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3 years ago

A function is created to represent the costs of living per person in the family. What restrictions would be made to the domain?

1 answer:

7 0

The domain would only include positive integers, assuming x is the number of people and y is the dollar amount. You can't have a negative number of people and you also cannot have a fraction of a person.

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Find the value of the variable y, where the sum of the fractions 6/(y+1) and y/(y-2) is equal to their product.

Blizzard [7]

Answer:

The answer is

$y = 3$

$y = - 4$

Step-by-step explanation:

We must find a solution where

$\frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2}$

Consider the Left Side:

First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get

$\frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1}$

Which equals

$\frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)}$

Add the fractions

$\frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2}$

Simplify the right side by multiplying the fraction

$\frac{6y}{(y + 1)(y + 2)}$

Set both fractions equal to each other

$\frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)}$

Since the denomiator are equal, we must set the numerator equal to each other

$6y = {y}^{2} + 7y - 12$

$= {y}^{2} + y - 12$

$(y + 4)(y - 3)$

$y = - 4$

$y = 3$

6 0

2 years ago

Read 2 more answers

2. The sum of two numbers is 30. Determine the two numbers if their product is a maximum.

SCORPION-xisa [38]

Answer:

X+y=30

X=30-y

Z=yx

Z=y(30-y)

D/dy

z=30–2y

At max 30–2y=0

2y=30 Y=15

Therefore x=15

Step-by-step explanation:

5 0

2 years ago

There is $500 in Holly's bank account. She takes out $50 from her account each month but doesn't put money back in. What is the

galina1969 [7]

Answer:

The rate of change or slope m = -50

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

m is the rate of change or slope

b is the y-intercept

Given that there is $500 in Holly's bank account.

Thus, the y-intercept b = 500

It is stated that she takes out $50 from her account each month but doesn't put money back in.

It means the rate of change or slope is decreasing.

Thus, the rate of change or slope m = -50

<u>EXTRA BONUS!</u>

We can also determine the line equation by substituting m = -50 and b = 500 in the slope-intercept form

$y = mx+b$

y = -50x + 500

Here:

The slope m = -50

The y-intercept = 500

3 0

2 years ago

Diego and Pablo disagree on whether 0.8759 is a rational number or not. Diego says it is not rational, and Pablo says that it is

mina [271]

Pablo is correct because , the number 0.8759 is rational number because it doesn't go on like pi or the square root of 2 it stops at a certain point and was probably rounded . I'm not sure if its 100% correct.

Hope this helps!

8 0

2 years ago

Read 2 more answers

Mary has 3 red marbles and 7 yellow marbles in a bag. What is the probability of she draw 3 marbles at the same time, all of the

LenaWriter [7]

The probability would be 3/10 or 30%

3 0

2 years ago