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For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve.
For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state
No Real Solution .
Technology
For the following exercises, enter the expressions into your graphing utility and find the zeroes to the equation (the
x -intercepts) by using 2
nd CALC 2:zero. Recall finding zeroes will ask left bound (move your cursor to the left of the zero,enter), then right bound (move your cursor to the right of the zero,enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth.
To solve the quadratic equation
we can graph these two equations
and find the points of intersection. Recall 2
nd CALC 5:intersection. Do this and find the solutions to the nearest tenth.
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To solve the quadratic equation
we can graph these two equations
and find the points of intersection. Recall 2
nd CALC 5:intersection. Do this and find the solutions to the nearest tenth.
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Extensions
Beginning with the general form of a quadratic equation,
solve for
x by using the completing the square method, thus deriving the quadratic formula.
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A person has a garden that has a length 10 feet longer than the width. Set up a quadratic equation to find the dimensions of the garden if its area is 119 ft.
2 . Solve the quadratic equation to find the length and width.
7 ft. and 17 ft.
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Abercrombie and Fitch stock had a price given as
where
is the time in months from 1999 to 2001. (
is January 1999). Find the two months in which the price of the stock was $30.
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Suppose that an equation is given
where
represents the number of items sold at an auction and
is the profit made by the business that ran the auction. How many items sold would make this profit a maximum? Solve this by graphing the expression in your graphing utility and finding the maximum using 2
nd CALC maximum. To obtain a good window for the curve, set
[0,200] and
[0,10000].
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Real-world applications
A formula for the normal systolic blood pressure for a man age
measured in mmHg, is given as
Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.
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The cost function for a certain company is
and the revenue is given by
Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of
x (production level) that will create a profit of $300.
The quadratic equation would be
The two values of
are 20 and 60.
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A falling object travels a distance given by the formula
ft, where
is measured in seconds. How long will it take for the object to traveled 74 ft?
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A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 378 ft
2 . Find the width of the walkway if the garden is 12 ft. wide by 15 ft. long.
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An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students,
who contracted the flu
days after it broke out is given by the model
where
Find the day that 160 students had the flu. Recall that the restriction on
is at most 6.
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Questions & Answers
If auger is pair are the roots of equation x2+5x-3=0
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
find product (-6m+6) ( 3m²+4m-3)
what is the solution
bill
how did you arrive at this answer?
bill
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
-6m(3mA²+4m-3)+6(3mA²+4m-3)
=-18m²A²-24m²+18m+18mA²+24m-18
Rearrange like items
-18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph.
1.x+2y=3
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
please why isn't that the 0is in ten thousand place
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
I am eliacin, I need your help in maths
Rood
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
how to reduced echelon form
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
d=r×t
the equation would be 8/r+24/r+4=3
worked out
Sheirtina
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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