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nevsk [136]
3 years ago
10

Juan has $120 in his checking account. He buys 4 equally priced shirts and pays with a check. If Juan now has -$60 in his accoun

t, how much was each shirt ?
Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
3 0

Answer:

45

Step-by-step explanation:

Step 1. 120+60=180

Step 2. 120-180=-60

Step 3. 180 divded by 4

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Suppose Richard walks 1 kilometer every 10 minutes. How many meters further can he walk in 1 hour at this new rate?
Andrej [43]
Richard walks
1 kilometer : 10 minutes

That would mean 

6 kilometers : 60 minutes

<span>Hope that helps and correct me if I'm wrong!</span>
5 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
Tic is an isosceles triangle with a vertex angle I. if the angle of I is 70. find the measure of t.
Colt1911 [192]
Angles of a triangle = 180 degrees
T + C = 110 degrees, and T=C (according to the definition of an isosceles triangle).
measure of T is 110/2 which equals 55 degrees
3 0
3 years ago
Read 2 more answers
Helpppoooooppppppp pllalsssssss
kiruha [24]

Answer:

Step-by-step explanation:

A)55 + 12 + 43=110

B) 55+14+40=98

C)55 + 16 +37 =108

HOW MUCH DOSE THE ENTERE THINK NEED TO BE WHAT THE AMOUNT ???

5 0
3 years ago
A stop sign is showing each sids measures 12.4 inch and the distance from any sides to the opposite slide is 30 inch
elixir [45]
Okay, so, simply,  the area of the hexagon would be <span>399.48 sq in

The perimeter would be </span><span>74.4 in</span>
8 0
3 years ago
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