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2 years ago

8

Please helppppp A. Yes;19 B. No

1 answer:

Vadim26 [7]2 years ago

7 0

Answer:

Yes

Step-by-step explanation:

You might be interested in

An oblique prism with a square base of edge length x United has a volume of 1/2 x3 cubic units. Which expression represents the

aleksklad [387]

Answer:

The answer is x units.

Step-by-step explanation:

We are tasked to solve for the expression that represents the height of the prism. We are given with the following values:

length = x² units

volume = x³ units

We will use the formula below:

V = length x height

x³ = x² * height

height = x³/x units

height = x units

The answer is x units.

7 0

2 years ago

Read 2 more answers

You gave the server at a restaurant a 22% tip and ended up paying $41.48. What was the price of your meal before you applied the

const2013 [10]

Answer: The price of meal before the tip = $34.

Step-by-step explanation:

Given : The percentage of tip = 22% = 0.22 ( we divide a percentage by 100 to convert it into decimal)

Total amount paid ( including tip) = $41.48

Formula for Total bill = Price of meal + Tip amount , where Tip amount= 22% of Price of meal.

Let x be the price of meal, then

Total bill =x + 0.22 x (x )

⇒ $41.48= x(1+0.22) [ By distributive property]

⇒ $41.48 = x (1.22)

⇒ x= ($41.48) ÷ 1.22

⇒ x= 34

Hence, the price of your meal before you applied the tip = $34.

7 0

3 years ago

I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).

Aleksandr-060686 [28]

Answer:

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

Step-by-step explanation:

$\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$

Let's first isolate the trig function.

Add 1 one on both sides:

$\sqrt{3} \tan(x-\frac{\pi}{8})=1$

Divide both sides by $\sqrt{3}$ :

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

Now recall $\tan(u)=\frac{\sin(u)}{\cos(u)}$ .

$\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

or

$\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

The first ratio I have can be found using $\frac{\pi}{6}$ in the first rotation of the unit circle.

The second ratio I have can be found using $\frac{7\pi}{6}$ you can see this is on the same line as the $\frac{\pi}{6}$ so you could write $\frac{7\pi}{6}$ as $\frac{\pi}{6}+\pi$ .

So this means the following:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

is true when $x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

where $n$ is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

$x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

Add $\frac{\pi}{8}$ on both sides:

$x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi$

Find common denominator between the first two terms on the right.

That is 24.

$x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi$

$x=\frac{7\pi}{24}+n \pi$ (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval $[0,2\pi)$ .

So if $\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$ and we let $u=x-\frac{\pi}{8}$ , then solving for $x$ gives us:

$u+\frac{\pi}{8}=x$ ( I just added $\frac{\pi}{8}$ on both sides.)

So recall $0\le x$ .

Then $0 \le u+\frac{\pi}{8}$ .

Subtract $\frac{\pi}{8}$ on both sides:

$-\frac{\pi}{8}\le u$

Simplify:

$-\frac{\pi}{8}\le u$

$-\frac{\pi}{8}\le u$

So we want to find solutions to:

$\tan(u)=\frac{1}{\sqrt{3}}$ with the condition:

$-\frac{\pi}{8}\le u$

That's just at $\frac{\pi}{6}$ and $\frac{7\pi}{6}$

So now adding $\frac{\pi}{8}$ to both gives us the solutions to:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$ in the interval:

$0\le x$ .

The solutions we are looking for are:

$\frac{\pi}{6}+\frac{\pi}{8}$ and $\frac{7\pi}{6}+\frac{\pi}{8}$

Let's simplifying:

$(\frac{1}{6}+\frac{1}{8})\pi$ and $(\frac{7}{6}+\frac{1}{8})\pi$

$\frac{7}{24}\pi$ and $\frac{31}{24}\pi$

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

5 0

3 years ago

Every five years in March, the Population of a certain town is recorded. In 1995, the town had a population of 4,500 people. Fro

alexgriva [62]

4,500 plus 15% is 5,175 minus 4% is 4,968 so your answer is 4,968.

5 0

3 years ago

a fall dance sold 18 tickets during the first day of sales. this was 25% of the total sales. how many tickets were sold to the f

alexandr402 [8]

Answer:

72

Step-by-step explanation:

I have a weird way of doing it

so if 18 is 25%

18+18=36

then 36 would be 50%

36+36=72

so then 72 would be 100%

72*.25=18

6 0

2 years ago

Read 2 more answers