89)
How much of each of a 25% (by volume) chemical solution and a 32% solution must be
combined to make 75 cubic centimeters of a 28% solution?
89)
90)
The price of computer technology has been dropping steadily for the past ten years. The
price of a certain desktop PC has decreased by $650 per year during this time period. If this
PC sold for $6770 ten years ago, what equation describes the cost C of the PC over the last
ten years? Graph your equation on a graphing calculator. Can you predict the price of a
desktop PC a few years into the future (T> 0) with this model?
90)
Explanation:
91)
Suppose f is a linear function such that f(0) = 6 and f(3) = 4. Find f(x).
91)
Explanation:
92)
Find the equation of a line having slope = 1 and x–intercept = – 2.
92)
Explanation:
93)
A swimming pool owner has two solutions which contain different concentrations of
chlorine. One is a 5% solution and the other is a 10% solution. How many liters of each
should she mix to obtain 8 liters with a 6% concentration?
93)
Explanation:
94)
State whether f(x) = 10 + 16x– 4x2 has maximum or minimum value and find that value.
94)
Explanation:
95)
Suppose that the vertex of the parabola y= 3x2– 6x+k is (1, 2); find k.
95)
Explanation:
96)
A manufacturer sells his product at $12.50 per unit, selling all he produces. His fixed cost is
$5,000 and his variable cost per unit is $8.50. (a) At what level of production will he break
even? (b) At what level of production will he have a profit of $10,000?
96)
Explanation:
97)
A delicatessen owner starts her business with debts of $100,000. After operating for 5 years
she has average profits of $40,000 per year. Use a graphing calculator to graph the resulting
equation and determine when the business will have accumulated $300,000 in profit.
97)
Explanation:
98)
Determine whether the following lines are parallel, perpendicular or neither.
12x+ 4y= 16
15x+ 5y= 23
98)
99)
Find a general linear equation of the line that passes through point (1, –2) and has slope 3.
99)
100)
The size of a human fetus more than 12 weeks old can be estimated by the formula L=
1.53t– 6.7, where L is in centimeters and t is in weeks. An obstetrician uses the length of a
fetus, measured in an ultrasound, to determine the approximate age of the fetus and
establish a due date for the mother. The formula must be rewritten to result in an age t,
given a fetal length L. Use a graphing calculator to graph the resulting equation and verify
the y–intercept.
100)
101)
Graph the general linear form of the equation for the size of a human fetus more than 12
weeks old whose slope–intercept form is L= 1.53t– 6.7.
101)
102)
Find the equation of a line which is perpendicular to the line 2x+ 3y– 57 = 0 and passes
through the point (1, –1).
102)
22
103)
Find the equation of a line which is parallel to the line 2x+ 3y– 7 = 0 and passes through
the point (–1, 2).
103)
104)
Graph the general linear form of the Olympic discus throw equation whose slope–intercept
form is d= 1.75t+ 175.
104)
105)
Determine the linear function f(t) with slope = – 1 and f(2) = 1.
105)
106)
The stock price of a company has risen at the rate of $5.00 per month over the last year. On
January 1 it was $75.00. Write an equation that shows this relationship.
106)
107)
The equation of a certain line is y+ 2 = – 2(x– 3). Find: (a) the slope–intercept form and (b)
a general linear form.
107)
23
108)
Two species of monkey, A and B, live in one enclosure at the zoo where they are fed two
vitamin supplements. Each day they receive 350 grams of the first supplement and 700
grams of the second supplement. Each monkey of species A requires 25 g of the first
supplement and 50 g of the second supplement. Each monkey of species B requires 15 g of
the first supplement and 30 g of the second supplement. How many of each species of
monkey will the enclosure support so that all of the supplements are consumed each day?
108)
109)
The daily profit for a lighting store from the sale of a table lamp is given by
P(x) =–x2+ 34x+ 35, where x is the number of table lamps sold. Use a graphing calculator
to graph the function.
109)
110)
Solve the system y= 2x2– 5
x2+y= 4
110)
111)
Solve the following nonlinear system: y=8 –x2
4x–y+ 11 =0
111)
112)
Determine whether the following lines are parallel, perpendicular or neither.
3x– 2y= 19
2x+ 3y= 4
112)
113)
Find the range of the function y=f(x) = 4x2– 16x+ 1.
