Answers
The valid solution for the positive demand is (6,3)
How to determine the valid solutions?The equation of the function is given as:
[tex]C(t) = -\sqrt{t^2 - 4t - 12} + 3[/tex]
Next, we test the options::
Option (a): (t, C(t)) = (2,3)
This gives
[tex]-\sqrt{2^2 - 4*2 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{-16} + 3 = 3[/tex] ---- this is not true (square root of -16 is a complex number)
Option (b): (t, C(t)) = (6,3)
This gives
[tex]-\sqrt{6^2 - 4*6 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{0} + 3 = 3[/tex]
Evaluate the root
0 + 3 = 3
Evaluate the sum
3 = 3 ---- this is true
Hence, the valid solution for the positive demand is (6,3)
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Related Questions
The solutions of the cubic function f(x) are -4, 5/3, and 1. identify a factor of this function.
a. 3x+5
b. 5x+3
c. x+1
d. x+4
Answers
The factor of the function from the given option is d. x+4
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
The solutions of the cubic function f(x) are -4, 5/3, and 1. WE need to identify a factor of this function.
So, the solution are
x = -4
Factor;
x + 4
now,
x = 5/3
Factor;
x - 5/3 = 0
3x - 5 = 0
also,
x = 1
Factor;
x - 1= 0
Therefore, the factor of the function from the given option is d. x+4
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28. sylvia researched changes in the deer population in her state's parks during her lifetime
and found that population has been halved every 8 years.
she wrote the equation 4800(8) { = 600 and plans to solve fort to determine in how
many years it will take for the current population of 4800 deer to reduce to 600.
Answers
Using an exponential function, it is found that it will take 24 years for the current population of 4800 deer to reduce to 600.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change, as a decimal.In this problem, considering the initial value of 4800, and that the population halves every 8 years, the equation is given by:
[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
The population will be of 600 when A(t) = 600, hence:
[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
[tex]600 = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{600}{4800}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{1}{8}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \left(\frac{1}{2}\right)^3[/tex]
Hence:
t/8 = 3.
t = 24.
It will take 24 years for the current population of 4800 deer to reduce to 600.
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Simplify please help me with this question
Answers
Answer:
a^4
Explanation:a^2×a^3= a^5(a^2+3)
a^5/a= a^4(a^5-1)
A can of soda can be modeled as a right cylinder. Suav measures its height as 11.6 cm and its radius as 2.7 cm. Find the volume of the can in cubic centimeters. Round your answer to the nearest tenth if necessary.
Answers
Answer:
16.4cm3
Step-by-step explanation:
hope this helps
Volume
πr²hπ(2.7)²(11.6)7.29(11.6)π84.564π265.5cm³What is the volume of a triangle with a radius of 5 and a height of 6
Answers
A new car is purchased for $29, 000 and over time its value
depreciates by one half every 3.5 years. What is the value of the car 20
years after it was purchased, to the nearest hundred dollars?
Answers
Answer:
290 take away 2 zeros wuxbeucheuxuejx
I need help asap pls help
Answers
Answer:
For the first triangle:
[tex]2.75 units^{2}[/tex]
For the second triangle:
[tex]3.98 units^{2}[/tex]
Step-by-step explanation:
To find area of right triangles:
[tex]A=\frac{ab}{2}[/tex]
Turn mixed numbers into improper fractions, then decimals. It's not required but I tend to find working with decimals much easier ;)Multiply them togetherDivide by 2And you are good to go!
Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!
Have a great day!
:)
Algebra please help!!
Answers
The airplane reaches its maximum height of 95 feet after 10 seconds
How to calculate the maximum height of an object?The maximum height of an object the point where the velocity of the object is zero.
Given the function that represents the height of the airplane is expressed as h(t) = -(t-10)² + 95
The maximum height is the point where h'(t) = 0
h'(t) = -2(t-10)
0 = -2t + 10
2t = 10
t = 5secs
Substitute t =10 into the function
h(5) = -(10-10)² + 95
h(5) = -0 + 95
h(5) = 95feet
Hence the airplane reaches its maximum height of 95 feet after 10 seconds
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Compare the equations represented in the table, equation, and graph over
the interval
[-5, 3]. Which function is increasing the fastest?
