Math 110 final
-65 + 72i
Perform the indicated operations and write the result in standard form. (-4 - √-81)²
7/2
Solve for "x" using the definition of a determinant.
g(x) = (x + 2)²- 2
The graph of a quadratic function is given. Determine the function's equation.
400 pretzels
The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = -0.002x² + 1.6x - 300. Find the number of pretzels that must be sold to maximize profit.
x=4, x=8
Find the vertical asymptote, if any, of the graph of the rational function. x-49/x²-12x+32
5225
For the given functions f and g , find the indicated composition. f(x) = 15x² - 10x, g(x) = 12x - 5 (f∘g )(2)
25x / 4-40x
For the given functions f and g , find the indicated composition. f(x) = 5 / x-8, g(x) = 5x-5 (f∘g)(x)
g(x) = x² + 6x + 9
The graph of a quadratic function is given. Determine the function's equation.
graph the function
use the graph of f(x) = 2 to obtain the graph of x-4 g(x) = 2
{e^4 -5}
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer In √x + 5 =2
{6}
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer log (x+2) + log (x-4) =2
{1/4}
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer log 4^(x+2) - log 4^(x-4) =2
[16] [ 1]
Find the product AB, if possible
x
Find the product of the two matrices and then find a21.
[-9, ∞)
Find the range of the quadratic function. y + 9 = (x + 3)²
no vertical asymptote
Find the vertical asymptote, if any, of the graph of the rational function. f(x)= x/x²+7
20x² + 25x + 15
For the given functions f and g , find the indicated composition. f(x) = 4x² + 5x + 4, g(x) = 5x - 5 (g∘f)(x)
graph the function
Use the graph of log x to obtain the graph of f(x)= - 1/2 log 3^x
graph dashed line
Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g. g(x) = -f(x + 1) + 2 y = f(x)
{2, -2+3i, -2-3i}
Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x³ + 2x² + 5x - 26
f(x)=x^4 - 45x^2 - 196
Find an nth degree polynomial function with real coefficients satisfying the given conditions. n = 4; 2i, 7, and -7 are zeros; leading coefficient is 1
graph both lines
Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph the given function. g(x) = 1/3 |x+2| + 6
f(x)= log 3^(-x)
Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is given. Select the function for the graph from the options.
{ In 2.8 /3 In 5 }
Solve the exponential equation. Express the solution set in terms of natural logarithms. 5^3x =2.8
[ 9 13] [ 5 18]
Solve the problem. Let A = [ 3 3] [ 2 4] and B= [ 0 4] [ -1 6] Find 3A+B
2006
The formula A = 209e0.035t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 277 thousand?
{( 4,-2,3)}
solve the system of equations 28 +4z = 4(x -3y) 2(x - 2y - z) =10 -3(2x + y) + 2z = -12
(2,-4)
Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = -7(x - 2)²- 4
y=-4/5
Find the horizontal asymptote, if any, of the graph of the rational function. h(x) = -4x+1/5x+4
12 + 28i
Perform the indicated operations and write the result in standard form. √-16(7-√-9)
{2}
Solve the equation by expressing each side as a power of the same base and then equating exponents 2^(1+2x) = 32
{-1, 1}
Solve the equation by finding an expression for the determinant on the left, and then solving using the appropriate method.
1.3766
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places log 20^61.8
log x^48
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expression. 2 log x^4 + log x^3
Graph the polynomial function
f(x) = 1/4 - 1/4x4
y= 2x² + 12x + 29
The table below shows the number of birds for three selected years after an endangered species protection program was started. x (Number of years after 1980) 1 5 10 y (Number of birds) 43 139 349 Use the quadratic function y = ax² + bx + c to model the data. Solve the system of linear equations involving a, b, and c using matrices. Find the equation that models the data.
Domain: (-∞ , ∞ ) Range: [-12 , ∞)
Find the domain and range of the quadratic function whose graph is described. The vertex is (-1, -12) and the graph opens up.
( 8,∞ )
Find the domain of the logarithmic function. f(x) = log 4^(x+8)
( 4,∞)
Find the domain of the logarithmic function. f(x)= log 4^(x-4)
y = 0
Find the horizontal asymptote, if any, of the graph of the rational function. f(x)= -25x/5x³ + x² + 1
f-1(x) = ³√x + 4
Find the inverse of the one-to-one function f(x) = (x-4)³
f-1(x) = x² + 6
Find the inverse of the one-to-one function f(x) = √x-6
f -1(x) = 5/3x - 7/3
Find the inverse of the one-to-one function f(x) =5 / 3x+7
-25.0479
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places log 0.9^14
minimum: 27
Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. Objective function: z = x +8y + 7 Find the minimum.
[ -1 15] [-6 10]
Find the product AB, if possible
(-∞, 7]
Find the range of the quadratic function. f(x) = -x² - 8x - 9
y = x
Find the slant asymptote, if any, of the graph of the rational function. f(x)= x²+16/x
y = x-13
Find the slant asymptote, if any, of the graph of the rational function. f(x)= x²-5x+4/x+8
(-6 ± √21, 0)
Find the x-intercepts (if any) for the graph of the quadratic function. f(x) = x² + 12x + 15 Give your answers in exact form.
