Find the sum 70.6+74.02+121.985=

What is the answer for this question?

grandymaker [24]

Answer:

A

Step-by-step explanation:

$\frac{11\pi }{6}$ is in the fourth quadrant where tan < 0

The related acute angle = 2π - $\frac{11\pi }{6}$ = $\frac{\pi }{6}$

Hence

tan( $\frac{11\pi }{6}$ )

= - tan( $\frac{\pi }{6}$ )

= - $\frac{1}{\sqrt{3} }$

= - $\frac{1}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$

= - $\frac{\sqrt{3} }{3}$ → A

5 0

2 years ago

Renata wins a $20 gift card to an online music site. After Renata purchases 16 songs, the gift card has a remaining balance of $

Sveta_85 [38]

$20 bought 16 songs
Therefore each song costs $20/16 = $5/4 = $1.25
So:
2 songs would cost 2 * $1.25
3 songs would cost 3 * $1.25
...
x songs would cost x * $1.25

Since Renata started with $20, then her balance (y) after buying x songs would be:

y = 20 - 1.25*x

3 0

3 years ago

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point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below

enot [183]

Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

To find angle CAB and;
Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using cosine rule to determine angle CAB, we have:

$\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}$

Here:

$\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}$

$\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}$

$\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}$

$\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}$

$\mathbf{Sin \hat {CAB} = 0.3451}$

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

$\mathbf{Tan \theta = \dfrac{GF}{BF}}$

$\mathbf{Tan \ 35.19 = \dfrac{1.8 \ m }{BF}}$

$\mathbf{BF = \dfrac{1.8 \ m }{Tan \ 35.19}}$

$\mathbf{BF = \dfrac{1.8 \ m }{0.7052}}$

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

8 0

3 years ago

Type a digit that makes this statement true.

Archy [21]

Answer:

So information at the bottom:

since every number in a thousand spot needs to have 3 digest, we need to add a zero onto 29,422,33<u>0</u>. If we didn’t add a zero, then the problem wouldn’t make much since. So if we divide 29,422,330 by 2, our answer would be 14,711,165. A whole bunch of numbers, but nothing that can’t be solved!

<h3>Hope this helps!✌️</h3>

5 0

2 years ago

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What is (4x-3)(7x+6)?

professor190 [17]

Answer:

28x^2+3x-18

Step-by-step explanation:

Formula: (a+b)(a+b) = a^2 + a*b + a*b + b*b

Following this: 28x^2 -21x +24x -18

Then you combine like terms: 28^2 +3x-18

hope this helped!! :)

4 0

2 years ago

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Find the sum 70.6+74.02+121.985=​

Find the sum 70.6+74.02+121.985=