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3 years ago

10 Pts + Brainliest for the best answer

Mathematics

1 answer:

LenaWriter [7]3 years ago

3 0

m∠PQR = m∠BQR + m∠PQB

We have m∠PQR = 116° and m∠BQR = 75°. Substitute:

116° = 75° + m∠PQB <em>subtract 75° from both sides</em>

41° = m∠PQB

<h3>Answer: m∠PQB = 41°</h3>

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Need help on these trig homework

allochka39001 [22]

8. The length of the support is 7. 9 m

9. The length of the conveyer is 12m

3. a = 59m

A = 44°

B = 52°

4. c = 88. 6 mm

b = 49. 1 m

B = 34°

<h3>How to solve the trigonometry</h3>

8. We have the angle to be 20 degrees

Opposite side = x

hypotenuse = 23m

Using the sine ratio

sin θ = opposite/ hypotenuse

$sin 20 = \frac{x}{23}$

Cross multiply

$sin 20$ × $23 = x$

$x = 0. 3420$ × $23$

x = 7. 9 m

The length of the support is 7. 9 m

9. The angle of elevation is 37. 3 degrees

Hypotenuse = 19 . 0m

Opposite = x

Using the sine ratio

sin θ = opposite/ hypotenuse

$sin 37. 3 = \frac{x}{19}$

cross multiply

$x = 0. 6059$ × $19$

x = 11.5

x = 12 m in 2 significant figures

The length of the conveyer is 12m

3. To determine the sides and angles, we use the sine rule;

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$

For side a, we use the Pythagorean theorem

$c^2 = a^2 + b^2$

$85^2 = a^2 + 67^2$

$a = \sqrt{89^2-67^2}$

$a = \sqrt{3432}$

a = 58. 58, a = 59m

To find angle A and B, use the sine rule

$\frac{59}{sin A } = \frac{85}{sin 90}$

cross multiply

$sin A$ × $85$ = $sin 90$ × $59$

make sin A subject of formula

$sin A = \frac{59}{85}$

$sin A = 0. 6941$

A = $sin^-^1(0. 6941)$

A = 44°

$\frac{67}{sin B} = \frac{85}{sin 90}$

cross multiply

$sin B$ × $85$ = $sin 90$ × $67$

make sin b subject of formula

$sin B = \frac{67}{85}$

$sin B = 0. 7882$

B = $sin^-^1( 0. 7882)$

B = 52°

4. To find the sides, we use the sine rule;

$\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}$

Cross multiply

$sin 56. 6$ × $c = sin 90$ × $74$

make 'c' subject of formula

$c = \frac{74}{0. 8348}$

c = 88. 6 mm

To find length b, we use the Pythagorean theorem

$c^2 = a^2 + b^2$

$b^2 = c^2 - a^2$

$b^2 = 88. 8^2 - 74^2$

$b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}$

b = 49. 1 m

$\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}$

cross multiply

$sin B = \frac{40. 99}{74. 0}$

B = $sin^-^1(0. 5539)$

B = 34°

Learn more about trigonometric identity here:

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3 0

1 year ago

Suppose you open a bank account. Every month you deposit $40. Write an equation that relates the total number of dollars deposit

alekssr [168]

$40=T >?=m

T= $40,$80,$120,etc.
m=1,2,3,etc

4 0

3 years ago

Help me will give brain

Aleonysh [2.5K]

Answer:

The answer is C

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x−2)=6x+18

Step 1: Simplify both sides of the equation.

4(x−2)=6x+18

(4)(x)+(4)(−2)=6x+18(Distribute)

4x+−8=6x+18

4x−8=6x+18

Step 2: Subtract 6x from both sides.

4x−8−6x=6x+18−6x

−2x−8=18

Step 3: Add 8 to both sides.

−2x−8+8=18+8

−2x=26

Step 4: Divide both sides by -2.

−2x/−2=26/−2

x=−13

Answer:

x=−13

3 0

2 years ago

Which recursive sequence would produce the sequence 8,-35,137,…?

vagabundo [1.1K]

The recursive sequence that would produce the sequence 8,-35,137,… is T(n + 1) = -3 - 4T(n) where T(1) = 8

<h3>How to determine the recursive sequence that would produce the sequence?</h3>

The sequence is given as:

8,-35,137,…

From the above sequence, we can see that:

The next term is the product of the current term and -4 added to -3

i.e.

Next term = -3 + Current term * -4

So, we have:

T(n + 1) = -3 + T(n) * -4

Rewrite as:

T(n + 1) = -3 - 4T(n)

Hence, the recursive sequence that would produce the sequence 8,-35,137,… is T(n + 1) = -3 - 4T(n) where T(1) = 8

Read more about recursive sequence at

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4 0

1 year ago

A swimming pool that is 10 feet, 20 feet long, and 4 1/2 feet deep. how much water can this swimming pool hold (to the top of th

Sever21 [200]

Answer:

900 cubic feet

Step-by-step explanation:

Volume = length x width x height

= 10 x 20 x 4.5

= 900

3 0

3 years ago