f(x) = (2x – 1)(3x + 5)(x + 1) has zeros at I = -
1
cole
2= -1, and x =
What is the sign of f on the interval
5
<<
3
เล
?
Choose 1 answer:
А
f is always positive on the interval.
B
f is always negative on the interval.
f is sometimes positive and sometimes negative on the interval.

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)

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

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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

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]

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%.

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

Answer:

let us do one night

Step-by-step explanation:

Agg-77182882

(#(+2+

Answer:

c  

Step-by-step explanation:

Answer:

the correct choice is B

Step-by-step explanation:

9514 1404 393

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.

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:

Answer:

36/39

Step-by-step explanation:

Cos(theta) = Base/Hypotenuse

Cos(X) = 36/39

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

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

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!

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.

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

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

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.

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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.

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

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

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

Answer:

B is correct .trust me

Step-by-step explanation:

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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.

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.