If x = 0, (x – 5)² = 25 and (x + 5)² = 25, so the quantities are equal.

If x = 1, (x – 5)² = (–4)² = 16 and (x + 5)² = 6² = 36, so B is greater.

This is a contradiction, so the answer cannot be determined.

If Molly was born 10 years ago, she is now 10 years old. If Ginny is twice Molly's age now, she is 20 years old, which made her 10 years old when Molly was born. If Ginny was 10 years old when Molly was born and was twice as old as Lily, Lily must have been 5 years old. If Lily was 5 years old 10 years ago, she must be 15 years old currently.

Since we know the mean is 7, and the number of terms is 5, we can first find the value of x:

((x – 2)+ (x) + (x + 1) + (x + 4) + (x + 7))/5 = (5x + 10)/5 = 7

x = 5

Since the terms are already listed in order, we can simpy plug in x = 5 to the middle value to get 5 + 1 = 6 as the median term. 

The answer is 98.

If the area of each square tile is 49 then each side of the tile is 7. The width of the floor is 98 so 14 tiles would fit across. The length of the floor is 49 so 7 tiles would fit down.

14 tiles * 7 tiles = 98 tiles total

Since both values are negative, in both situations the final result of the fraction will be positive regardless of the absolute value sign. Additionally, the definition of the exponent "^–1" means the value is becoming its reciprocal. Thus, "x" → "1/x" and "1/y" → "y", equating to y/x.

Set up two different equations:

\(\displaystyle f-8=j\) and \(\displaystyle f-2=2(j+2)\)

Note the importance in the second equation of accounting for the exchange of 2 chickens for both quantities: Jan loses the two that she gives to Fran, and Fran gains the two that she receives.

Solve for \(\displaystyle f\) by substituting \(\displaystyle f-8\) for \(\displaystyle \dpi{100} \small j\) in the second equation:

\(\displaystyle f-2=2(f-8+2)\)

Solving for \(\displaystyle f\) results in \(\displaystyle 10\).

In order to solve this problem we must go through the statement step by step to determine the correct algebraic expression.

The first part of the problem states "The square of x". Therefore we are certain the the expression contains \(\displaystyle x^2\). Following that, it says "multiplied by three", therefore we simply multiply the square of x by three, obtaining \(\displaystyle 3x^2\).

The statement then says, "the result subtracted by 18". This means that we take whatever we had previously, in this case, \(\displaystyle 3x^2\) and subtract 18, resulting in \(\displaystyle 3x^2-18\).

The final part of the statement says "the final result divided by 15". Therefore we once again take what we had previously, \(\displaystyle 3x^2-18\) and divide the entire thing by 15. Thus our final expression is \(\displaystyle \frac{3x^2-18}{15}\).

To solve this problem, we must work step by step through the information given to us.

The first part of the problem states "The difference between two positive integers is 9". If we assign variables \(\displaystyle x\) and \(\displaystyle y\) to the two integers, we can express the statement as \(\displaystyle x-y=9\). In this expression, \(\displaystyle y\) is the smaller variable.

The second part of the problem states "The larger number is 4 times larger than the smaller number". Using the same variables we can express this statement as \(\displaystyle x=4y\).

Plugging in \(\displaystyle x=4y\) into the equation obtained from the first part of the statement, \(\displaystyle x-y=9\), we find \(\displaystyle 4y-y=9\) or \(\displaystyle y=3\). Therefore the value of the smaller integer is \(\displaystyle 3\).

To solve this problem, we must simplify each quantity to its simpliest form, then compare the two.

Quantity A: \(\displaystyle \frac{x^5}{x^{-3}}=x^5x^3=x^8\)

Quantity B:\(\displaystyle \frac{x^8}{x^{2}}=x^6\)

After simplifying, we can tell that Quantity A will always be larger than Quantity B when \(\displaystyle x>1\).

The mean value of the houses can be determined by summing up all the values of the houses and dividing by the total number of houses. In 2014, the \(\displaystyle 5\) houses were worth a total of \(\displaystyle \$750\textup{,}000\).  This means the mean value is \(\displaystyle \frac{\$750,000}{5}=\$ 150,000\).

In 2015, two houses decreased in price by \(\displaystyle \$50,000\) while one house increased in price by \(\displaystyle \$100\textup{,}000\).  This means the net value of the \(\displaystyle 5\) houses is still \(\displaystyle \$750,000\).  This means that the mean value of the \(\displaystyle 5\) houses did not change from 2014-2015 meaning the two quantities are equal.