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4 years ago

Plz help it’s very confusing

Mathematics

1 answer:

zepelin [54]4 years ago

6 0

So the total is 120. You want 1/6 of those.
So do (1/6)*120
You get 20.

YAY

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2 tan 30°<br>II<br>1 + tan- 300

shusha [124]

Question:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Answer:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

Step-by-step explanation:

Given

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Required

Simplify

In trigonometry:

$tan(30^{\circ}) = \frac{1}{\sqrt{3}}$

So, the expression becomes:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}$

Simplify the denominator

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}$

Express the fraction as:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} / \frac{4}{3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} * \frac{3}{4}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{1}{\sqrt 3} * \frac{3}{2}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3}$

Rationalize

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3\sqrt{3}}{2* 3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\sqrt{3}}{2}$

In trigonometry:

$sin(60^{\circ}) = \frac{\sqrt{3}}{2}$

Hence:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

3 0

3 years ago

State whether or not the following triangles are similar. If not, explain why not. If so, write a similarity statement

valentinak56 [21]

9514 1404 393

Answer:

a) ∆RLG ~ ∆NCP; SF: 3/2 (smaller to larger)

b) no; different angles

Step-by-step explanation:

a) The triangles will be similar if their angles are congruent. The scale factor will be the ratio of any side to its corresponding side.

The third angle in ∆RLG is 180° -79° -67° = 34°. So, the two angles 34° and 67° in ∆RLG match the corresponding angles in ∆NCP. The triangles are similar by the AA postulate.

Working clockwise around each figure, the sequence of angles from lower left is 34°, 79°, 67°. So, we can write the similarity statement by naming the vertices in the same order: ∆RLG ~ ∆NCP.

The scale factor relating the second triangle to the first is ...

NC/RL = 45/30 = 3/2

b) In order for the angles of one triangle to be congruent to the angles of the other triangle, at least one member of a list of two of the angles must match for the two triangles. Neither of the numbers 57°, 85° match either of the numbers 38°, 54°, so we know the two triangles have different angle measures. They cannot be similar.

7 0

3 years ago

The parents organization bought 1,000 bumper stickers at $1.25 each to sell at football games.They want to make at least $750 pr

yuradex [85]

1000 x 1.25 = 1250
1000 x 2 = 2000
2000 - 1250 = 750
2000 divided by 1000 = 2

They should sell the bumper stickers for $2 each.
Hope this helped =)

5 0

3 years ago

We are driving to Las Vegas. The sign says that it is one hundred forty-five miles to Las Vegas.

nata0808 [166]

Answer:

233.35488 km (Rounded to 233 km)

Step-by-step explanation:

If you convert miles to kilometers then you would use this conversion factor:

1 mile = 1.609344 km (or 1.61 km)

so in this case,

145 mile = 1.609344 km x 145

145 mile = 233.35488 km

I could also round it to 233 km.

Since your on a trip... i hope u enjoy ur journey to Las Vegas!

5 0

1 year ago

The cross section of a parabolic sound reflector at the Olympics has a diameter of 20 inches and is 25 inches deep. Write an equ

Arturiano [62]

Answer: 69

Step-by-step explanation: Sorry I do not know the answer because I am not smart. I just need the points so I can answer more questions. Have a great day though and I wish you luck with your question:)

7 0

3 years ago