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3 years ago

Simplify: 5( 6-3) + 2

Mathematics

1 answer:

SashulF [63]3 years ago

5 0

Answer:

Step-by-step explanation:

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3. A telephone company offers its customers a discount of $15 for even

beks73 [17]

$180 is the annual discount

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3 years ago

How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)

Oxana [17]

Answer:

Make use of the fact that as long as $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ :

$\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ .

$\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}$ .

$\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ .

Step-by-step explanation:

Assume that $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ .

Make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ and $\csc(\theta) = (1) / (\sin(\theta))$ to rewrite the given expression as a combination of $\sin(\theta)$ and $\cos(\theta)$ .

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}$ .

Since $\cos(\theta) \ne 0$ :

$\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

By the Pythagorean identity, $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ . Rearrange this identity to obtain:

$\sin^{2}(\theta) = 1 - \cos^{2}(\theta)$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

Again, make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ to obtain the desired result:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}$ .

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2 years ago

Question 1(Multiple Choice Worth 2 points)

Roman55 [17]

OMG where do I start just comment below this post and I will help you with all promise

7 0

3 years ago

Read 2 more answers

What equation can I use to solve for x?<br><br> What equation can I use to solve for y?

lbvjy [14]

Answer:

125+9x-8=180

6x+13+6y+29=180

Step-by-step explanation:

4 0

3 years ago

Please answer for 10 points

Soloha48 [4]

Answer:

1. 4.7

2. 5,082

Step-by-step explanation:

1. To find the volume of a cone you use this formula $V=\pi r^{2} \frac{h}{3}$ . The diameter is 3 so to find the radius, divide it by 2 (3/2=1.5) and we know the height. Input the numbers into the formula and solve $V=\pi (1.5)^{2} \frac{4}{3}$ which is equal to $3\pi$ . To find HALF, divide that answer by 2. $3\pi /2= 4.71239$ , round to the nearest tenth, making the answer 4.7!

2. To find the volume of a rectangular prism you use $V=lwh$ . Input the numbers, $V=(30)(12)(16)$ to find the amount of water for the bigger tank (5,760). Now follow the same process to find the amount of water for the smaller tank $V=(12)(6)(9)$ which is 678. Now subtract the smaller tank amount (678) from the larger tank since you're taking the water from the bigger tank to fill the smaller one which equals 5,082.

4 0

3 years ago