Interval of function f(x) is sometimes negative and sometimes positive.
What is interval of function?The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.
Given function,
f(x) = (2x – 1)(3x + 5)(x + 1),
Zeros of function,
x = 1/2 = 0.5
x = -5/3 = - 1.6667
x = -1
From the graph
Interval of function is negative between -∞ < x < -1.6667
Interval of graph is positive between -5/3 < x < -1
Interval of function is negative between -1 < x < 0.5
Interval of graph is positive 0.5 < x < ∞
Hence, f(x) has sometimes positive interval and sometimes negative interval.
Learn more about interval of function here:
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I need the answer explained
Answer:
1.33
Step-by-step explanation:
62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.
Please help!
The quantities x and y are proportional.
x: 4 5 10
y: 10 12.5 25
Find the constant of proportionality (r) in the equation y=rx.
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Answer:
r = 2.5
Step-by-step explanation:
The constant of proportionality can be found by solving the equation for r:
r = y/x
Then any corresponding values of x and y can be used to find r:
r = 25/10 = 2.5
The constant of proportionality is 2.5.
If the area of a circle is 16π, the circumference of the circle is:
A. 8π
B. 16π
C. 2π
D. 4π
help! due august 12th
An Internet company reported that its earnings will be less than the 24 cents per share that was predicted. Write an inequality showing the possible earnings per share.
Answer:
e < 24 is the inequality which shows the possible earnings per share.
Explanation:
x, will stand for the variable for earnings and less than, means it will not be higher nor the same as 24. Thus, being leaves us with one sign. The open part facing 24 means that 24 is the bigger number, therefore the smaller side represents that x has to be smaller than 24.
Answer: x<24
Step-by-step explanation:
x, will stand for the variable for earnings and less than means it will not be higher nor the same as 24. Thus being leaves us with one sign. The open part facing 24 means that 24 is the bigger number therefore the smaller side represents that x has to be smaller than 24.
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Madison represented the sentence "The product of 3 and the difference of and the quotient of a number and is at most 5" by using the inequality . Which best describes Madison’s error?a) The difference of –4 and the quotient of a number and –2" should be written as . b) The product of 3 and the difference of –4 and the quotient of a number and –2" should be written as . c) The less than symbol should be replaced with the less than or equal to symbol. d) The less than symbol should be replaced with the greater than symbol.
Answer:
c) The less than symbol should be replaced with the less than or equal to symbol.
Step-by-step explanation:
3(-4 - n/-2) < 5
The equation written above could be interpreted as :
The product of 3 and the difference of -4 and the quotient of a number, n and -2 is less than 5
This means that the only error in Maddison's representation is the inequality sign, the inequality sign used by Maddison is wrong.
The equation should be used with a ≤ sign and expressed thus :
3(-4 - n/-2) ≤ 5
This means the left hand side (L. H. S) is less than or equal to 5 ; this means the L. H. S is at most 5
Answer:
C
Step-by-step explanation:
Find an equation of a plane containing the line r=⟨0,4,4⟩+t⟨−3,−2,1⟩ which is parallel to the plane 1x−1y+1z=−5 in which the coefficient of x is 1.
..?.. = 0.
The plane you want is parallel to another plane, x - y + z = -5, so they share a normal vector. In this case, it's ⟨1, -1, 1⟩.
The plane must also pass through the point (0, 4, 4) since it contains r(t). Then the equation of the plane is
⟨x, y - 4, z - 4⟩ • ⟨1, -1, 1⟩ = 0
x - (y - 4) + (z - 4) = 0
x - y + z = 0
The picture shows the graphs of the movement of a pedestrian (B) and a bicyclist (A) . Using the graphs, answer the following questions:
How many times is the distance covered by the bicyclist for 1 hour greater than the distance covered by the pedestrian for the same amount of time?
Answer:
15km
Step-by-step explanation:
hope it is well understood?
Answer:
5 times.
Step-by-step explanation:
First, look at the values of each line at the 1-hour mark.
For line A (the bicyclist), the distance is about 25 km.
For line B (the pedestrian), the distance is about 5 km.
To determine how many times greater the bicyclist distance is than the pedestrian, divide the values:
[tex]\frac{25\text{km}}{5\text{km}}=5[/tex]
Therefore, the distance covered by the bicyclist for 1 hour is 5 times greater than the distance covered by the pedestrian for the same amount of time.
Operaciones con funciones Suma, resta, multiplicación y división
F(x) 6x+2
G(x) 3x-2
AYUDAAA
Answer:
let us do one night
Step-by-step explanation:
Agg-77182882
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Surface Area of cones
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
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Answer:
64.1 ft²
Step-by-step explanation:
The area of the cone is given by ...
A = πr(r +h) . . . . for radius r and slant height h
A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²
I need help on this problem
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Answer:
see attached
Step-by-step explanation:
(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.
__
(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.