(-2,0) and (2,0)
Find the x-intercepts (if any) for the graph of the quadratic function. f(x) = x² - 4
log 4√r-4 / r
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expression. 1/2 (log 4 (r-4) - log 4 r)
In x^6 / 4√y
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expression. 6 In x - 1/4 In y
± 1/4 , ± 1/2 , ± 3/4 , ± 3/2 , ±1 , ±2 , ± 3, ±6
Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = -4x4 + 3x² - 2x + 6
± 1/6 , ± 1/3 , ± 1/2 , ± 2/3 , ±1 , ±2
Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = 6x4 + 2x³ - 4x² + 2
Graph the polynomial function
f(x)=x³ +2x² -5x-6
Graph the function by making a table of coordinates.
x f(x)= (3/2)
3, touches the x-axis and turns around; -5, crosses the x-axis; 5, crosses the x-axis
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = (x - 3)²(x² - 25)
0, touches the x-axis and turns around; -9, crosses the x-axis; 7, crosses the x-axis
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. x^4+ 2x³ - 63x² = 0
(0, -4)
Find the y-intercept for the graph of the quadratic function. f(x) = x² + 5x - 4
graph the function
Graph the functions in the same rectangular coordinate system. f(x)= 2^x and g(x)= log 2^x
graph the solution set
Graph the solution set of the system of inequalities or indicate that the system has no solution. -x + 6y < -30 x ≥ -4
graph the solution set
Graph the solution set of the system of inequalities or indicate that the system has no solution. x + 2y ≥ 2 x - y ≤ 0
1965 ; 21.2
In one U.S. city, the quadratic function f(x) = 0.0037x² - 0.48x + 36.78 models the median, or average, age, y, at which men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.)
(4 - √-15) + (2√3 + 2√5)i
Perform the indicated operations and write the result in standard form. (2 + √-5) (2 + √-3)
{-4}
Solve the equation by finding an expression for the determinant on the left, and then solving using the appropriate method.
{ 4/9 }
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer log (x+20) - log 4 = log (7x + 2)
{5}
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer log 3x = log 5 + log (x-2)
X= [ -6 -6 0] [ -6 2 2] [ 4 4 0]
Solve the matrix equation for X.
X= [ -4 -3] [ 4 -4]
Solve the matrix equation for X. Let A= [ 1 -1 ] [-3 -1] and B= [ -3 -4] [ 1 -5] X + A =
(2,8]
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation -x+8/x-2 ≥ 0
(-∞,7) or (9,∞)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation 2/ x-7 < 1
[-5/4,3)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation 4x+5/ 12-4x ≥ 0
(-∞,-2) or (-1/4,∞)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation x+9/x+2 < 5
(-∞,-7) U (-5,∞)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation x² + 12x + 35 > 0
(-∞,7) U (7,∞)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation x² - 14x + 49 > 0
[-2,2]
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. (x + 2)(x - 2) ≤ 0
[-12 24] [ 0 8]
Solve the problem. Let A = [-3 6 ] [ 0 2 ] Find 4A
{ (-1,-5), (5,19) }
Solve the system by the substitution method. 4x - y =1 y = x² - 6
{ (-1/8, -8), (1/6, 6)}
Solve the system by the substitution method. xy = 1 48x - y = 2
3
Solve the system of equations for the variable "z" using any method. x - y + z = 8 x + y + z = 0 x + y - z = -6
(-1,4)
Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = 3 - x² - 2x
-168
Evaluate the determinant.
8
Evaluate the determinant.
{-1, 4,-3+√5, -3-√5}
Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x4 + 3x³ - 18x² - 36x - 16
9.9 years
Find out how long it takes a $3000 investment to double if it is invested at 7% compounded monthly. Round to the nearest tenth of a year. Use the formula: nt A = P (1 + r/n)^nt
$90 for a tent, $50 for a sleeping bag; $10 for a camping stool
A store sells tents, sleeping bags, and camp stools. A customer buys a tent, 5 sleeping bags, and 2 camp stools for $360. The price of the tent is 9 times the cost of a camp stool. The cost of a sleeping bag is $40 more than the cost of a camp stool. Find the cost of each item.
7x + 9y ≤ 103 7x + 8y ≤ 97 x + y ≥ 7
An office manager is buying used filing cabinets. Small file cabinets cost $7 each and large file cabinets cost $9 each, and the manager cannot spend more than $103 on file cabinets. A small cabinet takes up 7 square feet of floor space and a large cabinet takes up 8 square feet, and the office has no more than 97 square feet of floor space available for file cabinets. The manager must buy at least 7 file cabinets in order to get free delivery. Let x = the number of small file cabinets bought and y = the number of large file cabinets bought. Write a system of inequalities that describes these constraints.