Math Cumulative Final
You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?
$1.25 for a soft taco and $2.50 for a burrito
An adult pass for a zoo costs $4 more than a children's pass. When 296 adult and children's passes were sold, the total revenue was $3,316. Find the cost of an adult pass.
$7.25
Write an equation in slope-intercept form with the given information: (-6, 5), (-4, 6)
y = (1/2)x + 8
Write an equation in slope-intercept form with the given information: (7, -9), perpendicular to y = (1/2)x + 9
y = -2x + 5
Solve the equation. Check for extraneous solutions: |3-y| = 2
y = 1, y=5
Write an equation in slope-intercept form with the given information: (2, -1), m = 4
y = 4x-9
What is the equation for slope-intercept form?
y = mx + b
Solve the equation for y: 7y=15-2xy
y=15/(2x+7)
Solve the equation for y: 8xy+4y-20=2y
y=20/(8x+2)
Can you graph a system of inequalities?
yes
Can you graph an equation or inequality? Examples from Chapter Test 2: y = -5x+3 3y - x = -12 2x + 2y > 2 y = (1/3)|x+2| - 4 y > -|x-5| + 6
yes
Can you graph piecewise functions? Example from Chapter Test 2: f(x) = {x+1, x ≥ 3} {-x-3, x < 3}
yes
Can you multiply and add/subtract matrices?
yes
Can you solve a system of equations by graphing?
yes
can you graph quadratic equations in standard, vertex, and intercept form
yes
Simplify: √11/√8
√22/4
Solve the equation: 1.1h + 1.3 = 6.8
h=5
A small business' profits over the last year have been related to the price of its product. The relationship is: R(p) = -0.4p^2 + 64p - 2400, where R is the revenue measured in thousands of dollars and p is the price of the product measured in dollars. What price would maximize the revenue?
$80
Solve the system using elimination: 2x + y = -4 5x - 3y = 1
(-1, -2)
Solve the system using substitution: 3x + 6y = 3 -x + 3y = 4
(-1, 1)
Solve the system using elimination: 4x - 7y = 4 7x - 10y = -2
(-6, -4)
Solve the system using elimination: 3x + 6y = 17 -6x - 3y = -13
(1, 7/3)
Simplify: (5 + 2i)/(3-2i)
(11/13) + (16/13)i
Simplify: 7/(4-√5)
(28+7√5)/11
Solve the system using substitution: 9x + y = 36 -6x - 10y = -24
(4, 0)
Solve the system using substitution: 4x + y = 28 y = 3x
(4, 12)
Find the slope of the line: thru (-5/2, -6), (1/2, -9)
-1
Find the slope of the line: thru (5, -2.3), (-3, 5.7)
-1
Simplify: (5-3i)/(2+4i)
-1/10 - (13/10)i
Find the slope of the line: thru (-3, -4), (1, -5)
-1/4
Solve the inequality: |x + 4| - 6 < 9
-19 < x < 11
Solve the inequality algebraically: x^2 - 5x - 14 ≤ 0
-2 ≤ x ≤ 7
Find the slope of the line: thru (5, 1), (7, -7)
-4
Solve the inequality: |10r - 5| < 45
-4 < r < 5
Evaluate the determinant of the matrix: [2 -7] [-8 4]
-48
Solve the inequality algebraically: 2x^2 + 13x + 6 < 0
-6 < x < -1/2
Evaluate the expression when x=-5 and y=3: (x-3y)/(2x^2)
-7/25
Evaluate the expression when x=2 and y=6 (4x-(1/2)y)/(2y-x)
1/2
Find the slope of the line: thru (0, -1), (4, 1)
1/2
Solve the inequality: -3.92 > 0.9u - 14 ≥ -25.16
11.2 > u ≥ -12.4
Evaluate the determinant of the matrix: [6 5 -3] [-5 4 -2] [1 -4 5]
139
Simplify the expression: 4(3n+6) + 2(n-3)
14n+18
Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height h (in meters above the ground), x seconds after Antoine threw it, is modeled by: h= -2x^2 + 4x + 16 What is the height of the ball at the time it is thrown?
16 meters
Suppose you launch a model rocket during a science lab. You can use the equation h = -16t^2 + 315t + 3 to find the rocket's altitude h (representing the height in feet), t seconds after launch. When will the rocket return to the ground? Round the answer to the nearest tenth.
19.7 seconds
Simplify the expression: 6(5b-7) - 4(b-2)
26b-34
A miniature ramp is 16 cm long and 12 cm high. What is the slope of the ramp?
3/4
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?
