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grigory [225]
3 years ago
6

A museum has 450 visitors each day. If they are open 5 hours, how many people do they see per hour?

Mathematics
1 answer:
il63 [147K]3 years ago
5 0

Answer: 90 visitors per hour

Explanation: "Per hour" means in 1 hour, so we can rewrite the given statement using fractions as <em>450 visitors/5 hours = __visitors/1 hour</em>.

To find out what goes in the bank, notice that we

have a 1 in the denominator of our second fraction.

So we want to find a fraction that is equivalent

to 450/5 that has a 1 in the denominator.

If we divide the numerator and denominator of 450/5 by 5,

we get the equivalent fraction 90/1 or <em>90 visitors/1 hour</em>.

So now we have <em>90 visitors/1 hour = __visitors/1 hour</em>.

So a 90 must go in the blank.

This means that the museum sees 90 visitors per hour.

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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times
rusak2 [61]

Answer:

x=30\\y=68\\z=82

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

y+z=5x

The third angle is 14 more than the second

z=y+14

And remember that the sum of these three angles must be equal to 180.

x+y+z=180

Let's take these equations

y+z=5x\\z=y+14\\x+y+z=180

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

x+y+z=180\\x+(y+z)=180\\x+(5x)=180

Distribute the + sign

x+5x=180

Combine like terms;

6x=180

Divide by 6.

x=\frac{180}{6}\\ x=30

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example z=y+14

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

x+y+z=180\\30+y+(y+14)=180

Distribute the + sign and Combine like terms;

30+y+y+14=180\\44+2y=180\\

Subtract 44 to isolate 2y.

2y=180-44\\2y=136

Now divide by 2.

y=\frac{136}{2}\\ y=68

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82

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3 years ago
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