Exam 7: The Basic Concepts of Algebra

From a point on a river, two boats are driven in opposite directions, one at 5 miles per hour and the other at 12 miles per hour. In how many hours will they be 51 miles apart?

If Gloria received a raise of 11 percent and is now making $23,310 a year, what was her salary before the raise?

Evaluate the expression. - $( - 3 ) ^ { 2 }$

Decide whether the statement translates into an expression or an equation. -9 times a number is 36.

Solve the equation. - $9 \mathrm { r } + 7 = 52$

Solve the equation. - $- 0.02 x + 0.1 ( x + 400 ) = 56$

If $f$ varies jointly as $q ^ { 2 }$ and $h$ , and $f = 24$ when $q = 2$ and $h = 3$ , find $q$ when $f = 160$ and $h = 5$ .

During the first four months of the year, Jack earned $740, $570, $1350 and $1410. If Jack must have an average salary of at least $1020 in order to earn retirement benefits, what must Jack earn in the Fifth month in order to qualify for benefits?

Solve the equation. - $- 0.7 ( 20 ) + 0.5 x = 0.2 ( 20 + x )$

Solve the equation. - $- [ 8 x + ( 4 x + 5 ) ] = 7 - ( 7 x + 7 )$

Solve and graph. - $\frac { 2 } { 5 } ( 5 x - 3 ) \leq \frac { 1 } { 2 } ( 6 x - 1 )$

Match the inequality with its correct representation. -

The equation is a contradiction. -The solution of the equation 7(4s - 2)= 28s - 14 is given as 0. Is this correct? Explain.

Each has the solution set {5}. -True or false? The solution of the equation 7y - 6 = 7y + 3 is 0.

Match the inequality with its correct representation. - $\{ x \mid x \leq - 1 \}$

Let x represent the unknown, and write an equation for the sentence. Do not solve. -If 6 times a number is added to -4, the result is equal to 10 times the number.

Determine the ratio and write it in lowest terms. -5 hours to 40 minutes

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -The difference between a number and 9.8

The volume of wood, V, obtained from a tree varies jointly as the height, $h$ , and the square of the girth (the distance around the tree trunk), g. If the volume is $38.4 \mathrm { ft } ^ { 3 }$ when the height is $30 \mathrm { ft }$ and the girth is $4 \mathrm { ft }$ , what is the volume when the height is $50 \mathrm { ft }$ and the girth is $6 \mathrm { ft }$ ?

Answer the question based on the given graph. - The data used to determine the graph were based on the number of tropical storms affecting Country X during the last ten years. A total of 672 tropical storms were reported. How many more tropical storms occurred during April than September? Round your answer to the nearest whole number, if necessary.