Find the domain of the function

Answers

Answer 1

Answer: For Domain, you just need to watch out for Square Roots and/or Fractions! 1) a POLYNOMIAL (no square roots or fractions), i.e. f(x) = x^2 + 3x + 1, domain is "all real numbers." 2) a FRACTION (w/ no square root), i.e. f(x) = (2x+1)/(x^2+5x+6). Set bottom "not equal" to zero.

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440 miles decreased by 95 percent

Answers

440 - 95%
440 x (1 - 95/100)
440 x 0,05
= 22

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The population of Florida in 2010 was 18,801,310 and the land area was 53,625 square miles. The population increased 5.8% by 2014. To the nearest whole number what is the population density in people per square mile for Florida in 2014? To the nearest whole number how much did the population density in people per square mile increase from 2010 to 2014?

Answers

In 2010 the population density was 341 people per square mile and the population density in 2014 was 361 people per square mile making a change of 20 ppl per sq mile

Two towns are 1,100 miles apart. A group of hikers Starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels 2 1/2 mile per hour slower than the other group, find the rate of each group.

Answers

Answer:

3.54 and 1.04

Step-by-step explanation:

Given:

Two towns are 1,100 miles apart.

A group of hikers Starts from each town and walks down the trail toward each other..

They meet after a total hiking time of 240 hours.

If one group travels 2 1/2 mile per hour slower than the other group.

Question asked:

Find the rate of each group.

Solution:

Let speed of faster hiker = $x\ mph$

Speed of slower hiker = $x-(5)/(2)\ mph$

As we know:

$Distance=speed* time$

Total distance between two town = Total combined speed of both hikers $*$ Total combined time taken

$1100=(x+x-(5)/(2) )*240\n \n Dividing\ both\ sides\ by\ 240\n \n 4.58=(x+x-(5)/(2) )\n \n 4.58=2x-(5)/(2) \n \nAdding\ both\ sides\ by\ (5)/(2) \n \n 4.58+ (5)/(2)=2x- (5)/(2)+ (5)/(2)\n \n (2*4.58+5)/(2) =2x\n \n (14.16)/(2) =2x\n \n By \ cross\ multiplication\n \n 2*2x=14.16\n \n 4x=14.16$

$By\ dividing\ both\ sides\ by \ 4\n \n x=3.54\ miles\ per\ hour$

Speed of faster hiker = $x\ mph$ = 3.54 miles per hour.

Speed of slower hiker = $x-(5)/(2)\ mph$ =

$3.54-(5)/(2) =3.54-2.5=1.04\ miles\ per\ hour$

Therefore, speed of faster hiker is 3.54 miles per hour and speed of slower hiker is 1.04 miles per hour.

You want to buy a house in 9 years. The estimated cost is $175,800.00. You want to make a 20% down payment and closing costs are 7%. How much in totality do you need to save each month to reach your goal if you cover closing costs and the down payment?

Answers

You have to save $439.50 each month to reach your goal if you cover closingcosts and the down payment.

What is the down payment?

A down payment is a sum of money that a buyer pays in the early stages of purchasing an expensive good or service.

You want to buy a house in 9 years.

The estimated cost is $175,800.00. You want to make a 20% down payment and closing costs are 7%.

The amount for the down payment:

175,800 x 20% = 35,160

The closing cost of house is;

175,800 x 7% = 12,306

Amount to save: 35,160 + 12,306 = 47,466

The monthlysavings is;

9 years x 12 months = 108 months

47,466 / 108 = 439.50 savings per month.

Hence, you have to save $439.50 each month to reach your goal if you cover closingcosts and the down payment.

Learn more about down payment here;

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Ryan has an eight-year loan for $6,000. He is being charged an interest rate of 5 percent, compounded annually. Calculate the total amount that he will pay.

Answers

Given:
Principal : $6,000
Interest Rate: 5%
Term : 8 years, compounded annually.

The term compounded annually is a hint that informs us to use the compounded interest formula instead of the simple interest formula.

Compounded interest formula is:

A = P(1 + r/n)^nt

where:
A = future value of loan or investment including the interest
P = principal
r = rate
n = the number of times the interest is compounded per year
t = the number of years the money is borrowed or invested

A = P (1 + r/n)^nt
A = 6,000 (1 + 0.05/1)¹ * ⁸
A = 6,000 (1.05)⁸
A = 6,000 (1.48)
A = 8,880

The total amount Ryan will pay after 8 years is $8,880.00

If the 1600m race is 4 laps, what is the path length raced?

Answers

it is 400 because you have to divide

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