Answers
Answer:
Tabled Function
Step-by-step explanation:
To determine which function is increasing the fastest over the interval [-5, 3], we need to calculate and compare each function's average rate of change over the given interval.
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given interval: -5 ≤ x ≤ 3
Therefore, a = -5 and b = 3
Tabled function[tex]f(3)=7[/tex]
[tex]f(-5)=-17[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-(-17)}{3+5}=3[/tex]
Equation: y = x² - 2[tex]f(3)=(3)^2-2=7[/tex]
[tex]f(-5)=(-5)^2-2=23[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-23}{3-(-5)}=-2[/tex]
Graphed functionFrom inspection of the graph:
[tex]f(3)\approx8[/tex]
[tex]f(-5) \approx 0[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)} \approx \dfrac{8-0}{3-(-5)}=1[/tex]
Therefore, the Tabled Function has the greatest average rate of change in the interval [-5, 3] and so it is increasing the fastest.
Please I need help I’m being timed.please
Answers
Answer:
C, D, and E
Step-by-step explanation:
85-20=65
t>65
This means all the numbers greater than 65.
Do not include 65 because it is not a greater than or equal to symbol.
Hope this helps!
If not, I am sorry.
What are the zeros of the function
f(x)=6x^2+x-40
Answers
Answer:
X= 2.667 or X= -2.5
Step-by-step explanation:
sorry if this isn't correct </3
This table displays the market share in percent of four companies.
Which of the following ranges would be appropriate to use in order to represent the numerical data on the vertical axis of a Bar Chart?
A. 0 to 40
B. 10 to 20
C. 0 to 20
D. 20 to 40
Answers
The right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is 0 to 40.
How do you set the vertical axis of a Bar Chart?In setting the vertical axis of a Bar Chart, note that it is vital for the categories to be natural as possible.
That is, the vertical axis should always begin with the number zero (0) and the scale values for the x axis must range from the lowest value on the left hand side to highest on the right hand side.
Therefore, due to the explanation given, the right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is 0 to 40 as it range from 0 to the highest value.
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Answer:
A
Step-by-step explanation:
i think i can be wrong
1. What effect does replacing x with x -4 have on the graph for the function f(x)?
f(x)= |x|-5
A vertical shift of 4 up.
A horizontal shift of 4 to the right.
A vertical shift of 5 down.
A horizontal shift of 4 to the left.
Question 4
Answers
Answer: Choice B
A horizontal shift of 4 to the right.
========================================================
Reason:
Replacing x with x-4 basically means we're decreasing each input by 4 units.
What this does is move the xy axis 4 units to the left. If we held the function curve fixed in place as the xy axis moved like this, then it would give the illusion the function is moving 4 units to the right.
Visual confirmation is shown below.
Solve system of equation using elimination by addition.
Will give brainliest!!
Answers
Answer:
x = 6
Step-by-step explanation:
Add the system of equations together:
2x - 3y = 12
4x + 3y = 24
you get
6x = 36
divide by the coefficient
6x/6 = 1
36/6 = 6
x = 6
Not sure if you need the y, but if so, let me know!
Hope this helps!
Simplify the expression.
(x6y-6)
————
(x8y-8)
Answers
Marissa jogged 5 miles on the first day.
Marissa jogged 6 miles on the second day.
Marissa jogged 9 miles on the third day.
Marissa jogged 3 miles on the fourth day.
Marissa jogged 3 miles on the ninth day.vvvvvThe scatterplot shows how many miles Marissa jogged over 10 days. Which statements are true? Check all that apply.
Marissa jogged 5 miles on the first day.
Marissa jogged 6 miles on the second day.
Marissa jogged 9 miles on the third day.
Marissa jogged 3 miles on the fourth day.
Marissa jogged 3 miles on the ninth day.Answer:
Step-by-step explanation:
tthe
PLEASE HELP!!!
Follow the guided instructions below to rotate the figure 270^{\circ}270
∘
clockwise about the origin.
Answers
Coordinates after 270 clockwise rotation is (-6,-2), (-3,-5) and (-8, -5).
