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3 years ago

If an equation is an identity, then how many solutions does it have?

Mathematics

2 answers:

7nadin3 [17]3 years ago

8 0

Infinite is the answer

olga2289 [7]3 years ago

3 0

Hello,

If an equation is an identity, then every value of the variable makes the egality true.

Generaly we resolve an equation in R.

In this case Sol=R

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Question in picture A) 16/63 B)-16/63 C) 63/16 D) -63/16

Orlov [11]

ANSWER
$\tan(x + y) = - \frac{63}{16}$

EXPLANATION

We were given that,

$\csc(x) = \frac{5}{3}$

This implies that,

$\sin(x) = \frac{3}{5}$

We use the Pythagorean identity

$\sin^{2} (x) + \cos^{2} (x)= 1$
to get,

$\cos(x) = \sqrt{1 - ( { \frac{3}{5} })^{2}} = \frac{4}{5}$

We were also given that,

$\cos(y) = \frac{5}{13}$

This means that,

$\sin(y) = \sqrt{1 - {( \frac{5}{13}) }^{2} } = \frac{12}{13}$

This is because,

$0 < \: x \: < \frac{\pi}{2}$

$0 < \: y \: < \frac{\pi}{2}$

This angles are in the first quadrant so we pick the positive values.

$\tan(x + y) = \frac{ \sin(x + y) }{ \cos(x + y) }$

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

$\tan(x + y) = \frac{ \frac{3}{5} \times \frac{5}{13} + \frac{12}{13} \times \frac{4}{5} }{ \frac{4}{5} \times \frac{5}{13} - \frac{3}{5} \times \frac{12}{13} }$

$\tan(x + y) = - \frac{63}{16}$

The correct answer is D

4 0

3 years ago

A table is on sale for 65% off. the sale price is $154 . what is the regular price?

Yuliya22 [10]

The original price is $254.10 or 254 rounded. 154 times .65 is 100.1. Add 100.1 to the sale price which is 154 and you'll get the original, 254.
Hope this helps :)

7 0

3 years ago

Drag steps in the given order to evaluate this expression. (4)(−3)−5−3(−6)

never [62]

Answer:

Step-by-step explanation:

using PEDMAS(parentheses, exponents, division, multiply, addition, subtraction) to solve the problem

First we multiply (4)(-3)

(4)(−3)−5−3(−6)

Then multiply -3(-6)

(-12)-5-3(-6)

=-12-5+18

subtract 12-5

-12-5+18

=-17+18

Adding -17+18 gives us 1.

Therefore, (4)(−3)−5−3(−6) is 1.

3 0

3 years ago

A right triangle has a height of 27 inches

ohaa [14]

Answer:

405 $inches^{2}$

Step-by-step explanation:

Area of a triangle = $\frac{1}{2}$ Base * Height

$\frac{1}{2}$ * 30* 27 = 405 $inches^{2}$

4 0

2 years ago

Read 2 more answers

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midni

Alex17521 [72]

Answer: It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.

Step-by-step explanation:

Since we have given that

n = 84

x = 11

So, $\hat{p}=\dfrac{x}{n}=\dfrac{11}{84}=0.13$

p = 0.20

So, hypothesis:

$H_0:p=\hat{p}\\\\H_a:\hat{p}$

so, test statistic value would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.13-0.20}{\sqrt{\dfrac{0.2\times 0.8}{84}}}\\\\z=-1.604$

At 1% level of significance, critical value would be

z= 2.58

Since 2.58>-1.604

So, We will accept the null hypothesis.

Hence, It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.

4 0

3 years ago

Read 2 more answers