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iragen [17]
3 years ago
5

A library contains 2000 books. There are 3 times as man non fiction books. Write and solve a systems of equations to determine t

he number of nonfiction and fiction books.
Mathematics
1 answer:
icang [17]3 years ago
4 0

Answer:

The number of fiction books is <u>500</u> and non fiction books is <u>1500</u>.

Step-by-step explanation:

Given:

Total book library contains = 2000.

There are 3 times as many non fiction books as fiction books.

Now, to determine the number of non fiction books and fiction books.

Let the fiction books be x.

And the non fiction books be 3x.

Total books = 2000.

Now, to get the number of non fiction books and fiction books we put an equation:

3x+x=2000.

4x=2000.

Dividing both sides by 4 we get:

x=500.

Fiction books = 500.

Non fiction books = 3x=3\times 500=1500.

Therefore, the number of fiction books is 500 and non fiction books is 1500.

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2. The registration at a preschool is $125. Then,
denis23 [38]

The equation of the total cost is y = 475 x + 125, where y is the total cost for x months

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Step-by-step explanation:

The given is:

  • The registration at a preschool is $125
  • The parents must also pay $475 per month for  tuition

Assume that the total cost is y for x months

∵ The registration fee = $125 ⇒ paid once

∵  The parents pay $475 per month for  tuition

∵ The number of months is x

∴ The total cost y = 475 x + 125

The equation of the total cost is y = 475 x + 125, where y is the total cost for x months

∵ y = 475 x + 125 is in the form of the linear equation y = m x + b,

  m is the slope of the line and b is the y-intercept

∵ The slope of the line m is the rate of change y with respect to x

∴ m = 475

∴ The rate of change is $475 per month

a) The rate of change is $475 per month

∵ b is the initial value of y at x = 0

∴ b = 125

∴ The initial value is $125

b) The initial value is $125

∵ The independent variable is x

∴ The independent variable is the number of months (x)

c) The independent variable is the number of months (x)

∵ The dependent variable is y

∴ The dependent variable is the total cost after each month (y)

d) The dependent variable is the total cost after each month (y)

Learn more:

You can learn more about the word problem in brainly.com/question/5059091

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Hence, we can see that from the given image, one can increase the size of the ball by making use of the scale factor which measures the scale diagram and then divides it from the original and this would retain the dimension but would make it larger.

Read more about scale factors here:

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