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3 years ago

1. Prove that 2 tan x / 2- sec^2 x = tan 2x.

Mathematics

1 answer:

Vikentia [17]3 years ago

8 0

Answer:

Step-by-step explanation:

Use trig identities:

tan

cos

sec

(

−

tan

)

tan

−

tan

sec

−

tan

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Help please.! and thank you

Alexxx [7]

Answer:

common difference is 4

Step-by-step explanation:

12-4=8

8-4=4

8 0

2 years ago

Mr. Wallace gave a test to his math classes. He created a histogram that showed the frequency of As, Bs, and Cs. He labeled the

Gennadij [26K]

Answer:

Step-by-step explanation:

I got it right on Khan Academy

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3 years ago

At the beginning of a basketball season, the Panthers won 20 games out of 80 games. At this rate, how many games will they win i

balu736 [363]

They will win 25 games in 100 game season at that rate.Since they win 5 games out of every 20.

The answer is 25

6 0

3 years ago

Which binomial is a factor of 49x^2+84xy+36y^2

sweet-ann [11.9K]

7x + 6y is a binomial that is a factor of given equation

Solution:

A binomial is a mathematical expression which has only two terms

Given expression is:

$49x^2 + 84xy + 36y^2$

We have to find the binomial that is a factor to given expression

Let us find the factors of given equation

$49x^2+84xy+36y^2\\\\\mathrm{Rewrite\:}49x^2+84xy+36y^2\mathrm{\:as\:}\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\\mathrm{Rewrite\:}49\mathrm{\:as\:}7^2\\\\7^2x^2+84xy+36y^2\\\\\mathrm{Rewrite\:}36\mathrm{\:as\:}6^2\\\\7^2x^2+84xy+6^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\7^2x^2=\left(7x\right)^2\\\\Therefore,\\\\\left(7x\right)^2+84xy+6^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\6^2y^2=\left(6y\right)^2\\\\$

$Therefore\\\\\left(7x\right)^2+84xy+\left(6y\right)^2\\\\\mathrm{Rewrite\:}84xy\mathrm{\:as\:}2\cdot \:7x\cdot \:6y\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\$

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=7x,\:b=6y\\\\Therefore,\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2 = \left(7x+6y\right)^2$

Thus we get,

$49x^2 + 84xy + 36y^2 = (7x+6y)^2\\\\49x^2 + 84xy + 36y^2 = (7x+6y)(7x+6y)$

Thus the binomial which is a factor is 7x + 6y

6 0

3 years ago

You went to the mall with $80. You spend 25% of your money on a pair of shorts and 65% of the remainder on sandals. How much did

murzikaleks [220]

The answer is $13

Explanation:

You would first have to find 25% of the original amount. To do so, you must multiply the decimal amount of the percentage (0.25) by the number. The product is 20, or $20. So now that you have found the amount that you have spent your money on shorts, now you must find 65% of 20 to find the sandal spending amount. 0.65 * 20 = 13, or $13. Therefore, you spent a total of $13 on the sandals.

Hope I helped and good luck!

6 0

3 years ago