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given coordinates are: (-2,6) , (-5, 3) and (-5, 8)
For 270° clockwise about the origin, we have the following rule:
(x, y)= (-y, x)
So,
coordinates (-2,6) change into (-6,-2)
coordinates (-5, 3) change into (-3,-5)
coordinates (-5, 8) change into (-8, -5).
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Which of the following rational functions is graphed below?
Answers
What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
O {x|x = -5, -4, -2, 0, 2}
Oyly=-9, -3, 0, 5, 7}
O {x|x = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Oyly = -9,-5, -4, -3, -2, 0, 2, 5, 7}
Answers
Answer:
see the attachment photo!
Investment increase exponentially by about 26% every 3 years. if you start with $2,000 investment how much money would you have after 45 years
Answers
Using an exponential function, it is found that you would have an amount of $64,060 in 45 years.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, considering the initial value of A(0) = 2000, with a growth rate of r = 0.26 each 3 years, the equation is given by:
[tex]A(t) = 2000(1.26)^{\frac{t}{3}}[/tex]
In 45 years, the amount will be given by:
[tex]A(45) = 2000(1.26)^{\frac{45}{3}} = 64060[/tex]
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i need help with this pls
Answers
Answer:
The answer is the first bullet. (number 1)
Solve tTwo researchers are studying the decline of orangutan populations. In one study, a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year. In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year. After how many years will the two populations be the same?
he linear equation 2.25 – 11j – 7.75 + 1.5j = 0.5j – 1.
Answers
Answer:
x2
Step-by-step explanation:
bcs yeah
Noah receives a 5$ discount each month on his cell phone bill because he signed up for an auto pay from his bank account over the last 8 months Noah has paid a total of 280$ for his cell phone bill. what would Noah be charged for his cell phone bill each month if he stopped using auto pay
Answers
Using proportions, it is found that Noah would be charged $40 each month for his cell phone bill each month if he stopped using auto pay.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
He paid a total of $280 during 8 months, hence the monthly amount he paid is given by:
M = 280/8 = $35.
Without the discount, he would have paid $5 more, hence Noah would be charged $40 each month for his cell phone bill each month if he stopped using auto pay.
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PLease help 5 stars + thanks
Answers
Answer:
B.80
Step-by-step explanation:
a straight line adds up to 180 degrees. you already have 100. 180-100=80
What is the value of x?
A x = 2
B = 3
C x = 5
D x = 8
Answers
Answer:
x=5 .........................................
How many solutions exist for the system of equations graphed below?
a.) none
b.) one
c.) two
d.) infinitely many
Answers
Considering the given graph, the number of solutions for the system of equations is given by:
b.) one
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In a graph, the number of solutions is given by the number of times the lines intersect. Hence, in this problem, the system has one solution, and option b is correct.
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Calculate the average speed of the object between 1 and 3 seconds.
Answers
1. so plug in whatever distance you have
2. get the difference between 3 and 1 second = which is 2 seconds
3. plug in 2 seconds for time
Which of these is a reason you might use a credit union instead of a bank? (flocabulary)
A
They often don’t have any fees associated with their accounts.
B
They often have higher interest rates on savings accounts.
C
They often have higher interest rates on loans.
D
They are out to make a profit on your money.
Answers
Is this a proportional relationship? Please help!
Answers
Answer:
No
Step-by-step explanation:
If you draw a line, it will not go through the origin and there isn't a constant rate of change.
simplify the radical expression -2√2p*2√22
Answers
Answer:
Simplest form = -4√44p
Step-by-step explanation:
● -2√2p × 2√22
⇒ (-2)(2)(√2p)(√22)
⇒ -4√44p ...Answer...
hope that helps...
What is the intermediate step in the form (x + a)2 = b as a result of completing the square for the following equation? x² + 4x = 12
Answers
The equation in the form (x + a)² = b is (x + 2)² = 16
How to determine the intermediate step?The equation is given as:
x² + 4x = 12
Take the coefficient of x
k = 4
Divide by 2
k/2 = 2
Square both sides
(k/2)² = 4
Add this result to both sides of x² + 4x = 12
x² + 4x + 4 = 12 + 4
Evaluate the sum
x² + 4x + 4 = 16
Express as a perfect square
(x + 2)² = 16
Hence, the equation in the form (x + a)² = b is (x + 2)² = 16
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