113)
114)
Find an equation of the line that passes through the origin and that has slope –5.
114)
115)
Suppose f is a linear function with slope 5 and such that f(1) = 4. Find f(x).
115)
116)
Suppose f is a linear function such that f(–2) = 5 and f(5) = 2. Find f(x).
116)
117)
Solve the following system algebraically: 3y– 2x=4
4x– 6y= – 8
117)
118)
The area of rain forest in a South American country has decreased by 500 acres per year for
the last 10 years. It had 12,000 acres 10 years ago. Use a graphing calculator to graph the
resulting equation and determine when all of the rain forest in this country will be
destroyed.
118)
119)
Find a general linear equation of the line that passes through the points (–2, 5) and (5, 2).
119)
120)
A pharmacist has two solutions that contain different concentrations of the same
medication. One solution contains a 12% concentration of the medication and the other
contains a 7% concentration. How many cubic centimeters of each should she mix to obtain
40 cc of an 8% concentration?
120)
121)
The daily profit for an electronics store from the sale of small televisions is given by P(x) =
–x2+ 40x + 825, where x is the number of small televisions sold. Find the function‘s vertex
and intercepts, and graph the function.
121)
122)
Sketch the graph of y= 3.
122)
123)
Suppose the supply and demand equations for a manufacturer’s product are p=3
100q+ 6
and p= – 1
50 q+ 14, respectively, where q represents number of units and p represents price
per unit in dollars. Determine (a) the equilibrium quantity; (b) the equilibrium price. If a
tax of $1.00 per unit is imposed on the manufacturer, (c) determine the new equilibrium
quantity; (d) the new equilibrium price.
123)
124)
The daily profit for the garden department of a store from the sale of trees is given by P(x)
=–x2+ 18x+ 144, where x is the number of trees sold. Use a graphing calculator to graph
the function.
124)
125)
Determine whether the following lines are parallel, perpendicular or neither.
3x– 2y= – 1
2x+ 3y= – 20
125)
126)
The shape of a decorative awning over a storefront can be described by the function y= f(x)
= 0.06x2+ 0.012x+ 8 where y is the height of the edge of the awning (in feet) above the
sidewalk and x is the distance (in feet) from the center of the store’s doorway. Use a
graphing calculator to graph the function.
126)
127)
Suppose that the supply and demand equations for a certain product are p=1
14 q– 9 and
p= – 1
70 q+ 3, respectively, where p represents the price per unit in dollars and q represents
the number of units per time period.
(a) Find the equilibrium price algebraically.
(b) Find the equilibrium price when a tax of 50 cents per unit is imposed.
127)
128)
A mathematical model can approximate the winning distance for the Olympic discus
throw by the formula d= 175 + 1.75t, where d is in feet and t= 0 corresponds to the year
1948. We might want to predict in what year a certain distance will be exceeded, so rewrite
the equation to solve for t. Use a graphing calculator to graph the resulting equation and
find the coordinates of any two points on the line and use them to estimate the slope.
Compare this with your answer.
128)
129)
Find the slope of the line passing through the points (5, –3) and (2, –1).
129)
130)
A printer charges a fixed setup cost plus a charge for every copy of single page flyers. If x is
the number of copies requested, the total cost of a printing job can be described by the
function f(x) = 0.02x+ 80. Graph the function on your graphing calculator.
130)
131)
For the parabola y= f(x) =x2– 2x – 8, find: (a) the vertex, (b) the y–intercept, and (c) the
x–intercepts.
131)
132)
Graph the function y=f(x) =x2– 6x and indicate the coordinates of the vertex and
intercepts.
132)
133)
Find the equation of the line with y–intercept 4 and slope –2
3.
133)
134)
Sketch the graph of x= 4.
134)
135)
Solve the following system algebraically: 3x+ 5y= – 6
2x– 6 =5y
135)
136)
Find an equation of the horizontal line that passes through the point (5, 6).
136)
137)
A man standing on a pitcher’s mound throws a ball straight up with an initial velocity of
32 feet per second. The height h of the ball in feet t seconds after it was thrown is described
by the function h(t) = – 16t2+ 32t+ 8. Use a graphing calculator to graph the function.
