Graph the following non-linear system of equations and identify the two solutions. y=2x −7x+3y=3 What type of function is the equation y=2x ? Linear [ ] Quadratic [ ] Exponential [ ] What type of function is the equation −7x+3y=3 ? Linear [ ] Quadratic [ ] Exponential [ ] Use your graph below to identify the two solutions to this non-linear system of equations. Note: All solutions to this problem are whole numbers. None of the answers are decimals or fractions. List the solution, (x,y), with the smallest x value below. x= __________ y= __________ List the solution, (x,y), with the largest x value below. x= __________ y= __________
Answers
The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value x = 3 , y = 8 .
What is a Equation ?An Equation is a mathematical statement which relates two algebraic expression with an equal sign in between.
The equations given in the question is
y = 2ˣ
This is an exponential function
-7x +3y = 3
This is a linear function
The equations have been plotted and the solution to the non linear system of equation has been determined
The point at which the graphs intersect is the solution to the system of non -linear equations.
(0,1) and (3,8)
x = 0 , y = 1 ; x = 3 , y = 8
The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value x = 3 , y = 8 .
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Related Questions
If the odds on a bet are 7:1 against, what is the probability of winning? Express your answer as a fraction.
Answers
Probability helps us to know the chances of an event occurring. The probability of winning the bet is 0.125.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given the odds on a bet are 7:1, therefore, there are a total of 8 cases out of which only one case is of winning. Thus, the probability of winning the bet will be,
Probability = 1/8 = 0.125
Hence, the probability of winning the bet is 0.125.
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Mrs. Martin brought 100 cookies to her class. She gave each student the same number of cookies, and had 5 cookies left over. there are more than 10 students and less than 50 students in Mrs. Martin's class. How many students are in her class?
Answers
Answer:
Mrs. Martin has 19 Students
Step-by-step explanation:
first step: 100-5=95
second step: 95/19=5
So, 95 divided by the possible number of students which is 19 it yields the answer of 5 which is the number of cookies each of her student recieved.
The following lots of Commodity Z were available for sale during the year. Beginning inventory 9 units at $50 First purchase 16 units at $50 Second purchase 21 units at $59 Third purchase 16 units at $62 The firm uses the periodic system, and there are 23 units of the commodity on hand at the end of the year. What is the ending inventory balance at the end of the year according to the FIFO method?
Answers
According to the FIFO method, the ending inventory balance for Commodity Z is $1,405
How much inventory is left under FIFO?FIFO means that earlier inventory is sold first and later inventory would be the last goods left.
Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:
= (16 x 62) + (7 x 59)
= 992 + 413
= $1,405
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In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F. The highest monthly average temperature occurs in July at 78 °F. Write and graph a sinusoidal curve equation to model the average monthly temperature in Michigan. Assume the period is 12 months and that January is at the origin of the graph of this function. (6 points)
ANSWER ATTACHED
Answers
sinusoidal curve equation 29 sin ([tex]\pi[/tex]/9 x)-49
What is Equation of a sinusoidal curve ?Given the graph of a sinusoidal function, we can write its equation in the form y = A·sin(B(x - C)) + D using the following steps. D: To find D, take the average of a local maximum and minimum of the sinusoid. y=D is the "midline," or the line around which the sinusoid is centered.
In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F.
The highest monthly average temperature occurs in July at 78 °F
Assume the period is 12 months and January is at the origin of the graph of this function.
sinusoidal curve equation that models the data y
Then, Graph the curve using x = 0 for January, and x = 11 for December, so that x = 12 will be the start of the next year, or end of the period.
So, using the property of sinusoidal curve equation we have
=29 sin ([tex]\pi[/tex]/9 x)-49
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Pls help! Answer the question in the pic. I will give five stars, thanks, and brainliest!
*20 POINTS*
Answers
71°
Step-by-step explanation: Let's have look on triangle BDH
Angle B + Angle D + Ange H = 180
Angle DHB = 180 - 71
Angle DHB = 109
Angle X = 180 - 109
Angle X = 71 ° Ans .
Lines b and care parallel.
1/2
(7x+1)/(18x+4)
5/6
7/8
b
What is the measure of 22?
