Chapter 5

Choose which lines are perpendicular. Line \(p\) passes through \((4,0)\) and \((6,4)\) Line \(q\) passes through \((0,4)\) and \((6,4)\) Line \(r\) passes through \((0,4)\) and \((0,0)\) A line \(p\) and line \(q\) (B) line \(p\) and line \(r\) (C) line \(q\) and line \(r\) (D) none of these

Use a calculator to evaluate $$7^{8}$$

Write an equation in standard form of the horizontal line and the vertical line that pass through the point. $$(10,-3)$$

Use a graph to determine whether the given three points seem to lie on the same line. If they do, prove algebraically that they lie on the same line and write an equation of the line. $$ (-3,-1),(0,1),(12,9) $$

Use a calculator to evaluate $$6^{9}$$

In Exercises 62 and \(63,\) describe the error. $$\begin{aligned}&y=\frac{1}{3} x-2\\\&\begin{array}{l}y=3\left(\frac{1}{3} x-2\right) \\ y=x-6\end{array}\end{aligned}$$

In Exercises 62 and \(63,\) a mountain climber is scaling a 300 -foot cliff at a constant rate. The climber starts at the bottom at 12: 00 P.M. By 12: 30 P.M., the climber has moved 62 feet up the cliff. Write an equation that gives the distance \(d\) (in feet) remaining in the climb in terms of the time \(t\) (in hours), What is the slope of the line?

Use a graph to determine whether the given three points seem to lie on the same line. If they do, prove algebraically that they lie on the same line and write an equation of the line. $$ (4,-2),(-1,2),(-8,9) $$

Use a calculator to evaluate $$5^{11}$$

In Exercises 62 and \(63,\) a mountain climber is scaling a 300 -foot cliff at a constant rate. The climber starts at the bottom at 12: 00 P.M. By 12: 30 P.M., the climber has moved 62 feet up the cliff. At what time will the mountain climber reach the top of the cliff?

Use a graph to determine whether the given three points seem to lie on the same line. If they do, prove algebraically that they lie on the same line and write an equation of the line. $$ (-2,-1),(3,2),(7,5) $$

Use a calculator to evaluate $$9^{13}$$

Use the following information. You are buying 20 dollars worth of bird seed that consists of two types of seed. Thistle seed attracts finches and costs 2 dollars per pound. Dark oil sunflower seed attracts many kinds of song birds and costs 1.50 dollars per pound. Write an equation that represents the different amounts of 2 dollars thistle seed \(x\) and 1.50 dollars dark oil sunflower seed \(y\) that you could buy.

The time \(t\) (in hours) needed to produce \(x\) units of a product is modeled by \(t=p x+s .\) If it takes 265 hours to produce 200 units and 390 hours to produce 300 units, what is the value of \(s ?\) (A) 1.25 (B) 15 (C) 100 (D) 125

Use a graph to determine whether the given three points seem to lie on the same line. If they do, prove algebraically that they lie on the same line and write an equation of the line. $$ (3,-3),(-1,13),(1,5) $$

Find the sum. $$-7+(-1)$$

What is an equation of the line that passes through the points \(\left(3 \frac{1}{2}, 4\right)\) and \(\left(-5,-\frac{9}{2}\right) ?\)

Find the sum. $$4+\left(-4 \frac{1}{2}\right)$$

Simplify the expression. $$ \frac{6 x+12 y}{24} $$

Find the sum. $$-9+11$$

You are in charge of buying prizes for a school contest. A one-strand rosette ribbon costs 2.00 dollars and a three-strand rosette ribbon costs 3.00 dollars . You have 10 dollars to spend. Write an equation that represents the different numbers of one-strand and three-strand rosette ribbons that you can purchase.

Find the value of \(k\) so that the line through the given points has slope \(m .\) $$ (2 k, 3),(1, k) ; m=2 $$

Simplify the expression. $$ \frac{48 a-56 b}{16} $$

Find the sum. $$-10+(-1)$$

You are in charge of buying prizes for a school contest. A one-strand rosette ribbon costs 2.00 dollars and a three-strand rosette ribbon costs 3.00 dollars . You have 10 dollars to spend. What is the greatest number of students that can receive a ribbon?

Find the value of \(k\) so that the line through the given points has slope \(m .\) $$ (k+1, k-1),(k,-k) ; m=k+1 $$

Simplify the expression. $$ \frac{14 x}{-28 y-1} $$

Find the sum. $$2+(-6)$$

You are in charge of buying prizes for a school contest. A one-strand rosette ribbon costs 2.00 dollars and a three-strand rosette ribbon costs 3.00 dollars . You have 10 dollars to spend. What is the least number of students that can receive a ribbon?

Find the value of \(k\) so that the line through the given points has slope \(m .\) $$ (k, k+1),(3,2) ; m=3 $$

Solve the equation. $$ 4 x-11=-31 $$

Find the sum. $$-18+(-2)$$

Find the value of \(k\) so that the line through the given points has slope \(m .\) $$ (k+1,3+2 k),(k-1,1-k) ; m=k $$

Solve the equation. $$ 5 x-7+x=19 $$

Find the sum. $$6+(-8)-4$$

Check whether the given number is a solution of the inequality. $$ 2 x<24 ; 8 $$

Solve the equation. $$ 18=4-\frac{2 x}{5} $$

Find the sum. $$4-(-7)+3$$

Check whether the given number is a solution of the inequality. $$ 7 y+6 \geq 10 ; 3 $$

Solve the equation. $$ 2 x-6=20 $$

Find the sum. $$5+(-3)+(-5)$$

Check whether the given number is a solution of the inequality. $$ 16 p-9 \leq 71 ; 5 $$

Solve the equation. $$ \frac{1}{2} a+8 \frac{1}{2} a=3 $$

Check whether the given number is a solution of the inequality. $$ 12 a \leq a-9 ;-2 $$

Solve the equation. $$ 7 y=9 y-8 $$

Choose the equation in standard form of the line that passes through the point \((-1,-4)\) and has a slope of 2. (A) \(2 x+y=-2\) (B) \(-2 x+y=-2\) (C) \(2 x+y=2\) (D) \(2 x-y=-2\)

Check whether the given number is a solution of the inequality. $$ 4 x \leq 28 ; 7 $$

Plot the points in the table. Determine whether the slope of the line given by the points is positive or negative. $$ \begin{array}{|c|c|c|c|c|c|c|} \hline x & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & -7 & -4 & -1 & 2 & 5 & 8 \\ \hline \end{array} $$

Check whether the given number is a solution of the inequality. $$ 6 c-4>14 ; 3 $$

Plot the points in the table. Determine whether the slope of the line given by the points is positive or negative. $$ \begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & 7 & 5 & 3 & 1 & -1 & -3 \\ \hline \end{array} $$