35 hot dogs and 52 sodas
Simplify: (4-2i)(7+5i)
38 + 6i
Solve the inequality: |x - 7| < 3
4 < x < 10
You ride up a hill on a ski lift, which rises 275 feet over a horizontal distance of 880 feet. What is the slope of the hill?
5/16
Find the inverse: [3 -3] [-7 6]
[-2 -1] [-7/3 -1]
Perform th[e indicated operation: -2/3 [33 -9/4] [8 -21]
[-22 3/2] [-16/3 14]
Perform the indicated operation: [5 9] [-4 2] [-2 8] [-3 1]
[-47 19] [-16 4]
Perform the indicated operation: [ 6 -11] [2 -13] [-5 2/3] - [10 -5/4] [-15 4 ] [-7 9]
[4 2] [-15 23/12] [-8 -5]
Solve the inequality: a + 22 > -3a - 10
a > -8
Is this equation an "and" or "or" compound inequality? |x + 10| < 13
and ( -23 < x < 13)
What is the equation for standard form? (linear)
ax + by = c
For first time customers, a bank will open an account with $25 included. This bank also charges a monthly $2.95 service fee on the account. Write an equation that shows the balance b after m months, assuming no other activity is made on the account.
b = -2.95m + 25
Solve the inequality: |3-4b| ≥ 11
b ≤ -2 or b ≥ 7/2
Solve the equation. Check for extraneous solutions: |2x + 5| = x+1
both extraneous solutions
Solve the equation: (4/9)c +(1/3)c = -6
c=-54/7
Solve the equation using factoring: 3a^2 + a - 5 = 0
can't factor
Solve the equation: 9d = 4(d+10)
d=8
A music store offers guitar lessons at a rate of $20 an hour and piano lessons at a rate of $30 an hour. Last week, the studio spent a total of 24 hours giving guitar and piano lessons and earned a total of $570 from these lessons. What is the system of equations can you use to find the number of guitar and piano lessons given?
g + p = 24 20g + 30p = 570
Solve the equation. Check for extraneous solutions: |4m-7| = 15
m = 11/2, m=-2
Solve the inequality: n+1 < -3 or 2n-10 > 0
n < -4 or n > 5
Do these slopes mean the lines are parallel, perpendicular, or neither? m = -1/4 m = -4
neither
Solve the inequality: |5x + 6| + 4 < 1
no solution
Is this equation an "and" or "or" compound inequality? 2|3x + 9| > 36
or (x > 3 or x < -9)
Do these slopes mean the lines are parallel, perpendicular, or neither? m = -1 m = -1
parallel
Do these slopes mean the lines are parallel, perpendicular, or neither? m = 2 m = -1/2
perpendicular
Solve the equation: 12(r+3) = 2(r+5)-3r
r=-2
Solve the inequality: (1/2)(14-12w) ≤ 39
w ≥ -16/3
Solve the inequality algebraically: 3x^2 - 11x > 4
x < -1/3 or x > 4
Solve the equation using the quadratic formula: 4x^2 + 6x + 7 = 0
x = (-3 +- i√19)/4
Solve the equation using the quadratic formula: x^2 = -14 - 3x
x = (-3 +- i√47)/2
Solve the equation using square roots: 8x^2 + 7 = -47
x = +-(3i√3)/2
Solve the equation using square roots: 2x^2 + 3 = 131
x = +-8
Solve the equation using complete the square: 2x^2 + 8x + 104 = 0
x = -2 +- i√43
Solve the equation using complete the square: x^2 + 4x - 1 = 0
x = -2+-√3
Solve the equation using factoring: 5x^2 + 14x + 8 = 0
x = -2, x = -4/5
Solve the equation using factoring: x^2 − 3x −10 = 0
x = -2, x = 5
Solve the equation using factoring: x^2 - 5x = 36
x = -4, x = 9
Solve the equation using factoring: 2x^2 + 21x + 54 = 0
x = -6, x = -9/2
Solve the equation using factoring: 10x^2 + 5x = 6x
x = 0, x = 1/10
Solve the equation using square roots: 2(x-4)^2 - 30 = 2
x = 0, x = 8
Solve the equation using the quadratic formula: 2x^2 - 5x - 45 = -12
x = 11/2, x = -3
Solve the equation using the quadratic formula: x^2 - 6x + 4 = 0
x = 3 +- √5
Solve the equation using factoring: 2x^2 - 5 = 4x^2 - 9x - 23
x = 6, x = -3/2
What is the equation for point-slope form?
y - y₁= m(x - x₁)
Write an equation in slope-intercept form with the given information: (-2, 4), parallel to y=(-5/3)x-2
y = (-5/3)x + (2/3)