O m2 = 31°
Om42 = 50°
Om42 = 120°
Om22 130°
Answers
Answer:
Option 2angle 2 = 7x + 1 ( vertically opposite angles)
7x + 1 + 18x + 4 = 180° ( forming linear pair).
7x + 18x + 4 +1 = 180°
25x + 5 = 180°
25x = 180 - 5
25x = 175
x = 7°
angle 2 = 7(7)+ 1
= 50°
The measure of angle ∠2 of the parallel lines is ∠2 = 50°
What are angles in parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Given data ,
Let the parallel lines be b and c
Now , the measure of ∠1 + ∠2 = 180° ( angles on the same line )
And , the measure of ∠2 = ( 7x + 1 )° ( alternate angles are equal )
So , ( 7x + 1 ) + ( 18x + 4 ) = 180° ( angles on the same line )
On simplifying , we get
25x + 5 = 180
25x = 175
x = 7
So , the measure of angle ∠2 = ( 7 ( 7 ) + 1 )
The measure of angle ∠2 = 50°
Hence , the angle is ∠2 = 50°
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Migdalia is a consultant. She works 3 days a week in the company's headquarters and 2
week at a production site.When she works at the company headquarters, she takes a bus
from work. When she goes to production sites, she uses her car and travels 52 ms
cast for using the bus is $48.00 for 10 one-way trips. The cost of using her car she
30 per mile Migdalia budgets $50 per week for travel expenses to and from work whether or not she has set aside enough money.
Answers
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
How to find the expenses and know if it's enough?She works 3 days in a week in the headquarter and 2 days a week at the production site.
When she works at the company headquarters, she takes a bus to and from work. The cost for using the bus is $48.00 for 10 one-way trips.
Therefore,
each one way trip = 48 / 10 = $4.8
To and from the headquarters = 4.8 × 2 = $9.6
Hence,
Therefore,
three days cost = 9.6 × 3 = $28.8
The cost of using her car she estimates at 30 cent per mile. When she goes to production sites, she uses her car and travels 52 miles per day. Therefore,
cost of travelling to production site in a week = 2 × (52 × 0.3) = $31.2
Hence,
cost of expenses per week = 31.2 + 28.8 = $60
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
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Which of the following is a solution to the equation x[tex]x^{2}[/tex]– 6x + 5 = 0?
Answers
Answer:
[tex]\huge\boxed{\sf x =5 \ \ \ OR \ \ \ x = 1}[/tex]
Step-by-step explanation:
Given equation:[tex]x^2-6x+5=0[/tex]
Using mid-term break formulaMultiply -5 and -1 gives +5 (side term) and adding them gives -6 (mid term).So, split -6 into -5 and -1[tex]x^2-5x-x+5=0\\\\Take \ common\\\\x(x-5)-1(x-5)=0\\\\Take \ (x-5) \ common\\\\(x-5)(x-1)=0[/tex]
Either,
x - 5 = 0 OR x - 1 = 0
x = 5 OR x = 1[tex]\rule[225]{225}{2}[/tex]
Hello,
I need help with this exercise.
A ball is launched upward at a speed of 20 meters per second (m/s) from a 60-meter tall platform. The equation for the ball’s height (h in meters) at time t seconds after launch is h = -4.9t2 + 20t + 60. How long before the ball hits the ground? What is the maximum height of the ball?
Answers
Answer:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Answer: I HOPE THAT MY ANSWER WILL HELP U
Step-by-step explanation:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Write a function rule for the table.
Days
1
2
3
4
Cost to Rent a Truck
29
47
65
83
Answers
Answer:
can you give upload the pictures
Here it is: y = 18x + 11
Draw a
box-and-whisker plot for the set of data.
27, 35, 44, 51, 52, 54, 56, 69, 69, 79, 80, 100, 100
a.
b.
C.
d.
0510 15 20 25 30 35 40 45 50 55 60 65 70
05 10 15 20 25 30 35 40
45 50-55
HHH
05
#2
0 5 10 15 20 25 30 35 40 45 50 55
60 65 70
60 65 70
10 15 20 25 30 35 40 45 50 55 60 65 70
75 80 85 90
75 80 85 90
75
75
95 100
80 85 90
95 100
80 85 90 95 100
95 100
Answers
Answer: B
Step-by-step explanation:
The maximum is 100 and the minimum is 27.
