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3 years ago

Yes or no? Please help

Mathematics

1 answer:

rusak2 [61]3 years ago

6 0

Answer:

yes

Step-by-step explanation:

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Am I correct on question #6?

pashok25 [27]

Option A:

$\tan(105^\circ)=-(2+\sqrt{3})$

Solution:

<u>To evaluate tan(105)°:</u>

105° can be written as sum of 60° and 45°.

tan(105)° = tan(45 + 60)°

Using the summation identity:

$$\tan (x+y)=\frac{\tan (x)+\tan (y)}{1-\tan (x) \tan (y)}$

$$\tan \left(105^{\circ}\right)=\frac{\tan \left(45^{\circ}\right)+\tan \left(60^{\circ}\right)}{1-\tan \left(45^{\circ}\right) \tan \left(60^{\circ}\right)}$

We know that, tan(45)° = 1 and tan(60)° = √3

Substitute this in the above equation.

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

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

To rationalize the denominator multiply by the conjugate $\frac{1+\sqrt{3}}{1+\sqrt{3}}$ .

$$=\frac{(1+\sqrt{3})(1+\sqrt{3})}{(1-\sqrt{3})(1+\sqrt{3})}$

Using exponent formula: $a^{b} \cdot a^{c}=a^{b+c}$ and $(x-y)(x+y)=x^2-y^2$

$$=\frac{(1+\sqrt{3})^2}{(1^2-(\sqrt{3})^2)}$

Using exponent formula: $(a+b)^{2}=a^{2}+2 a b+b^{2}$

$$=\frac{1^{2}+2 \cdot 1 \cdot \sqrt{3}+(\sqrt{3})^{2}}{1-3}$

$$=\frac{4+2 \sqrt{3}}{-2}$

$$=\frac{2(2+ \sqrt{3})}{-2}$

$=-(2+\sqrt{3})$

$\tan(105^\circ)=-(2+\sqrt{3})$

Hence option A is the correct answer.

6 0

4 years ago

Rachel traveled to five different areas (A, B, C, D, and E) to study the number of buckeye butterflies and the number of monarch

Ivenika [448]

Answer:

As we can see our our ration in Area B and Area D gives the same answer, so they are in proportion

Step-by-step explanation:

Given that

Rachel traveled to 5 areas to find number of Buckeye and Monarch butterflies.

Areas Rachel Traveled to = A, B, C, D, E

The table given below shows her findings.

Area Buckeye Monarch

A 15 16

B 27 36

C 12 25

D 24 32

E 44 33

Now lets find the ratio of Buckeye and Monarch Butterflies in these areas

Area A

Buckeye : Monarch = 15:16 = 0.9375

Area B

Buckeye : Monarch = 27:36 = 0.75

Area C

Buckeye : Monarch = 12:25= 0.48

Area D

Buckeye : Monarch = 24:32 = 0.75

Area E

Buckeye : Monarch = 44:33 = 1.334

As we know that if two ratios give same answer after solving the fraction then these ratios are in proportion.

As we can see our our ration in Area B and Area D gives the same answer, so they are in proportion.

4 0

3 years ago

Read 2 more answers

Marcus solved this problem and found that 190% of 20 is 380. Is he correct? Explain why or why not. 190 percent = 1. 90. 1. 90 t

Ghella [55]

Answer:

not correct, 190% of 20 is 38

150% of 20 is 20 x 1.5 which equals 30

200% of 20 is 20 x 2.0 which equals 40

190% of 20 cannot be more than what 200% of 20 is

Step-by-step explanation:

200% is the same as 'double' a number

8 0

3 years ago

Hey again can you help me with this

Liono4ka [1.6K]

Answer:

The answer is 125 degrees.

3 0

3 years ago

Find 0.35 percent of 80

Flura [38]

I got 28 just multiply then .35 (0.35) x 80 = 28 Hope this helped :)))

4 0

3 years ago