Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 1155881: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form,
The solutions are -8 and 4.
Click here to see answer by Edwin McCravy(20054)

Question 1155921: 19. The product of two consecutive positive integers is 42. Write and solve a quadratic equation to find the solutions. Then show how you use those solutions to find the two consecutive positive integers.

20. A cannon ball is shot from a cannon on top of a hill that is 73.5 meters above sea level. The cannon ball leaves the cannon with a velocity of 9.8 m/s. Write and solve a quadratic equation to determine when the cannon ball will reach sea level
Click here to see answer by MathLover1(20849)

Question 1156020: Tyrone built a model rocket for his science project. The equation h= -16t2+260t models the flight of the rocket, launched from ground level at a velocity of 260 feet per second, where h is the height of the rocket in feet after t seconds. How long does it take the rocket to hit the ground?

Click here to see answer by josmiceli(19441)

Question 1156081: The area of the window is 20 square feet. Find its dimensions (in ft).
A rectangular window has two labeled sides.
One of the shorter, vertical sides is labeled x ft.
One of the longer, horizontal sides is labeled 2x − 3 ft.
smaller value
ft
larger value
ft
Click here to see answer by MathLover1(20849)

Question 1156080: Solve the formula for the indicated variable. (Simplify your answer completely.) See Example 4. (Objective 2)
A = 2πr2 + 2πhr, for r
(The formula for the surface area of a right circular cylinder)
r =

Click here to see answer by josgarithmetic(39616)

Question 1156079: Solve the application. See Examples 11-12. (Objective 4)
The height h (in feet) of an object that is dropped from a height of s feet is given by the formula h = s − 16t2, where t is the time the object has been falling. A 5-foot-tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from 6 stories up. How long does she have to get out of the way? (A story is 10 feet. Round your answer to two decimal places.)
The woman has about
seconds to move.
Click here to see answer by josmiceli(19441)

Question 1156077: A housing contractor lists the following costs.
Fee and permits $13,000
Cost per square foot $104
(a) Write a linear function that describes the cost of building a house with s square feet.
C(s) =

(b) Find the cost to build a house having 1,800 square feet.
$

Click here to see answer by MathLover1(20849)

Question 1156107: Find the value given that
f(x) = 9x + 8.
(Simplify your answer completely.)
f(b) − f(0)
Click here to see answer by josgarithmetic(39616)

Question 1156105: For the function, find
f(4), f(3), and f(−1).
f(x) = (x + 1)2
f(4) =
f(3) =
f(−1) =

Click here to see answer by josgarithmetic(39616)

Question 1156106: For the function, find
f(2), f(3), and f(−1).
f(x) = 5x2 + 2x
f(2) =
f(3) =
f(−1) =
Click here to see answer by josgarithmetic(39616)

Question 1156110: The x y-coordinate plane is given. The curve enters the window in the second quadrant, goes down and right becoming less steep, crosses the x-axis at approximately x = −2.6, changes direction at the point (0, −7), goes up and right becoming more steep, crosses the x-axis at approximately x = 2.6, and exits the window in the first quadrant.
State the domain and range of the graph in interval notation. See Example 2. (Objective 2)
domain

range

Click here to see answer by ikleyn(52776)

Question 1156109: A mortar shell is s feet above the ground after t seconds, where
f(t) = −16t2 + 512t + 64.
Find the height of the shell 26 seconds after it is fired.
The shell will have a height of?
Click here to see answer by ikleyn(52776)

Question 1156108: For the following exercise, write a linear function to model the given data and make the indicated estimation. See Example 7. (Objective 6)
Suppose that the average tuition for a full-time undergraduate student in a public college in 2002 was $5,370. Suppose it was $8,720 in 2012. Using the linear function model, estimate the cost (in dollars) of tuition in 2018.
$

Click here to see answer by josmiceli(19441)

Question 1156160: Find the possible value of k for which the quadratic expression 9x² - 2(k + 7)x + k is perfect square
Click here to see answer by josgarithmetic(39616)

Question 1156078: The approximate pulse rate (in beats per minute) of an adult who is t inches tall is given by the following formula.
p2 =
348,100
t
Find the pulse rate of an adult who is 70 inches tall. (Round your answer to the nearest integer.)
The rate is about
beats per minute.
Click here to see answer by greenestamps(13198)

Question 1156217: explain why completing the square to solve x^2 - 5x - 7 = 0 is a better strategy than graphing the related function or factoring
Click here to see answer by josgarithmetic(39616)

Question 1156217: explain why completing the square to solve x^2 - 5x - 7 = 0 is a better strategy than graphing the related function or factoring
Click here to see answer by ikleyn(52776)

Question 1156268: A Square has its length increased by 6 feet and it’s with by 8 feet. If the resulting rectangle has an area of 239.25 ft.² what was the perimeter of the original square
Click here to see answer by josgarithmetic(39616)

Question 1156274: The width of a rectangular pool is 12 feet less than its length. The area of the pool is 800 ft.². To the nearest 10th, what is the width of the pool?
Click here to see answer by josgarithmetic(39616)

Question 1156309: If the sides of a square measure 10√6 units, then find the length of the diagonal.
Click here to see answer by ikleyn(52776)