The only option that shows this is B.Find three consecutive integers such that the
sum of the first and the third is 32.
Answers
The three consecutive integers are 15 16 and 17.
Step 1:
Let X be the first integer. Since they are consecutive, it means that the second number will be X + 1 and the third number will be X + 2 and sum of the first and the third should add up to 32. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) be the three consecutive integers.
Step 2:
The sum of the first and the third should add up to 32.
X + ( X + 2 )= 32
2X + 2= 32
2X = 32 - 2
2X = 30
X = 30/2
X=15
Hence the first number is 15, the second number is 15 + 1, and the third number is 15 + 2.
Therefore, three consecutive integers in which the sum of the first and the third is 32 are 15 16, and 17.
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Step-by-Step Explanation:
Let the first integer be ‘a’
Therefore, since they are consecutive, the next 2 integers will be (a + 1) and (a + 2). We know, sum of first integer (a) and third integer (a + 2) is 32.
Therefore,
a + a + 2 = 32
2a + 2 = 32
2a = 32 - 2
2a = 30
a = 30/2
=> a = 15
Finding each Integer :-
1st No. = 15
2nd No. = 15 + 1 = 16
3rd No. = 15 + 2 = 17
Hence, the 3 integers are 15, 16 and 17.
Which expression is equivalent to this quotient?
Answers
Answer: C
Step-by-step explanation:
[tex]\frac{3x^{2}-3}{x^{2}+3x}=\frac{3(x^{2}-1)}{x(x+3)}=\frac{3(x-1)(x+1)}{x(x+3)}[/tex]
So, the original fraction is equal to
[tex]\frac{\frac{3(x-1)(x+1)}{x(x+3)}}{\frac{x+1}{x(x+3)}}=\boxed{3(x-1)}[/tex]
Mrs. jones has a body fat to body mass of 1:3.She has a body mass of 60kg.
Answers
Answer:
20 kg of body fat
Step-by-step explanation:
Multiple both sides of the ratio so that the side with body mass is 60 kg:
body fat : body mass
1 : 3
× 20 × 20
20 kg : 60 kg
Mrs. Jones has 20 kg of body fat.
Factor
4m^2+16m+16.
Answers
Answer:
4(m+2)²
Step-by-step explanation:
Hope this help!!
Solve for x: |x − 2| + 10 = 12 (1 point)
Answers
Answer:
I think that would be 1
Step-by-step explanation:
Do everything in the lines before anything else. -2 becomes a 2 and then you add that with the 12 and divide 12 on both sides to get one.
Answer:
x = 0 or 4
Step-by-step explanation:
The absolute value function can be resolved into two equations. These one- or two-step equations can be solved in the usual way.
__
negative argument-(x -2) +10 = 12
-x = 0 . . . . . . . . . simplify, subtract 12
x = 0 . . . . . . . . . multiply by -1. Check: 0 -2 is negative.
positive argumentx -2 +10 = 12
x = 4 . . . . . . . . . simplify, subtract 8. Check: 4 -2 is positive.
The two solutions are x=0 and x=4.
The school is planning a field trip to the science center. Tickets are originally $28, but school
groups receive an $8 discount on each ticket that is purchased. The expression t(28 - 8)
represents the total cost for t tickets.
What does the quantity 28 - 8 represent?
the number of tickets
the original price of a ticket
4) the amount of the discount
the total cost
the number of students
the discounted price of each ticket
Answers
28-8 is the discount price of each ticket, and the (28-8) is equal to (=) -----> 24(28-8
Step-by-step explanation:
that is the answer
A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
Answers
A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. The correct option is D.
What is a relative frequency table?A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. When we look at relative frequency, we are comparing the number of times a given event occurs to the overall number of events.
The complete question is mentioned in the below image with the relative frequency table.
As per the relative frequency table, the value 0.2 highlighted in the table represents that 20% of his customers ordered cheese but no chili on their hot dogs.
Hence, the correct option is D.
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graph f(x)= x if x < 2, 2 if x ≥ 2
Answers
The graph is shown below:
What is graph?A graph is a mathematical diagram which shows the relationship between two or more sets of numbers or measurements.
Given function: f(x) = x
We have to draw the graph for the function ,f(x) =x with two cases.
