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svetlana [45]
2 years ago
13

The sum of two numbers is 25. Their difference is 7. Find the numbers.

Mathematics
1 answer:
antoniya [11.8K]2 years ago
7 0

Answer:

The writing isn't clear though hope it helps

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Which inequality is shown in the graph
pentagon [3]

Answer:

Less than.

Step-by-step explanation:

3 0
2 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
I need help...I don't understand
Andrej [43]
Keep change change [keep the first integer change the opperation and change the integer on your number or fraction ... Rember the answer takes the sign of the larger number .
3 0
3 years ago
DIRECT VARIATION
aivan3 [116]
Y\alphax
y=kx
36=6k
k=6
42=6x
x=\frac{42}{6}
x=7
8 0
3 years ago
3 Parts with a picture. Thanks!
tatuchka [14]

We have $8.50 an hour gross minus $2.15 an hour tax and bennys.  Then $3.75 daily expense.  In one week our net take-away y after x hours is

y = x(8.50 - 2.15) - 5(3.75)

That's the answer, or we can simplify it to

Answer: y = 6.35 x - 18.75

Answer: The slope, 6.35, is the net dollars per hour <em>before weekly expenses.</em>

Answer: The y intercept, -18.75, is the weekly expense, negative because it's an expense.

To make $120 in a week, we solve for x where y=120

120 = 6.35x - 18.75

138.75 = 6.35 x

x = 138.75 / 6.35 = 21.8503937007874

That wasn't the nice round number I was expecting/hoping for.  I don't see a mistake so let's go with

Answer: 21.85 hours to make $120

7 0
3 years ago
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