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2 years ago

Find the length of side x in simplest radical form with a rational denominator.

Mathematics

2 answers:

olga_2 [115]2 years ago

6 0

Answer:

Step-by-step explanation:

$\sin 30\degree = \frac{5}{x}\\\\ \frac{1}{2}= \frac{5}{x}\\\\x = 5\times 2\\\\x = 10 \\$

hram777 [196]2 years ago

5 0

Officer: "How old was she?!"

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Question 2. I have another question on my feed. Please help me solve!!!!

Maru [420]

Answer:

A' (11, 4), B' (-10, -6), C' (7, -9)

Step-by-step explanation:

Since you are reflecting over the y-axis, you take the opposite of the x value. So if the x is positive, make it negative. If the x is negative, make it positive. The y coordinate stays the same.

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3 years ago

A plumber charges $25 for a service call plus $50 per hour for service. Write a linear equation in slope-intercept form to repre

Reptile [31]

Answer:

y= $50x + $25

Step-by-step explanation:

Slope-intercept form is y=mx+b

x is something that is constant

b is something you add on to the constant

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3 years ago

The library surveyed 240 people about their favorite movie. If 15% people chose documentaries, how many people chose documentari

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3 years ago

Read 2 more answers

A hotel offers a reward program based on the number of night stayed. The function f(x) represents the number of free nights earn

iris [78.8K]

Answer:

a. A customer earns 1 free night per 10 nights stayed.

Step-by-step explanation:

The missing function is:

f(x) = x/10

The missing options are:

a. A customer earns 1 free night per 10 nights stayed.

b. A customer starts with 1 free night and then earns another free night after every 10 nights stayed.

c.A customer earns x – 10 free nights for every 10 nights stayed.

d. A customer earns 10 free nights after x number of nights stayed.

The function means that after a customer stayed 10 nights, a free night is earned. That is, replacing x = 10 into the function, we get:

f(10) = 10/10 = 1

which means 10 nights are equivalent to 1 free night.

7 0

3 years ago

Futhe Mathematics <img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

Derivation of cos²x - sin²x = cos2x :-

We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

$\longrightarrow cos(x+x) = cos^2x - sin^2x$

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

2 years ago