For x<2 and for x ≥ 2
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i need help please very fast thanks
Answers
how to make 27 using 1,2,3,4 only once
Answers
Answer:
1) (4 - 2 + 1)^3
2) 3^2(4 - 1)
3) 3^4/2 + 1
It can be either one of those
Answer:
(2 * 4 + 1) * 3 =Step-by-step explanation:
how to make 27 using 1,2,3,4 only once
Remember Pemdas
(2 * 4 + 1) * 3 =
(8 + 1) * 3 =
9 * 3 =
27
An object’s position in meters and motion in meters per second can be described by x = −12 − 5t + 3t^2 during the time interval 0[tex]\leq[/tex]t[tex]\leq[/tex]1.
Which of the following statements is the best description of the object’s motion?
A
The acceleration of the object is zero.
B
The initial position of the object is −12 meters.
C
The object’s speed is increasing.
D
The average velocity of the object is −5 m/s.
Answers
Answer:
B
Step-by-step explanation:
Comment
Thank you for editing the choices.
The reason the answer is B is because the object begins to move when t = 0. Only - 12 will be left after that.
The acceleration is 3. I don't know how to explain that because I'm using calculus and I don't know if you have taken that or not. I assume not by the right answer you are not in a calculus class. You'll have to ask your instructor about the actual answer. Not A
The same is true of D. The answer is - 5 m/s. It is - 4 Not D
All the minus signs indicate a decrease during that interval. Not C
Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2
Answers
Answer:
Option B is correct.
Step-by-step explanation:
Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.
The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.
Here, [tex]sin 30[/tex]° [tex]=\frac{4}{8}[/tex]
[tex]sin 30[/tex]° [tex]=\frac{1}{2}[/tex]
[tex]cos 30[/tex]° [tex]=\frac{4\sqrt{3}}{8}[/tex]
[tex]cos30[/tex]°[tex]=\frac{\sqrt{3} }{2}[/tex]
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evaluate 2b^3 where b = 3
Answers
Answer:
Answer=54
Step-by-step explanation:
Given:- b=3
2b³
Solution:-
2 x b³
2 x 3 x 3 x 3
6 x 9
54 (answer)
Hope this helps you
Have a good day.
i need help can someone give me answers
Answers
Answer:
Step-by-step explanation:6 type
5/25=1/5=20%
1-1/5=4/5=80%
The types of candles are 6. And the probability of a small pink candle and NOT a small pink candle will be 0.20 and 0.80, respectively
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The table is given below.
Small Medium Large Total
White 9 3 5 17
Pink 5 2 1 8
Total 14 5 6 25
The types of candles are given as,
⇒ 2 x 3
⇒ 6
The probability of a small pink candle is as,
P = 5/25
P = 0.20
The probability of NOT a small pink candle is as,
Q = 1 - P
Q = 1 - 0.20
Q = 0.80
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What is the circumference of a circle with a diameter of 5 feet? Use 3.14 for
TT.
Answers
Answer: 15.7
Step-by-step explanation:
[tex]C=\pi d\\\\C=5\pi[/tex]
Using [tex]\pi=3.14[/tex], we get [tex]C \approx 5(3.14)=\boxed{15.7 \text{ ft}}[/tex]
[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]
___________________________________________________________
Answer: Circumference = 15.7 ft ✅
Step-by-step explanation:
Do you need to know the circumference of a circle with a diameter of 5 ft? No problem! Luckily, there's a formula to find it! (:
CircumferenceLet's work out the circumference. This is the formula that is going to help us. [tex]\rightsquigarrow\boldsymbol{C=\pi d}[/tex] C=circumference π=pi d=diameter
Now, stick in the values (note that we can use 3.14 for pi; pi is irrational, so we use 3.14 instead of pi to avoid irrational numbers)
[tex]\boldsymbol{C=3.14\cdot5}[/tex]. Upon simplifying we obtain
[tex]\boldsymbol{C=15.7\;ft}[/tex]. Which is our final answer.
------
Hope that this helped! Best wishes.
[tex]\boldsymbol{Reach \quad far. \quad Aim \quad high. \quad Dream \quad big.}[/tex]
#StudyWithBrainly (:
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---------
In a statistics class with 36 students the professor wanted to know the probability that at least two students share the same birthday. The probability would be
Answers
The probability that at least two students share the same birthday is 83.22 %.
