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andrezito [222]
3 years ago
8

A copy machine makes

Mathematics
1 answer:
IrinaK [193]3 years ago
7 0
This problem can be represented in a formula with fractions. To make it more simple, we are converting 5m30s to just pure seconds, which = 154 copies in 330 seconds.

You set up the formula like this: 154/330 = x/60. (it is x/60 because you want to know the x amount of copies per 60 seconds)

Cross multiply, you get 330x = 9240. Divide both sides by 330, you get:

 x = 28 copies.

The final answer is 28 copies per minute
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Marks's dad drove 123 miles in 2 hours. At that rate, how many miles would he drive in 5 hours?
mihalych1998 [28]

Answer:

307.5

Step-by-step explanation:

He drove 123 miles in 2 hours. If you go 100 miles in 2 hours that means you went 50 miles in one hour right? Using the same logic we can convert 123 miles in 2 hours to 61.5 miles per hour and then multiply it by 5.

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2 years ago
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Tomtit [17]
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Solve sin 0 + 1 = cos20 on the interval 0 ≤ 0 < 2pi. Show work please!
yan [13]

Answer:

\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}

Step-by-step explanation:

You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

cos(2\theta)=1-2sin^2(\theta)

so we will make that replacement, getting everything in terms of sin:

sin(\theta)+1=1-2sin^2(\theta)

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

2sin^2(\theta)+sin(\theta)=0

We can factor out the sin(theta), since it's common in both terms:

sin(\theta)(2sin(\theta)+1)=0

Because of the Zero Product Property, either

sin(\theta)=0 or

2sin(\theta)+1=0

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi.  They are:

\theta=\frac{\pi}{2},\frac{3\pi}{2}

The next equation needs to first be solved for sin(theta):

2sin(\theta)+1=0 so

2sin(\theta)=-1 and

sin(\theta)=-\frac{1}{2}

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

\theta=\frac{2\pi}{3},\frac{4\pi}{3}

7 0
3 years ago
In the figure shown to the right, two angle measurements are given. Determine the others.
creativ13 [48]

The figure is shown below

From the figure

Angle 150 degree and angle p forms angles on a straight

Since the sum of angles on a straight line equals 180 degrees

Hence

150^{\circ}+p=180^{\circ}

Solve for p in the equation

\begin{gathered} p=180^{\circ}-150^{\circ} \\ p=30^{\circ} \end{gathered}

Hence, p = 30

From the figure

Angle p and angle q are vertically opposite angles

Since vertically opposite angles are equal then

p=q=30^{\circ}

Hence, q = 30

Applying the rule of angles on a straight line

This implies

q+w+60=180

Substitute q = 30 into the equation

30+w+60=180

Solve for w

\begin{gathered} w+90=180 \\ w=180-90 \\ w=90 \end{gathered}

Hence, w = 90

8 0
1 year ago
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