186)
Graph the function y=f(x) =–x2+ 5 – 4 and indicate the coordinates of the vertex and
intercepts.
186)
187)
Solve the following system algebraically:
x–z=14
y+z=21
x –y+z= – 10
187)
188)
Find the slope and y–intercept of a line 2y+ 3(x– 1.9) = 0.
188)
41
189)
Graph the function y=f(x) = 2x2+ 2x– 12 and indicate the coordinates of the vertex and
intercepts.
189)
190)
Solve the following system algebraically:
1
2x–1
4y=1
6
x +1
2y=2
3
190)
191)
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.
191)
192)
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.
192)
193)
Solve the following system algebraically: 3x– 4y= 18
2x+ 5y= – 11
193)
194)
Find the slope–intercept form of the line that passes through (2,–3) and (–4,7).
194)
195)
An accountant can complete a simple tax return in about 1.5 hours and a complicated
return in about 4 hours. If she works 8 hours per day, find an equation that shows the
possible ways that both types of returns can be completed in a 5–day work week.
195)
196)
Find the slope–intercept form of an equation of the line that passes through the point (2, 0)
and has slope 4.
196)
197)
Find a general linear equation of the line that passes through the points (4, –3) and (6, –7).
197)
198)
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?
198)
199)
The slope of the line passing through the points (4, 9) and (6, k) is 5. Find k.
199)
200)
A nut shop packages mixtures of different nuts for sale. From peanuts, cashews and
almonds, the owner wants to prepare a mixture which will sell for $4.45 for a 1 pound bag.
The cost per pound of these nuts is $1.50, $6.00, and $4.00, respectively. The amount of
peanuts is to be three times the amount of almonds. How much of each type of nut will be
in the final blend?
200)
201)
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.
201)
202)
The shape of a paper streamer suspended above a dance floor can be described by the
function y=f(x) = 0.01x2+ 0.01x+ 7, where y is the height of the streamer (in feet) above
the floor and x is the horizontal distance (in feet) from the center of the room. Use a
graphing calculator to graph the function.
202)
203)
Determine whether the following lines are parallel, perpendicular or neither.
0.21x– 0.35y + 8 = 0
x+ 0.6y– 9 = 0
203)
204)
Find the slope–intercept form of the line that passes through (0,4) and (1,1).
204)
205)
For the straight line 2x+y– 3 = 0 find: (a) the slope; (b) the y–intercept; and
(c) sketch the graph.
205)
Answer:
(a) –2(b) 3
(c)
Explanation:
206)
Find the vertex and axis of symmetry of the parabola y= 2x2+ 3x– 5.
206)
207)
By sketching the graphs (using a graphing calculator or graphing paper) solve the system
of equations. 2x+ 3y= 26
3x– 2y= 13
207)
Answer:
Explanation:
208)
A toy rocket is launched straight up from the roof of a garage with an initial velocity of 80
feet per second. The height h of the rocket in feet t seconds after it was thrown is described
by the function h(t) = – 16t2+ 80t+ 16. Use a graphing calculator to graph the function.
208)
Answer:
Answer:
Explanation:
209)
A deep sea diver has spent a week in a submerged research facility at 2000 feet below sea
level. He is now ready to move to a deeper facility at 3500 feet below sea level. He
descends at the rate of 50 feet per minute. Write an equation that shows this relationship,
and determine when the diver will reach 3500 feet below sea level.
209)
210)
Solve the following questions algebraically: 2p+ 3q= 5
2p+ 6q = 10
210)
211)
For the parabola y= f(x) = 4 –x– 3x2, find: (a) the vertex, (b) the y–intercept, and (c) the
x–intercepts.
211)
212)
Determine whether the following lines are parallel, perpendicular or neither.
3x– 2y= 19
2x+ 3y= 4
212)
213)
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.
213)
214)
In 1986 the stock in a biotechnology company traded for $30 per share. In 1996 the
company started having trouble, and the stock price dropped to $10 per share. Use a
graphing calculator to show the relationship between price per share and the year in which
it traded. Find and interpret the slope.
214)
215)
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.
215)
216)
Sketch the graph of x= 4.
216)
217)
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.
217)
218)
Find the Equilibrium Quantity for a product with Demand Equation and Supply Equation
as follows:
Demand: p= 300 – 8q
Supply: p=19
5q + 5
218)
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