Question 1156398: Add the proper constant to the binomial so that the resulting trinomial is a perfect square. Then factor the trinomial.
problem: r^2+22r
Click here to see answer by ankor@dixie-net.com(22740)

Question 1156409: Add the proper constant to the binomial so that the resulting trinomial is a perfect square. Then factor the trinomial.
x^2+22x

Click here to see answer by ikleyn(52776)

Question 1156424: Add the proper constant to the binomial so that the resulting trinomial is a perfect square. Then factor the trinomial.
r^2 +12r

Click here to see answer by MathLover1(20849)

Question 1156459: Find the equation of the quadratic function f whose graph is shown below. (5, -7) (6, -4)

Click here to see answer by Alan3354(69443)

Question 1156479: Use the product rule to multiply.
problem: 5√81 multiplied by 5√3
Click here to see answer by Shin123(626)

Question 1156595: One leg of a right triangle is
44
inches more than
twicetwice
the length of the other leg. The hypotenuse is
5
inches more than the shorter leg. Find the lengths of all the sides.
Click here to see answer by MathLover1(20849)

Question 1156643: Find the values of a, b, and c so that (ax^2+bx+c)(4x−1) = −12x^3+11x^2+18x−5
I honestly do not know where to start with this.
I try to factor but I do not think it works.
Click here to see answer by josgarithmetic(39616)

Question 1156645: Solve. Use a graphing calculator if necessary. See Examples 9 - 11. (Objective 8)
From the top of the building, a ball is thrown straight up with an initial velocity of 64 feet per second. The equation
s = −16t2 + 64t + 80
gives the height s of the ball t seconds after it is thrown. Find the maximum height (in feet) reached by the ball and the time (in seconds) it takes for the ball to hit the ground. (Hint: Let s = 0 and solve for t.)
80 ft
A rectangular building is 80 ft tall.
A curved path starts at the top-right side of the building and goes up and to the right past the right edge of the building. The path gets less steep as it reaches a high point, and then it goes down and to the right, getting steeper as it goes.
The ball is at the end of the path midway between the top of the building and the ground, and its height above the ground is labeled s.
A vertical dashed line starts at the ball and goes down to touch the ground.
The maximum height reached by the ball is-
feet. The ball hits the ground after-
seconds.
Click here to see answer by ikleyn(52776)

Question 1156646: Solve. Use a graphing calculator if necessary. See Examples 9 - 11. (Objective 8)
The total annual enrollment (in millions) in a country's elementary and secondary schools for the years 1975 - 1996 is given by the function
E(x) = 0.056x2 − 1.154x + 50.604.
For this period, what was the lowest enrollment? (Round your answer to one decimal place.)
The lowest enrollment was about-
million.
Click here to see answer by Boreal(15235)

Question 1156800: A flying squirrel jumped from a tree 11 feet in the air at an initial velocity of 9 ft./s. The equation H equals negative 2t squared +9t +11 model is his jump we’re h is height in feet and t is time in seconds. When did the squirrel reach the ground?
Click here to see answer by Alan3354(69443)

Question 1156798: The income for a company producing electronic components is given by
y= -20x2-50x+200, where x is the price in dollars of each component. The cost for the production is given by y = 60x −10 . Determine the price that will allow the production to break even.

Click here to see answer by Boreal(15235)

Question 1156797: A punter kicks a football. Its height, h, in metres, t seconds after the kick is given by the equation h(t)=-4.9t2+18.24t+0.8 . The height of an approaching blocker’s hands is modelled by the equation b(t) = -1.43t +4.26 using the same time. Can the blocker knock down the punt? If so, at what point will it happen?
Click here to see answer by Boreal(15235)

Question 1156900: Working backwards write a quadratic equation that will have solutions of x = 3 and x = -7.
Working backwards write a quadratic equation that will have solutions of x = 12 and x = 2.
Thank you

Click here to see answer by josmiceli(19441)

Question 1156901: A tennis ball is launched straight upward with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:
4.9t2 + 24.5t + 117.6 = 0
-4.9t2 - 24.5t + 117.6 = 0
-4.9t2 + 24.5t - 117.6 = 0
4.9t2 + 24.5t - 117.6 = 0
-4.9t2 + 24.5t + 117.6 = 0
Thank you

Click here to see answer by Edwin McCravy(20054)

Question 1156897: What is the highest point of the parabola, the point with the greatest y value
Click here to see answer by Boreal(15235)

Question 1156924: An arrow is shot into the air, a function representing the relationship between the number of seconds it is in the air, t and the height of the arrow in meter, h, is given by: h(t) = -4.9t^2 + 29.4t + 2.5, what is the maximum height of the arrow ?
Click here to see answer by Alan3354(69443)

Question 1156938: An arrow is shot into the air a function representing the relationship between the number of seconds is in the air t and the height of the arrow in them in meters h is given by t equals -4.90x squared + 29.40x + 2.5 how long does it take the arrow to hit the ground
Click here to see answer by Alan3354(69443)

Question 1156940: The floor of a shed has an area of 70 square ft. The floor is in the shape of a rectangle whose length is 4 feet less than twice the width. Find the length and the width of the floor. Use the formula, area=length•width
Click here to see answer by josgarithmetic(39616)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 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7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 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23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 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