Probability of sharing the same birthdayLet P(A) = Probability that no two students share same birthdayLet P(A') = Probability at least two students share same birthday
There are 365 days in year and there 36 students in the class.
Total sample space, n = 365³⁶
36 students will be selected as [tex]365P_{36}[/tex]
[tex]P(A) = \frac{365P_{36}}{365^{36}} = 0.1678[/tex]
Probability at least two students share same birthdayP(A') = 1 - P(A)
P(A') = 1 - 0.1678
P(A') = 0.8322
P(A') = 83.22 %
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An entertainment company is opening a theme park in a nearby city. They are in the process of designing the theatre where a water show will take place. The following design is already under construction and will house the dolphins that perform in the show:
Main Show Tank Calculation:
The main show tank has a radius of 70 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
Holding Tank Calculations:
The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 35 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
You must show all steps and provide any evidence needed in your solution to receive full credit.
The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
Using the information from above answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answers
1) The volume of the quarter sphere shaped tank is; V = 20510 ft³
2) The volume of the smaller mock-up tank is; 230790 ft³
How to find the area and volume of a composite shape?1) The volume of the quarter sphere shaped tank is;
V = ⁴/₃πr²
V = ⁴/₃π * 70 * 70
V = 20510 ft³
2) We multiply dimensions by 2 not radius to make 1 whole cylinder. Thus
r = 35 feet remains the same as radius can only be half of a joined circle,
Since vertically cut, we have;
h = 125 * 2 = 250ft
Let's find the Area;
A = πr²
A = π * 35 * 35
A = Surface Area = 3846.5 ft²
Volume = Surface area * h
V = 3846.5 * 120 = 461580 combined.
For each; V = 461580/2 = 230790 ft³
3) Volume of smaller mock-up tank is;
V = (1/6) * 20510
V = 3418.33 ft³
4) 5/6 * 20510 = 17091.66 ft³
For the larger tank the increase is 17092 ft rounded up (0.165 value) of that of the smaller mock up tank. Therefore percentage is 1/6 = 16.67% and 5/6 = 83.33%
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answers
Answer: A
Step-by-step explanation:
We can rewrite [tex]8^x[/tex] as follows:
[tex]8^{x}=\left(8^{9} \right)^{x/9}=\left(\frac{1}{8^{9}} \right)^{-x/9}[/tex]
Hence, [tex]A=\frac{1}{8^{9}}=\boxed{8^{-9}}[/tex]
Jeff and Kirk can build a 75-ft retaining wall together in 4 hours. Because Jeff has more experience, he could build the wall by himself 1 hour quicker than Kirk. How long would it take Kirk (to the nearest minute) to build the wall by himself?
Answers
Answer:
8 hours 32 minutes
Step-by-step explanation:
Working together, the construction rates add. We can use the given relation to write an equation for the total time when the pair work together.
__
setupLet k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...
1/k +1/(k -1) = 1/4
__
solutionMultiplying by 4k(k-1), we have ...
4(k-1) +4k = k(k -1)
k² -9k = -4 . . . . . . . . subtract 8k and simplify
k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square
k -4.5 = √16.25 . . . . . . . . . take the square root
k = 4.5 +√16.25 ≈ 8.531129 . . . hours
The fractional hour is ...
0.531129 × 60 min ≈ 31.9 min ≈ 32 min
It would take Kirk about 8 hours 32 minutes to build the wall by himself.
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Additional comment
For most "working together" problems the rates of completing work need to be expressed in jobs per unit time. Usually, the rates are given in terms of time per job, as they are here. That is why reciprocals get involved.
It will take Kirk about 8 hours 32 minutes to build the wall by himself.
What is Quadratic Polynomial?Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.
Here, Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...
1/k +1/(k -1) = 1/4
Multiplying by 4k(k-1), we have ...
4(k-1) +4k = k(k -1)
k² -9k = -4 . . . . . . . . subtract 8k and simplify
k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square
k -4.5 = √16.25 . . . . . . . . . take the square root
k = 4.5 +√16.25 ≈ 8.531129 . . . hours
The fractional hour is ...
0.531129 × 60 min ≈ 31.9 min ≈ 32 min
Thus, It will take Kirk about 8 hours 32 minutes to build the wall by himself.
Learn more about Quadratic Polynomial from:
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