137)
138)
Graph the general linear form of the child dosage equation whose slope–intercept form is
y=1080
24 t+1080
24 .
138)
139)
In testing an experimental diet for goats, it was determined that the (average) live weight w
(in kilograms) of a goat was statistically a linear function of the number of days d after the
diet was started where 0 d 100. The weight of a goat starting the diet was 12 kg and 25
days later it was 20 kg. Determine w as a linear function of d and find the average weight of
a goat when d= 80.
139)
140)
Find a general linear equation of the line that passes through point (–6, 4) and has slope –2.
140)
141)
Find a general linear equation of the line that passes through the points (4, –3) and (6, –7).
141)
142)
Solve the following system algebraically: 8x– 4y=7
y =2x– 4
142)
143)
Find the Equilibrium Quantity for a product with Demand Equation and Supply Equation
as follows:
Demand: p= 300 – 8q
Supply: p=19
5q + 5
143)
144)
Suppose f is a linear function with slope 2 and such that f(–3) = 8. Find f(x).
144)
145)
Find the equilibrium point if the demand equation for a product is p=q
20 – 3 and the
supply equation is p=80
q.
145)
146)
The demand per week for a new automobile is 400 units when the price is $16,700 each,
and 500 units when the price is $14,900 each. Find the demand equation for the cars,
assuming that it is linear.
146)
147)
True or False: The function (2x2 + 3)2 is a Quadratic Function.
147)
148)
For the parabola y= f(x) = 4 –x– 3x2, find: (a) the vertex, (b) the y–intercept, and (c) the
x–intercepts.
148)
32
149)
For the linear function f(x) = 2x+ 1, find: (a) the slope and (b) the vertical axis intercept. (c)
Sketch the graph of f.
149)
150)
Determine whether the following lines are parallel, perpendicular or neither.
0.1x– 7y + 81 = 0
2x– 140y+ 9 = 0
150)
151)
Suppose consumers will demand 30 units of a product when the price is $12 per unit and
22 units when the price is $16 each. Find the demand equation assuming that it is linear.
151)
152)
Determine an equation of the vertical line that passes through the point (3, –6).
152)
153)
A bank charges $10 for a money order. What is an equation for the relationship between
the fee F charged and the amount of the money order?
153)
154)
The demand function for a manufacturer’s product is p=f(q) = 600 – 2q, where p is the
price (in dollars) per unit when q units are demanded (per week). Find the level of
production that maximizes the manufacturer’s total revenue and determine this revenue.
154)
155)
What is the slope of a horizontal line?
155)
156)
Two species of deer, A and B, living in a wildlife refuge are given extra food in the winter.
Each week they receive 3.5 tons of food pellets and 7 tons of hay. Each deer of species A
requires 4 pounds of the pellets and 8 pounds of hay. Each deer of species B requires 2
pounds of the pellets and 4 pounds of hay. How many of each species of deer will the food
support so that all of the food is consumed each week? Use a graphing calculator to graph
both of your equations at the same time. What do you notice about the graphs?
156)
157)
Find the slope–intercept form of the line that passes through (2,–3) and (–4,7).
157)
158)
Solve the system: y=4x–x2
y=x2– 6
158)
159)
Sketch the graph of 5(x+ 3) – 3(y– 1) = 0.
159)
160)
For the parabola y= f(x) = 2x2– 4x – 6, find: (a) the vertex, (b) the y–intercept, and (c) the
x–intercepts.
160)
161)
Suppose the cost to produce 100 units of a product is $5000, and the cost to produce 125
units is $6000. If cost c is linearly related to output q, find an equation relating c and q.
161)
162)
Show that the points A(–1, 2), B(3, –2), and C(–6, –3), are the vertices of a right triangle.
162)
163)
A hobby store packages mixtures of different beads for sale. From wood beads, glass
beads, and metal beads, the owner wants to prepare a mixture which will sell for $4.20 for
a 200 count bag. The cost per bead of these beads is $0.01, $0.03, and $0.05, respectively.
The number of wooden beads is to be four times the number of metal beads. How many of
each type of bead will be in the final package?
163)
164)
The equation of a certain line is 3(x– 4) – (y+ 1) = 4. Find: (a) the slope–intercept form and
(b) a general linear form.
