Chapter 5

One base of a trapezoid is 8 feet longer than the other base and the height of the trapezoid is equal to the length of the shorter base. The area of the trapezoid is 20 square feet. a. Find the lengths of the bases and of the height of the trapezoid in simplest radical form. b. Show the lengths of the basezoid is equal to one-half the height times the sum of the lengths of the bases. c. Write, to the nearest tenth, rational approximations for the lengths of the bases and for the height of the trapezoid.

Write a quadratic equation with integer coefficients for each pair of roots. \(1,0\)

In \(26-37,\) find each product. $$ \left(-\frac{1}{8}+\frac{1}{8} i\right)(4+4 i) $$

Steve and Alice realized that their ages are consecutive odd integers. The product of their ages is \(195 .\) Steve is younger than Alice. Determine their ages by completing the square.

Write a quadratic equation with integer coefficients for each pair of roots. \(2+\sqrt{3}, 2-\sqrt{3}\)

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ 1+i $$

In \(35-43,\) write each number in simplest form. $$ 2 i^{5}+7 i^{7} $$

Write a quadratic equation with integer coefficients for each pair of roots. \(\frac{1+\sqrt{5}}{2}, \frac{1-\sqrt{5}}{2}\)

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ 2+4 i $$

In \(35-43,\) write each number in simplest form. $$ i+i^{3}+i^{5} $$

Write a quadratic equation with integer coefficients for each pair of roots. \(\frac{-1+\sqrt{3}}{3}, \frac{-1-\sqrt{3}}{3}\)

In \(35-43,\) write each number in simplest form. $$ 4 i+5 i^{8}+6 i^{3}+2 i^{4} $$

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ -1+2 i $$

Write a quadratic equation with integer coefficients for each pair of roots. \(3+i, 3-i\)

In \(35-43,\) write each number in simplest form. $$ i^{2}+i^{12}+i^{8} $$

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ 3-3 i $$

Write a quadratic equation with integer coefficients for each pair of roots. \(\frac{3-2 i}{2}, \frac{3+2 i}{2}\)

In \(35-43,\) write each number in simplest form. $$ i+i^{2}+i^{3}+i^{4} $$

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ \frac{1}{2}-\frac{1}{4} i $$

Write a quadratic equation with integer coefficients for each pair of roots. \(\frac{3}{2} i,-\frac{3}{2} i\)

In \(38-43,\) match the inequality with its graph. The graphs are labeled \((1)\) to \((6)\) graph can't copy $$ 4 x^{2}-2 x-y-2<0 $$

In \(35-43,\) write each number in simplest form. $$ i^{57} $$

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ 2-\frac{1}{2} i $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ x^{2} \leq 2 x+y ;(5,4) $$

One root of a quadratic equation is three more than the other. The sum of the roots is 15. Write the equation.

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ \frac{5}{6}+3 i $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ x^{2}+5 \geq y ;(-1,3) $$

The difference between the roots of a quadratic equation is 4i. The sum of the roots is 12. Write the equation.

In \(38-45,\) find the multiplicative inverse of each of the following in \(a+b i\) form. $$ 9+\pi i $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ x(x-13)>y ;(-5,130) $$

Write a quadratic equation for which the sum of the roots is equal to the product of the roots.

In \(44-51,\) locate the point that corresponds to each of the given complex numbers. $$ 4-2 i $$

In \(46-60,\) write each quotient in \(a+b i\) form. $$ (8+4 i) \div(1+i) $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ x^{2}-18 \geq y+3 x ;(0,-18) $$

Use the quadratic formula to prove that the sum of the roots of the equation \(a x^{2}+b x+c=0\) is \(-\frac{b}{a}\) and the product is \(\frac{c}{a}\)

In \(44-51,\) locate the point that corresponds to each of the given complex numbers. $$ -4-2 i $$

In \(46-60,\) write each quotient in \(a+b i\) form. $$ (2+4 i) \div(1-i) $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ 2(x-3)^{2}+3

A root of \(x^{2}+b x+c=0\) is an integer and \(b\) and \(c\) are integers. Explain why the root must be a factor of \(c .\)

In \(44-51,\) locate the point that corresponds to each of the given complex numbers. $$ \frac{1}{2}+4 i $$

In \(46-60,\) write each quotient in \(a+b i\) form. $$ (10+5 i) \div(1+2 i) $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ -4(x+2)^{2}-5 \leq y ;\left(1, \frac{2}{3}\right) $$

In \(44-51,\) locate the point that corresponds to each of the given complex numbers. $$ 0+3 i $$

In \(46-60,\) write each quotient in \(a+b i\) form. $$ (5-15 i) \div(3-i) $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ 4 x^{2}-4 x<3+y ;\left(0, \frac{5}{3}\right) $$

In \(44-51,\) locate the point that corresponds to each of the given complex numbers. $$ -3+0 i $$

In \(46-60,\) write each quotient in \(a+b i\) form. $$ \frac{2+2 i}{4-2 i} $$

In \(44-51 :\) a. Graph the given inequality. b. Determine if the given point is in the solution set. $$ 6 x^{2}+x \leq 2-y ;(10,0) $$

In \(44-51,\) locate the point that corresponds to each of the given complex numbers. $$ 0+0 i $$

In \(46-60,\) write each quotient in \(a+b i\) form. $$ \frac{10-5 i}{2+6 i} $$