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mathematics
linear algebra
Questions and Answers of
Linear Algebra
Solve and graph the solution set. (a) 4x - 3 > 2x + 7 (b) 8x + 1 ≥ 5x - 5 (c) x + 6 < 5x - 6
Find the domain of the function. (a) h(x) = √x - 7 (b) g(x) = √x + 8 (c) f(x) = √ 1 - 5x + 2
Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator. (a) x2 + y2 = 4 (b) x2 + y2 = 81 (c) x2 + (y - 3)2 = 16
Solve and write interval notation for the solution set. Then graph the solution set. (a) -2 ≤ x + 1 < 4 (b) -3 < x - 4 < 7 (c) 5 ≤ x - 3 ≤ 7
The equation y = 31.7x + 487 estimates the amount that small and midsize businesses spend, in billions of dollars, on information technology, where x is the number of years after 2007. For what years
The equation y = 1.393x + 19.593 estimates the percentage of U.S. households that have three or more televisions, where x is the number of years after 1985. For what years will the percentage of U.S.
Acme Movers charges $100 plus $30 per hour to move a household across town. Hank's Movers charges $55 per hour. For what lengths of time does it cost less to hire Hank's Movers?
Gina plans to invest $12,000, part at 4% simple interest and the rest at 6% simple interest. What is the most that she can invest at 4% and still be guaranteed at least $650 in interest per year?
Dillon plans to invest $7500, part at 4% simple interest and the rest at 5% simple interest. What is the most that he can invest at 4% and still be guaranteed at least $325 in interest per year?
A university invests $600,000 at simple interest, part at 6%, half that amount at 4.5%, and the rest at 3.5%. What is the most that the university can invest at 3.5% and be guaranteed $24,600 in
A foundation invests $50,000 at simple interest, part at 7%, twice that amount at 4%, and the rest at 5.5%. What is the most that the foundation can invest at 4% and be guaranteed $2660 in interest
Tori can be paid in one of two ways for selling insurance policies: Plan A: A salary of $750 per month, plus a commission of 10% of sales; Plan B: A salary of $1000 per month, plus a commission of 8%
Achal can be paid in one of two ways for the furniture he sells: Plan A: A salary of $900 per month, plus a commission of 10% of sales; Plan B: A salary of $1200 per month, plus a commission of 15%
If the point (p, q) is in the fourth quadrant, in which quadrant is the point (q, -p)?
Given that f(x) = x - 2x2, find f(-4), f(0), and f(1).
Given that g(x) = x + 6 / x - 3, find g(-6), g(0), and g(3).
Find the domain of the function. (a) g(x) = x + 9 (b) f(x) = -5 / x + 5 (c) h(x) = 1 / x2 + 2x - 3
Graph the function. (a) f(x) = -2x (b) g(x) = x2 - 1
Determine the domain and the range of the function.
Find the slope of the line containing the given points.(a) (-, 13) and (-2, -5)(b) (10, -1) and (-6, 3)(c) (5/7, 1/3) and (2/7, 1/3)
Determine the slope, if it exists, and the y-intercept of the line with the given equation. (a) f(x) = - 1/g x + 12 (b) y = -6 (c) x = 2
Explain as you would to a fellow student how the numerical value of the slope of a line can be used to describe the slant and the steepness of that line.
Explain how you could find the coordinates of a point 78 of the way from point A to point B.
Find the intercepts of the graph of the line -8x + 5y = -40.
Find the distance between the pair of points and find the midpoint of the segment having the given points as endpoints. (a) (a, 1/a) and (a + h, 1/a +h) (b) (a, √a) and (a + h, √a + h)
Find an equation for a circle with center (-5, 2) and radius of length 13.
Find the center and the radius of the circle given by the equation (x - 3)2 + (y + 1)2 = 4.
Graph the equation. (a) 3x - 6y = 6 (b) y = - 1/2 x + 3
Graph the equation. (a) y = - 2/3 x + 1 (b) 2x - 4y = 8 (c) y = 2 - x2
Find the distance between (3, 7) and (-2, 4).
Find the midpoint of the segment with endpoints (3, 7) and (-2, 4).
Find the center and the radius of the circle with equation (x + 1)2 + (y - 3)2 = 9. Then graph the circle.
