Factor completely 6x - 18.
6(x + 3)
6(x-3)
6X (-18)
Prime

Negative Integers are :

Answer:

see details in graph and below

Step-by-step explanation:

There are many ways to generate the function.

We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.

1. f(x) has a local minimum at x = -3, and

2. a local maximum at x = 3

Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.

Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.

f'(x) = -x^2+9

will satisfy the above conditions.

Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.

Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0  so ok.

f(x) can then be obtained by integrating f'(x) :

f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3

A graph of f(x) is attached, and is found to satisfy all three conditions.

A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

Given that:

The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]

The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:

[tex]x = -3[/tex] or [tex]x = 3[/tex]

Equate both equations to 0

[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]

Multiply both equations to give y'

[tex]y' = (3 - x) \times (x + 3)[/tex]

Open bracket

[tex]y' = 3x + 9 - x^2 - 3x[/tex]

Collect like terms

[tex]y' = 3x - 3x+ 9 - x^2[/tex]

[tex]y' = 9 - x^2[/tex]

Integrate y'

[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]

[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]

[tex]y = 9x - \frac{x^3}{3} + c[/tex]

Express as a function

[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(-5) < 0[/tex] implies that:

[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]

[tex]-45 - \frac{-125}{3} + c < 0[/tex]

[tex]-45 + \frac{125}{3} + c < 0[/tex]

Take LCM

[tex]\frac{-135 + 125}{3} + c < 0[/tex]

[tex]-\frac{10}{3} + c < 0[/tex]

Collect like terms

[tex]c < \frac{10}{3}[/tex]

[tex]c <3.33[/tex]

We can then assume the value of c to be

[tex]c=3[/tex] or any other value less than 3.33

Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

See attachment for the function of f(x)

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Answer:

False

Step-by-step explanation:

Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.

From your earlier questions, we found

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

so the wave has amplitude √29. The weight's maximum negative position from equilibrium is then -√29, so you are solving for t in the given interval for which

[tex]\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac{\sqrt{29}}2[/tex]

Divide both sides by √29:

[tex]\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac12[/tex]

Take the inverse sine of both sides, noting that we get two possible solution sets because we have

[tex]\sin\left(\dfrac{7\pi}6\right)=\sin\left(\dfrac{11\pi}6\right)=-\dfrac12[/tex]

and the sine wave has period 2π, so [tex]\sin x=\sin(x+2\pi)=\sin(x+4\pi)=\cdots[/tex].

[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{7\pi}6+2n\pi[/tex]

OR

[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{11\pi}6+2n\pi[/tex]

where n is any integer.

Now solve for t :

[tex]t=\dfrac{\frac{7\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]

OR

[tex]t=\dfrac{\frac{11\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]

We get solutions between 0 and 0.5 when n = 0 of t ≈ 0.196946 and t ≈ 0.363613.

Answer:

Step-by-step explanation:

No of books in Preeti's shelf = 56

No of books in Shikha's shelf = 35

56 > 35

∴ Preeti's shelf is more full by 21 books

as 56 - 35 = 21

Hope this helps

plz mark as brainliest!!!

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

================================================

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

Step-by-step explanation:

-6x²+26x+20

=-2(3x²-13x-10)

=-2(3x²-15x+2x-10)

=-2[3x(x-5)+2(x-5)]

=-2(x-5)(3x+2)

Answer:

6 lockers have both students' stickers

Step-by-step explanation:

There are 130 lockers in the hallway

Janine goes down a hallway in the school and puts a sticker on every fourth locker.

Janine= 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 52nd, 56th, 60th, 64th, 68th, 72nd, 76th, 80th, 84th, 88th, 92nd, 96th, 100th, 104th, 108th, 112th, 116th, 120th, 124th, 128th.

Thor goes down the same hallway, putting one of his stickers on every fifth locker

Thor= 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, 95th, 100th, 105th, 110th, 115th, 120th, 125th, 130th.