164)
165)
Solve the system 2x– 5y= 10
y=x + 4
165)
166)
For the parabola y= f(x) = – x2+ 7x – 6, find: (a) the vertex, (b) the y–intercept, and (c) the
x–intercepts.
166)
167)
An automobile factory produces two models. The first model requires 7 widgets and 10
shims. The second model requires 15 widgets and 21 shims. The factory can obtain 800
widgets and 1130 shims per hour. How many cars of each model can it produce per hour if
all parts available are used?
167)
168)
The diagram below shows lines with slopes 0, 1, –1, 3, and –3. What is the slope of (a) line
L1 and (b) line L4?
168)
169)
State whether the following function has a maximum value or minimum value and find it:
f(x) = 2 + 10x–x2
169)
170)
Determine the equation of the line which is perpendicular to 2x–y + 3 = 0 and has
y–intercept 6.
170)
171)
Two species of monkey, A and B, live in one enclosure at the zoo where they are fed two
vitamin supplements. Each day they receive 350 grams of the first supplement and 500
grams of the second supplement. Each monkey of species A requires 25 g of the first
supplement and 10 g of the second supplement. Each monkey of species B requires 15 g of
the first supplement and 30 g of the second supplement. How many of each species of
monkey will the enclosure support so that all of the supplements are consumed each day?
171)
172)
A retired couple has $500,000 invested in two bond funds that earn 5% and 7%. If the total
yearly income from the investments is $30,000, how much is invested at each rate?
172)
173)
Graph the general linear form of the Fahrenheit–Celsius conversion equation whose
slope–intercept form is F=9
5C+ 32.
173)
174)
Solve the following nonlinear system of equations by sketching its graph (using graphing
calculator or using graph paper.) If the equations have no solutions, please say so.
y=x2– 2x+ 5
y= – x
174)
175)
10 square yards of a good quality wool carpet costs $400 and 20 square yards costs $800.
Use a graphing calculator to show the relationship between cost and amount purchased.
Find and interpret the slope.
175)
176)
Find the Point of Equilibrium for a product with Demand Equation and Supply Equation
as follows:
Demand: p= 300 – 8q
Supply: p=19
5q + 5
176)
177)
An orthodontist charges $3000 for the phase of treatment for a nine–year old which will
provide better alignment and more room for permanent teeth in the future. What is an
equation for the relationship between cost C of the treatment and the number of visits
required to attain the desired result?
177)
178)
Suppose f(p) is a linear function given by f(p) =3p– 2
5. Find the slope and the y–intercept.
178)
179)
Find the equation of a line which is parallel to the line x= 0.521 and passes through the
point (0.1, –7).
179)
180)
Find the slope–intercept form of an equation of the line that passes through the point (2, 0)
and has slope 4.
180)
181)
Find the slope of the line passing through the points (3, 9) and (2, –5).
181)
182)
The demand function for an appliance company’s line of washing machines is p= 300 – 5q,
where p is the price (in dollars) per unit when q units are demanded (per week) by
consumers. Find the level of production that will maximize the manufacturer’s total
revenue, and determine this revenue.
182)
183)
Two species of fish, A and B, are raised in one pond at a fish farm where they are fed two
vitamin supplements. Each day they receive 100 grams of the first supplement and 200
grams of the second supplement. Each fish of species A requires 20 mg of the first
supplement and 30 mg of the second supplement. Each fish of species B requires 10 mg of
the first supplement and 40 mg of the second supplement. How many of each species of
fish will the pond support so that all of the supplements are consumed each day? Use
elimination by substitution to solve the systems.
183)
184)
Solve the following system of equations algebraically. (If the system does not have a
solution, then say so or if it has more than one unique solution, then please describe the
solutions.)
4x– 10y= 6
2
3x–5
3y= 7
184)
185)
A prediction made by early psychology relating the magnitude of a stimulus x to the
magnitude of a response y is expressed by the equation y=kx2, where k is a constant of the
experiment. In an experiment on noise levels, k= 4. Use a graphing calculator to graph the
equation.
185)
186)
A coffee wholesaler blends together three types of coffee that sell for $1.95, $2.10, and $2.25
per pound so as to obtain 100 pounds of coffee worth $2.13 per pound. If the wholesaler
uses the same amount of the two higher–priced coffees, how much of each type must be
used in the blend?
186)