Pat deposits $600 in a savings account at a simple interest rate 6% per year for 5 years. How much money will Pat have earned in interest at the end of 5 years?

In this problem, we take the triangle as a right-angled triangle and label it as follows:

From the Pythagoras theorem A2 + B2= C2, we can look for a combination of A and B that when the squares of A and B are summed give a square of 13.  Mathematically,

But C=13 inches

If we take A=5 inches and B=12 inches, then

Next, we take A=2.5 inches, B=6 inches

Next, we take A=2.5 inches, B=4 inches

6.25+16=169

22.25≠169

Taking A=5 inches and B=8 inches

From the above computation, the combination of A=5 inches and B=12 inches give a triangle with a hypothenuse of 13 inches.

Looking at the given trend, it is observed that the price increases with years. From 2008 to 2012, the price is fairly constant but we expect it to be more than $130,000 in the year 2016. The expected price in 2016 is $140,000.

We use the properties of exponent with the same base to solve for above expression.

Multiplication of exponents with same base, we add the exponents

Division of exponents with same base, we subtract the exponents

Using these two properties, we can solve the expression:

Now we use the following properties:

y0 =1, and, thus

Here we collect like terms together and solve for the unknown value of x.

7x-6=3x-26

Add 6 to both sides of the equation

7x-6+6=3x-26+6

7x=3x-20

Subtract 3x from both sides of the equation

7x-3x=-20

4x=-20

Divide both sides by 4

4x/-4=-20/4

x = -5

The value of x = -5

To answer this question, we need to observe the trend of the number of days with dollars. On day 2, the dollars were 8, after 5 days, the dollars decreased to 3, after 13 days, the dollars increased to 10. After 14 days, the dollars declined to 6 and again rose to 16 dollars after 19 days.

From this observation, we cannot be able to establishany correlation between days and dollars.

From the given scenario:

Initial charge is $40

Additional charge per circular cloth=$5c

Additional charge per rectangular cloth=$3.50r

Total cost = additional charge per circular rectangular cloths + Initial charge

Total cost, T = 5c + 3.5r + 40

We solve the problem by first finding the amount of gallons needed for the whole trip then find the cost of the gallon.

The car uses 1 gallon to cover 25 miles, which is same as:

Now, in 3000 miles, the car will use how many gallons of gasoline?

A trip of 3000 miles will need 120 gallons. And to find the cost of 120 gallons, we proceed as follows:

The family will spend $199.20 to drive for 3000 miles.

When dividing fractions, the division sign is changed into multiply sign and the first fraction is multiplied by the inverse of the second fraction.

Change division to multiply sign and find invers of 5/8. The inverse of a fraction is inverting the given fraction. The denominator becomes the numerator and the numerator becomes the denominator.

From the given options, we can arrange the numbers from the smallest to the largest as:

-271.906, -193.823, 145.884, 235.971

From the above, it can be noted that -271 is less than -193 while 235 is more than 145.

from the provided table, the first option represents the amount of gas in gallons while the second column shows the distance in miles. Thus, (6, 144) will denote that the car can 144 miles by consuming 6 gallons of a gas.