Find an equation for a circle satisfying the given conditions. (a) Center: (0, - 4), radius of length 3/2 (b) Center: (- 2, 6), radius of length √13
Determine whether the relation is a function. Identify the domain and the range. (a) {(3, 1), (5, 3), (7, 7), (3, 5)} (b) {(2, 7), (-2, -7), (7, -2), (0, 2), (1, -4)}
Given that f(x) = x2 - x = 3, find each of the following. (a) f(0) (b) f(- 3) (c) f(a - 1) (d) f(- x)
Find an equation of a circle satisfying the given conditions. (a) Center (-5, 8) with a circumference of 10π units (b) Center (2, -7) with an area of 36π square units
Given that f(x) = x - 7 / x + 5, find each of the following. (a) f(7) (b) f(x + 1) (c) f(-5) (d) f (- 1/2)
A graph of a function is shown below. Find f(2), f(-4), and f(0).
Find the domain of the function. (a) f(x) = 4 - 5x + x2 (b) f(x) = 3 / x + 2 (c) f(x) = 1 / x2 - 6x + 5
Graph the function. Then visually estimate the domain and the range. (a) f(x) = √16 - x2 (b) g(x) = | x - 5 |
Answer the following questions. (a) Is the change in the inputs, x, the same? (b) Is the change in the outputs, y, the same? (c) Is the function linear? (1) x y -3 ................................
Find the slope of the line containing the given points. (a) (2, - 11), (5, - 6) (b) (5, 4), (-3, 4) (c) (1 / 2, 3), (1 / 2, 0)
The minimum wage was $5.15 in 1990 and $7.25 in 2010. Find the average rate of change in the minimum wage from 1990 to 2010.
Find the slope and the y-intercept of the line with the given equation. (a) y = - 7 / 11 x - 6 (b) - 2x - y = 7
Graph y = - 1 / 4 x + 3 using the slope and the y-intercept.
Clear County Cable Television charges a $110 installation fee and $85 per month for basic service. Write an equation that can be used to determine the total cost C(t) of t months of basic cable
Find the point on the x-axis that is equidistant from the points (-4, -3) and (-1, 5).
The function T given by T(d) = 10d + 20 can be used to determine the temperature T, in degrees Celsius, at a depth d, in kilometers, inside the earth. (a) Find T(5), T(20), and T(1000). (b) The
Write a slope-intercept equation for a line with the following characteristics. (a) m = - 2 / 3, y-intercept (0, -4) (b) m = 3, passed through (-2, -1) (c) Passes through (4, 1) and (-2, -1)
Write equations of the horizontal line and the vertical line that pass through (-4, 2 / 5).
Find a linear function h given h(-2) = -9 and h(4) = 3. Then find h(0).
Determine whether the lines are parallel, perpendicular, or neither. 3x - 2y = 8, 6x - 4y = 2
Find an equation of the line containing the given point and parallel to the given line. Given the point (1, -) and the line 2x + 3y = 4:
Find an equation of the line containing the given point and perpendicular to the given line. Given the point (1, -1) and the line 2x + 3y = 4:
Sample data in the table below show the height at the shoulders H, in centimeters, of an adult Indian elephant (Elephas maximus indicus) that corresponds to the right forefoot circumference c, in
Candaleria makes an investment at 5.2% simple interest. At the end of 1 year, the total value of the investment is $2419.60. How much was originally invested?
Use substitution to determine whether the given ordered pairs are solutions of the given equation. (a) (3, 24/9), (0, -9); 2x - 9y = - 18 (b) (0, 7), (7, 1); y = 7
Find the point on the y-axis that is equidistant from the points (-2, 0) and (4, 6).
Find the zero(s) of the function (a) f(x) = 6x - 18 (b) f(x) = x - 4 (c) f(x) = 2 - 10x (d) f(x) = 8 - 2x
Solve and write interval notation for the solution set. Then graph the solution set. (a) 2x - 5 < x + 7 (b) 3x + 1 ≥ 5x + 9 (c) -3 ≤ 3x + 1 ≤ 5
The equation y = 0.08x + 0.83 estimates the number of homeschooled children in the United States, n millions, where x is the number of years after 1999 (Source: Department of Education's National
Find the point on the x-axis that is equidistant from the points (1, 3) and (4, -3).
Find the domain.(a) f(x) = √1 - x / x - | x |(b) f(x) = (x - 9x-1)-1
Discuss why the graph of f (x) = - 3 / 5 x + 4 is steeper than the graph of g(x) = 1 / 2 x - 6.
Find the intercepts and then graph the line. (a) 2x - 3y = 6 (b) 10 - 5x = 2y
Explain in your own words why a linear function f(x) = mx + b, with m ≠ 0, has exactly one zero.
