ - 3w}{ - 3} = \frac{ - 33}{ - 3}$

$= > w = 11$

6) $- 4 = \frac{q}{8} - 19$

Adding 19 on both the sides ,

$\frac{q}{8} - 19 + 19 = - 4 + 19$

$= > \frac{q}{8} = 15$

Multiplying both the sides by 8 ,

$= > \frac{q}{8} \times 8 = 15 \times 8$

$= > q = 120$

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part 3. Find the value of the trig function indicated, use Pythagorean theorem to find the third side if you need it.

Nat2105 [25]

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

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