Write the equation of the line that passes through the points (0, 4) and (- 4, - 5) . Put your answer in fully reduced slope intercept form , unless it is a vertical or horizontal line
Answer:
y=9/4x+4
Step-by-step explanation:
Start by finding the slope
m=(-5-4)/(-4-0)
m=-9/-4 = 9/4
next plug the slope and the point (-4,-5) into point slope formula
y-y1=m(x-x1)
y1=-5
x1= -4
m=9/4
y- -5 = 9/4(x - -4)
y+5=9/4(x+4)
Distribute 9/4 first
y+5=9/4x + 9
subtract 5 on both sides
y=9/4x+4
please explain it step by step
Gant Accounting performs two types of services, Audit and Tax. Gant’s overhead costs consist of computer support, $267000; and legal support, $133500. Information on the two services is:
(See screenshot)
Answer:
$240,300
Step-by-step explanation:
Given :
Overhead cost :
Computer support = $267000
legal support = $133500
Overheads applied to audit services = (Number of CPU minutes used by Audit services * activity rate per CPU minute)
+
(number of legal hours used by Audit services * activity rate per legal hour)
The overhead applied to audit is thus :
40,000 * (267,000 / (40,000 + 10,000)) +
200 * (133500 / (200 + 800)
(40000 * 5.34) + (200 * 133.5)
= $240,300
find the value of the trigonometric ratio. make sure to simplify the fraction if needed.
Answer:
36/39
Step-by-step explanation:
Cos(theta) = Base/Hypotenuse
Cos(X) = 36/39
What is the measure of 7 shown in the diagram below?
110°
O A. 74.5°
B. 32°
X
O C. 71°
Z
D. 35.5°
Answer:
c
Step-by-step explanation:
Answer:
the correct choice is B
Step-by-step explanation:
Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms. At one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct
Answer:
The probability of making a correct random guess is 0.00053%.
Step-by-step explanation:
Since Clue is a board game in which you must deduce three details surrounding a murder, and in the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms, and at one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms, to determine what is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices , and the guess being correct, the following calculation must be performed:
(1 / (44x55x77)) x 100 = X
(1 / 186,340) x 100 = X
0.0005366 = X
Therefore, the probability of making a correct random guess is 0.00053%.
Mrs. Gomez has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden is 5:2
If there are 20 lilies, what is the total number of flowers in her garden?
Answer:
28
Step-by-step explanation:
5 : 2
since this is a simplified ratio, they have a common factor. let's say it is 'x'
so now :
5x : 2x
we know that 5x is lilies, and we also know that she has 20 lilies, so:
5x = 20
x = 4
the daisies would be 2x so 2*4 = 8
total flowers is 20 + 8
28
If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.
Answer:
The maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]
And we want to find the maximum value of f(x) on the interval [0, 2].
First, let's evaluate the endpoints of the interval:
[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]
And:
[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]
Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]
By the Product Rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]
By the Zero Product Property:
[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]
The solutions to the first equation are x = 0 and x = 2.
First, for the second equation, note that it is undefined when x = 0 and x = 2.
To solve for x, we can multiply both sides by the denominators.
[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]
Simplify:
[tex]\displaystyle a(2-x) - b(x) = 0[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]
So, our critical points are:
[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]
We already know that f(0) = f(2) = 0.
For the third point, we can see that:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]
This can be simplified to:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.
To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:
[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]
The critical point will be at:
[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]
Testing x = 0.5 and x = 1 yields that:
[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]
Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.
Therefore, the maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
what is an example of a quintic bionomial?
Scientists have steadily increased the amount of grain that farms can produce each year. The yield for farms in France is given by y=−2.73x2+11000x−11000000 where x is the year and y is the grain yield in kilograms per hectare (kg/ha).
What does the y-intercept of this function represent?
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Answer:
the yield in year 0
Step-by-step explanation:
The y-value is the yield for farms in France in year x. The y-value when x=0 is the yield for farms in France in year 0.
_____
Additional comment
The reasonable domain for this function is approximately 1843 ≤ x ≤ 2186. The function is effectively undefined for values of x outside this domain, so the y-intercept is meaningless by itself.
Write the quadratic equation whose roots are 2 and -4 and whose leading coefficient is 2
Answer:
2x^2+4x-16
Step-by-step explanation:
The quadratic can be written as
f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots
f(x) = a (x-2)(x- -4)
a is the leading coefficient
f(x) = 2(x-2)(x+4)
= 2(x^2 -2x+4x-8)
= 2(x^2 +2x-8)
= 2x^2 +4x-16
could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)
Answer:
-2, - 1, - 2 and - 3
Step-by-step explanation:
As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)
I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
Will give brainliest answer
Help me out!! Anyone
Answer:
4:10
Step-by-step explanation:
if they have to wait for plane B and it arrives every 10 mins then 4:10 is the anser
A triangle has base of 7 1/8 feet and height 6 1/4 feet. Find the area of a triangle as a mixed number.
Answer: The area is 22 17/64.
Step-by-step explanation:
base = 7 1/8 = 57/8
height = 6 1/4 = 25/4
area = 1/2*b*h
= 1/2*57/8*25/4
= 1425/64
= 22 17/64
Is u=−12 a solution of 8u−1=6u?
Answer:
No, -12 is not a solution.
Step-by-step explanation:
8u-1=6u
8(-12)-1=6(-12)
-96-1=-72
-97=-72
Untrue, to it’s not a solution
Solve the following formula for a.
Answer:
B is correct .trust me
Step-by-step explanation:
