MATH-0990 FINAL EXAM PREP
Solve, write the answer in interval notation, and graph: x - 7 < AND -2x + 1 < 9
(AND) X-7 < 2 X<2+7 X < 9 -2X < 8 -2X > 8 X > -4 (-4,9) (O--------O)
4w/5 = w+1/10
(criss cross) 5(w+1)=10(4w) 5w+5=40w 5w-40w= -5 -35=-5 w=5/35=1/7
Solve, write the answer in interval notation, and graph: -1 ≤ 3x + 5 < 2
-1 ≤ 3X + 5 < 2 -5 -5 -5 -6 ≤ 3X < -3 (DIVIDE BY 3) -2 ≤ X < -1 [-2,-1) ●-----o
−2(5y − 1) − y = −4(y − 3)
-10y + 2 -y = -4y + 12 -11y + 4y = 12 - 2 -7y = 10 y = -10/7
Graph the inequality: −3x + y < 1
-3x + y < 1 -3(0) + 0 < 1 0 < 1 y < 3x + 1 m= 3/1, (0,1)
Graph −2x − 5y = 10
-5Y = 2X + 10 (DIVIDE BY 5) Y = -2/5 - 2 M = -2/5, (0,-2)
Apply the absolute value definitions and solve: |x − 1| < 7 (-- a)
-7 < x -1 < 7 +1 +1 +1 -6 < x < 8 o----o (-6, 8) x-1 < 7 AND x-1 > -7 x < 8 x > -6
The sum of two consecutive numbers is -43, find the numbers.
CONSECUTIVE NUMBERS: X,X+1,X+2 X+X+1= -43 2X= -43-1 2X=-44 X= -22,-21
The sum of two consecutive even numbers is 122. Find the numbers
CONSECUTIVE: EVEN/ODD NUMBERS: X,X+2, X+4 X+X+2=122 2X=120 X=60,62
Solve, write the answer in interval notation, and graph: 13y - (9y+2) < 5(y-6) +10
13y - 9y - 2 < 5y - 30 + 10 4y - 2 < 5y -20 4y - 5y < -20 +2 -y <-18 y > 18 (18, INFINITY) OPEN CIRCLE, RIGHT 18 < X
A rental company charges a daily rate of $18.95 plus 19 cents for each mile driven. If you have $50 to spend on the car rental, what is the maximum number of miles you can drive
18.95 + 0.19 x ≤ 50 0.19x ≤ 50 -18.95 0.19x ≤ 31.05 x ≤ 163.4 miles x ≤163 miles (DIVIDING BY - NUMBER, FLIP INEQUALITY)
Solve, write the answer in interval notation, and graph: 5x-3 ≤ 10 OR x + 1 ≥ 5
5x ≤ 10 + 3 5x ≤ 13 x ≤ 13/5 x ≥ 5 -1 x ≥ 4 <---● ●---> (-INFINITY, 13/5] U [4, INFINITY)
A student has score 85, 65, and 82 on the first three tests. The student needs at least 80 to earn a grade of B in the course. What is the minimum score that the student needs on the fourth tests to earn the B?
85 + 65 + 82 + X/4 ≥ 80 (4) 232 + X/4 ≥ 80 (4) 232 + X ≥ 320 X ≥ 88 POINTS
Solve the system of equations by elimination: 5x + 4y = -30 3x - 9y = -18
9(5x + 4y = -30) = 45x +36y = -270 4(3x - 9y = -18) = 12x -36y = -72 57 x = -342 x = -6 5(-6) +4y = -30 -30 + 4y = -30 4y = -30+30 y= 0 (-6,0)
Find the domain, range, and determine if the relation is a function: {(2, 7), (3, -1), (6, 4), (-2, 7), (0, 8)}
DOMAIN= X VALUE {2,3,6,-2,0} RANGE = Y VALUE: {7,-1,4,8} IS A FUNCTION: ALL X VALUES ARE DIFFERENT
Apply the absolute value definitions and solve: −4 − 2|x + 3| = −30
IxI = a, a ≥ 0 -7 < x -1 < 7
1/3y - 1/4y = 4 + 1/6y
LCD: 12 (12/1) 1/3y - (12/1) 1/4y = 4 (12) + (12/1) 1/6y 4y-3y = 48 + 2y y-2y= 48 y=-48
Solve, write the answer in interval notation, and graph: 2/5(x-6) ≥ x-1
LCD: 5 2/5X - 12/5 ≥ X - 1 (5/1) 2/5 X - (5/1) 12/5 ≥ 5 (X-1) 2X-12 ≥ 5X-5 2X - 5X ≥ -5 +12 -3X ≥ 7 -3X ≤7 X ≤ -7/3 (-INFINITY, -7/3] CLOSED CIRCLE, LEFT ARROW
Find the equations: a. the line passing through the points (2, 1) and (-1, -5)
M = -5-1/-1-2 = -6/3 = 2 Y-Y = M (X-X1) Y -1 = 2 (X-2) Y-2 = 2X - 4 Y = 2X - 3 Y= MX + B 1 = 2(2)+B 1 = 4+ B -3 = B Y=2X-3
Find the equation according to the graph: a. (0,4) (4,1)
M = Y2 -Y1/X2 - X1 = 1-4/4-0 = -3/4 Y = MX + B (Y-INT) Y= -3/4X + 4
Find the equations: b. the line that is parallel to x − y = 5 and passing through the point (-2, 1)
M1 = M2 -y = -x + 5 (divide by -y) y = x- 5 m1=1 m2 = 1 y-y1 = m (x-x1) y-1 = 1 (x (2) ) y-1 = x + 2 y= x+ 3 y= mx + b 1=1(-2) + b 1= -2+b 3= b y = x+ 3
A rectangular garden box is 7 meters longer than its wide. Find the dimensions if the perimeter of the garden box is 62 meters
P = 2L + 2W 62 = 2(W + 7) + 2(W) 62 = 2W + 14 + 2W 62 - 14 = 4W 48= 4W W = 12M L=W+7 = 12+7 =19M
Michelle rides her bicycle for 3 hours and is 35 miles from home. After riding for 10 hours, she is 112 miles away. What is Michelle's average rate in miles per hour?
RATE OF CHANGE = SLOPE RISE/RUN (3,35) , ( 10 ,112) M = Y2-Y1/ X2- X1 = 112-35/10-3 = 77/7 = 11 MPH
IF > OR ≥
SHADE ABOVE THE LINE
IF < OR ≤
SHADE BELOW THE LINE
IF < OR >
THE LINE IS DASHED
IF ≤ OR ≥
THE LINE IS SOLID
The water temperature in the ocean varies inversely with the depth of the water. The deeper the person dives, the colder the water becomes. At a depth of 1,000 meters, the water temperature is 5oC. What is the water temperature at a depth of 500 meters
WATER TEMP= Y DEPTH = X Y=K/X (1,000) 5 = K/1000 (1000) K= 5000 Y= 5000/500 Y=10 C
Find the equation according to the graph: b. VERTICAL / HORIZONTAL
Y = -2 X = 3
The weight of a synthetic ball varies directly with the cube of its radius. A ball with a cubic radius of 8 in^3 weighs 1.20 pounds. Find the weight of a ball with a cubic radius of 27 in^3.
Y= KX WEIGHT = Y Y^3=X STEP 1: K 1.2=K *8 K=0.15 STEP 2: Y=0.15(27) Y=4.05 POUNDS
Y varies inversely as x. If x = 5, y = 20. Find y when x = 12
Y=K/W STEP 1: (5) 20 = K/5 (5) K=100 STEP 2: Y= 100/12 Y= 8.3 OR 25/3
Given the function f(x) = −x^2 − x + 1, find f(-3)
f(-3) = -3(-3)^2 - (-3) + 1 = -9 + 3 + 1 = -6+1 f(-3) = -5
Find the equations: c. the line that is perpendicular to −2x + y = −6 and passing through the point (1, 5)
m1 = -1/m2 y = 2x -6 m1 = 2 m2 = 1/2 y-y1 = m(x-x1) y - 5 = -1/2 (x-1) y-5 = -1/2 +1/2 y = 1/2x + 1/2 + 5 y = 1/2 x + 1/2 +10/2 y = -1/2x + 11/2 5 = -1/2 (1) + b 5 = -1/2 + b 10/2 + 1/2 = b b = 11/2 y= -1/2x + 11/2
Solve the system of equations by substitution: 2x + 5y = 19 -3x + y = -3
step 1: y = 3x - 3 step 2: 2x + 5 (3x - 3) = 19 2x + 15x - 15 = 19 17x = 19 +15 17x = 34 x = 2 step 3: y= 3(2)-3 y= 3 (2,3)
Apply the absolute value definitions and solve: |x + 6| ≥ 8
x + 6 ≥ 8 OR x + 6 ≤ -8 x ≥ 2 x ≤ -14 <---● ●---> (-INFINITY, -14] U [2, INFINITY)
Y varies directly as x. If x = 4, y = 12. Find y when x = 16
y= kx STEP 1: 12=K * 4 K= 3 STEP 2: Y=KX Y= 3(16) Y=48