Why can the conjunction 3 < x and x < 4 be written as 3 < x < 4, but the disjunction x < 3 or x > 4 cannot be written 3 > x > 4?
Determine whether the ordered pair (1 / 2, 9 / 10) is a solution of the equation 5y - 4 = x.
Determine whether the points (-1, -3), (-4, -9), and (2, 3) are collinear.
Determine whether each graph is that of a function.Answer yes or no.(a)(b)
Find the domain of the function. (a) f(x) = 1 / x - 4 (b) g(x) = x3 + 2 (c) h(x) = √25 - x2
(a) Graph: f 1x2 = | x - 2 | + 3. (b) Visually estimate the domain of f(x). (c) Visually estimate the range of f(x).
Find the slope of the line containing the given points.(a) (- 2, 2 / 3), (-2, 5)(b) (4, - 10), (-8, 12)(c) (-5, 6), (3 / 4, 6)
Daily use of cigarettes by U.S. 12th graders is declining. In 1995, 21.6% of 12th graders smoked daily. This number decreased to 11.4% in 2008. Find the average rate of change in the percent of 12th
Find the intercepts of 5x - 2y = -10 and graph the line.
Find the slope and the y-intercept of the line with equation -3x + 2y = 5.
Clear Signal charges $80 for a cell phone and $49.95 per month under its standard plan. Write an equation that can be used to determine the total cost C(t) of operating a Clear Signal cell phone for
Write an equation for the line that passes through (-5, 4), and (3, -2).
Determine whether the lines are parallel, perpendicular, or neither. 2x + 3y = -12, 2y - 3x = 8
Matt is remodeling the front entrance to his home and needs to cut an arch for the top of an entranceway. The arch needs to be 8 ft wide and 2 ft high. To draw the arch, he will use a stretched
Find an equation of the line containing the point (-1, 3) and parallel to the line x + 2y = -6.
Find an equation of the line containing the point (-1, 3) and perpendicular to the line x + 2y = -6.
The data in the table below show a decrease in the average number of miles per passenger car from 2005 to 2008. Year, x Average Number of Miles per passenger Car 2005, 0
Find the distance between (5, 8) and (-1, 5).
The parking lot behind Kai's Kafé has a perimeter of 210 m. The width is three-fourths of the length. What are the dimensions of the parking lot?
Jessie's Juice Bar prices its bottled juices by raising the wholesale price 50% and then adding 25¢. What is the wholesale price of a bottle of juice that sells for $2.95?
Find the zero(s) of the function f(x) = 3x + 9.
Solve and write interval notation for the solution set. Then graph the solution set. (a) 5 - x ≥ 4x + 20 (b) - 7 < 2x + 3 < 9 (c) 2x - 1 ≤ 3 or 5x + 6 ≥ 26
Morgan Movers charges $90 plus $25 per hour to move households across town. McKinley Movers charges $40 per hour for cross town moves. For what lengths of time does it cost less to hire Morgan Movers?
The graph of g(x) = 1 - 1 / 2 x is which of the following?(a)(b) (c) (d)
Consider any right triangle with base b and height h, situated as shown. Show that the midpoint of the hypotenuse P is equidistant from the three vertices of the triangle.Determine whether each of
Suppose that for some function h, h(x + 2) = 1 / 2 x. Find h(-2)
Find the center and the radius of the circle (x + 4)2 + (y - 5)2 = 36
(a) Determine whether the relation 51{(-4, 7), (3, 0), (1, 5), (0, 7) is a function. Answer yes or no. (b) Find the domain of the relation. (c) Find the range of the relation.
Given that f(x) = 2x2 - x + 5, find each of the following. (a) f(-1) (b) f(a + 2)
Given that f(x) = 1 - x / x, find each of the following. (a) d(0) (b) f(1)
Find the intercepts and then graph the line. (a) 5x - 3y = -15 (b) 2x - 4y = 8 (c) 2x + y = 4
Graph the equation. (a) y = 3x + 5 (b) y = -2x - 1 (c) x - y = 3
Graph and label the given points by hand. (a) (4, 0), (-3, -5), (-1, 4), (0, 2), (2, -2) (b) (1, 4), (-4, -2), (-5, 0), (2, -4), (0, 3) (c) (-5, 1), (5, 1), (2, 3), (2, -1), (0, 1)
Use a graphing calculator to graph the equation in the standard window. (a) y = 2x + 1 (b) y = 3x - 4 (c) 4x + y = 7
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