college algebra questions 16 through 40

Question 16 (2.5 points)

Evaluate the following expression without using a calculator.

8log8 19

Question 16 options:

	17
	38
	24
	19

Question 17 (2.5 points)

Find the domain of following logarithmic function.

f(x) = log5 (x + 4)

Question 17 options:

	(-4, ∞)
	(-5, -∞)
	(7, -∞)
	(-9, ∞)

Question 18 (2.5 points)

Write the following equation in its equivalent logarithmic form.

3√8 = 2

Question 18 options:

	LOG2 3 = 1/8
	LOG8 2 = 1/3
	LOG2 8 = 1/2
	LOG3 2 = 1/8

Question 19 (2.5 points)

Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0 to 2A0 ) is given by t = ln 2/k.

Question 19 options:

	A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t$A_0=A_0{e}^{kt};\ln =e^{kt};\ln 2=\ln e^{kt};\ln 2=kt;\ln 2/k=t$
	2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t$2A_0=A_{0}e;2=e^{kt};\ln =\ln e^{kt};\ln 2=kt;\ln 2/k=t$
	2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t$2A_0=A_0{e}^{kt};2=e^{kt};\ln 2=\ln e^{kt};\ln 2=kt;\ln 2/k=t$
	2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe$2A_{}0=A_0{e}^{kt};2=e^{kt};\ln 1=\ln e^{kt};\ln 2=kt;\ln 2/k=t^{oe}$

Question 20 (2.5 points)

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution.

ex = 5.7

Question 20 options:

	{LN 5.7}; ≈1.74
	{LN 8.7}; ≈3.74
	{LN 6.9}; ≈2.49
	{LN 8.9}; ≈3.97

Question 21 (2.5 points)

Solve each equation by the addition method.

x2 + y2 = 25 (x – 8)2 + y2 = 41

Question 21 options:

	{(3, 5), (3, -2)}
	{(3, 4), (3, -4)}
	{(2, 4), (1, -4)}
	{(3, 6), (3, -7)}

Question 22 (2.5 points)

Write the partial fraction decomposition for the following rational expression.

ax +b/(x – c)2 (c ≠ 0)

Question 22 options:

	a/a – c +ac + b/(x – c)2$a/a–c+ac+b/(x–c{)}^{\mathrm{}}$
	a/b – c +ac + b/(x – c)$a/b–c+ac+b/(x–c)$
	a/a – b +ac + c/(x – c)2$a/a–b+ac+c/(x–c{)}^{\mathrm{}}$
	a/a – b +ac + b/(x – c)$a/a–b+ac+b/(x–c)$

Question 23 (2.5 points)

Solve the following system.

3(2x+y) + 5z = -1 2(x – 3y + 4z) = -9 4(1 + x) = -3(z – 3y)

Question 23 options:

	{(1, 1/3, 0)}
	{(1/4, 1/3, -2)}
	{(1/3, 1/5, -1)}
	{(1/2, 1/3, -1)}

Question 24 (2.5 points)

Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.

(-1, 6), (1, 4), (2, 9)

Question 24 options:

	y = 2x2 − x + 3$y=2x^2–x+3$
	y = 2x2 + x2 + 9$y=2x^2+x2+9$
	y = 3x2 − x − 4$y=3x^2–x–4$
	y = 2x2 + 2x + 4$y=2x^2+2x+4$

Question 25 (2.5 points)

A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.

Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.

Question 25 options:

	Z = 200X + 125Y
	Z = 125X + 200Y
	Z = 130X + 225Y
	Z = -125X + 200Y

Question 26 (2.5 points)

Let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers.

The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

Question 26 options:

	X + Y = 7; X – Y = -1; 3 AND 4
	X + Y = 7; X – Y = -1; 5 AND 6
	X + Y = 7; X – Y = -1; 3 AND 6
	X + Y = 7; X – Y = -1; 2 AND 3

Question 27 (2.5 points)

Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.

(-1, -4), (1, -2), (2, 5)

Question 27 options:

	y = 2x2 + x − 6$y=2x^2+x–6$
	y = 2x2 + 2x − 4$y=2x^2+2x–4$
	y = 2x2 + 2x + 3$y=2x^2+2x+3$
	y = 2x2 + x − 5$y=2x^2+x–5$

Question 28 (2.5 points)

Solve each equation by the substitution method.

y2 = x2 – 9 2y = x – 3

Question 28 options:

	{(-6, -4), (2, 0)}
	{(-4, -4), (1, 0)}
	{(-3, -4), (2, 0)}
	{(-5, -4), (3, 0)}

Question 29 (2.5 points)

Solve each equation by the substitution method.

x2 – 4y2 = -7 3×2 + y2 = 31

Question 29 options:

	{(2, 2), (3, -2), (-1, 2), (-4, -2)}
	{(7, 2), (3, -2), (-4, 2), (-3, -1)}
	{(4, 2), (3, -2), (-5, 2), (-2, -2)}
	{(3, 2), (3, -2), (-3, 2), (-3, -2)}

Question 30 (2.5 points)

Solve the following system.

2x + y = 2 x + y – z = 4 3x + 2y + z = 0

Question 30 options:

	{(2, 1, 4)}
	{(1, 0, -3)}
	{(0, 0, -2)}
	{(3, 2, -1)}

Question 31 (2.5 points)

Perform the long division and write the partial fraction decomposition of the remainder term.

x5 + 2/x2 – 1

Question 31 options:

	x2 + x − 1/2(x + 1) + 4/2(x − 1)$x^2+x–1/2(x+1)+4/2(x–1)$
	x3 + x − 1/2(x + 1) + 3/2(x − 1)$x^3+x–1/2(x+1)+3/2(x–1)$
	x3 + x − 1/6(x − 2) + 3/2(x + 1)$x^3+x–1/6(x–2)+3/2(x+1)$
	x2 + x − 1/2(x + 1) + 4/2(x − 1)$x^2+x–1/2(x+1)+4/2(x–1)$

Question 32 (2.5 points)

Write the partial fraction decomposition for the following rational expression.

4/2×2 – 5x – 3

Question 32 options:

	4/6(X – 2) – 8/7(4X + 1)
	4/7(X – 3) – 8/7(2X + 1)
	4/7(X – 2) – 8/7(3X + 1)
	4/6(X – 2) – 8/7(3X + 1)

Question 33 (2.5 points)

Write the form of the partial fraction decomposition of the rational expression.
7x – 4/x2 – x – 12

Question 33 options:

	24/7(x − 2) + 26/7(x + 5)$24/7(x–2)+26/7(x+5)$
	14/7(x − 3) + 20/7(x2 + 3)$14/7(x–3)+20/7(x^2+3)$
	24/7(x − 4) + 25/7(x + 3)$24/7(x–4)+25/7(x+3)$
	22/8(x − 2) + 25/6(x + 4)$22/8(x–2)+25/6(x+4)$

Question 34 (2.5 points)

Solve the following system by the addition method.

{4x + 3y = 15
{2x – 5y = 1

Question 34 options:

	{(4, 0)}
	{(2, 1)}
	{(6, 1)}
	{(3, 1)}

Question 35 (2.5 points)

Write the partial fraction decomposition for the following rational expression.

x + 4/x2(x + 4)

Question 35 options:

	1/3x + 1/x2 − x + 5/4(x2 + 4)$1/3x+1/x^2–x+5/4(x^2+4)$
	1/5x + 1/x2 − x + 4/4(x2 + 6)$1/5x+1/x^2–x+4/4(x^2+6)$
	1/4x + 1/x2 − x + 4/4(x2 + 4)$1/4x+1/x^2–x+4/4(x^2+4)$
	1/3x + 1/x2 − x + 3/4(x2 + 5)$1/3x+1/x^2–x+3/4(x^2+5)$

Question 36 (2.5 points)

Write the form of the partial fraction decomposition of the rational expression.
5×2 – 6x + 7/(x – 1)(x2 + 1)

Question 36 options:

	A/x − 2 + Bx2 + C/x2 + 3$A/x–2+B{x}^2+C/x^2+3$
	A/x − 4 + Bx + C/x2 + 1$A/x–4+Bx+C/x^2+1$
	A/x − 3 + Bx + C/x2 + 1$A/x–3+Bx+C/x^2+1$
	A/x − 1 + Bx + C/x2 + 1$A/x–1+Bx+C/x^2+1$

Question 37 (2.5 points)

Solve each equation by the substitution method.

x + y = 1 x2 + xy – y2 = -5

Question 37 options:

	{(4, -3), (-1, 2)}
	{(2, -3), (-1, 6)}
	{(-4, -3), (-1, 3)}
	{(2, -3), (-1, -2)}

Question 38 (2.5 points)

Solve the following system by the substitution method.

{x + 3y = 8
{y = 2x – 9

Question 38 options:

	{(5, 1)}
	{(4, 3)}
	{(7, 2)}
	{(4, 3)}

Question 39 (2.5 points)

Write the partial fraction decomposition for the following rational expression.

6x – 11/(x – 1)2

Question 39 options:

	6/x − 1 − 5/(x − 1)2$6/x–1–5/(x–1{)}^{\mathrm{}}$
	5/x − 1 − 4/(x − 1)2$5/x–1–4/(x–1{)}^{\mathrm{}}$
	2/x − 1 − 7/(x − 1)$2/x–1–7/(x–1)$
	4/x − 1 − 3/(x − 1)$4/x–1–3/(x–1)$

Question 40 (2.5 points)

Perform the long division and write the partial fraction decomposition of the remainder term.

x4 – x2 + 2/x3 – x2

Question 40 options:

	x + 3 − 2/x − 1/x2 + 4x − 1$x+3–2/x–1/x^2+4x–1$
	2x + 1 − 2/x − 2/x + 2/x + 1$2x+1–2/x–2/x+2/x+1$
	2x + 1 − 2/x2 − 2/x + 5/x − 1$2x+1–2/x^2–2/x+5/x–1$
	x + 1 − 2/x − 2/x2 + 2/x − 1