Common multiples of Janine fourth locker and Thor fifth locker= 20, 40, 60, 80, 100, 120

Therefore,

6 lockers have both students' stickers

Answer:

5x+4f-1(x)=3 this is short answer

Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:

x= 5.5

Step-by-step explanation:

(segment piece) x (segment piece) =    (segment piece) x (segment piece)

x*4 = 11*2

4x = 22

Divide each side by 4

4x/4 = 22/4

x =5.5

Answer:

c is congruent to e congruent means to be the same

Step-by-step explanation:

Answer:

James town is 5 meters higher than Takoradi​ .

Step-by-step explanation:

Given:

Height of James town = 2 meters below sea level

Height of Takoradi town = 7 meters below sea level

To find:

How much higher is James town that Takoradi = ?

Solution:

As we can see the standard of height is how much the town is below the sea level.

So, the height of town having lesser value will be at a higher level.

Value of Height of James town is lesser than that of Takoradi town.

Therefore, James town is at a higher level.

Difference of height = 7 meters - 2 meters = 5 meters

So, the answer is:

James town is 5 meters higher than Takoradi.

Answer:

1,2 and 6

Step-by-step explanation:

pie symbol

2/3

0.333333....

Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

Answer:

7

Step-by-step explanation:

it's simply 13 - 6

7 it the answer, that was easy

Answer: 8

Step-by-step explanation:

Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.

Total marbles other than green = 8

Total marbles other than green and yellow = 6

Then the number of sets of seven marbles include at least one yellow one but no green ones:-

[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]

Number of sets of seven marbles include at least one yellow one but no green ones = 8

Answer:

Hope this helps :)

Step-by-step explanation:

A scatter plot is a two-dimensional diagram that displays individual data points based on the intersection of two variables, shown as vertical and horizontal axes. Individual data points or values are plotted at particular coordinates of the two variables being studied. Patterns of data points provide a visual representation of relationship between the two variables. A wide range of jobs and careers use this valuable analytical tool for data analysis and decision making.

My conclusion,

They help organize important data for future occurences.

Answer:

sine and tangent

will be positive.

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer:

The 95% confidence interval is  [tex]0.3795 < p < 0.4405[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 1000[/tex]

      The  number of approved loan is  k =  410

Generally the sample proportion is mathematically represented as

       [tex]\r p = \frac{k}{n}[/tex]

substituting values

      [tex]\r p = \frac{410}{1000}[/tex]

       [tex]\r p = 0.41[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

       [tex]\alpha = 100 - 95[/tex]

        [tex]\alpha = 5\%[/tex]

       [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is  

         [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }[/tex]

substituting values

        [tex]E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }[/tex]

        [tex]E = 0.03048[/tex]

The 95% confidence interval for p is mathematically represented  as

     [tex]\r p - E < p < \r p + E[/tex]

substituting values

     [tex]0.41 - 0.03048 < p < 0.41 + 0.03048[/tex]

    [tex]0.3795 < p < 0.4405[/tex]

Answer:

The answer is 1/14w-8

Answer:

Step-by-step explanation:

12x - 9 = 8x + 7

4x - 9 = 7

4x = 16

x = 4

solution is C

The solution is Option C.

The value of x is given from the equation x = 4

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as CD

Let the second line be represented as XY

Now , CD is the perpendicular bisector of XY

So , the point F is the midpoint of the line segment XY

The measure of line segment XF = 12x - 9

The measure of line segment FY = 8x + 7

From the perpendicular bisector theorem ,

The measure of line segment XF = The measure of line segment FY

Substituting the values in the equation , we get

12x - 9 = 8x + 7

Subtracting 8x on both sides of the equation , we get

4x - 9 = 7

Adding 9 on both sides of the equation , we get

4x = 16

Divide by 4 on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]

Cheers.

Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

The composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.

In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.

Solving a composite function means finding the composition of two functions.

The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].

The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:

s(t)= q[p(t)]

4t -21= 4[p(t)]³ – 1

Solving:

4t -21 +1= 4[p(t)]³

4t -20 = 4[p(t)]³

(4t -20)÷ 4 = [p(t)]³

4t÷4 -20÷ 4 = [p(t)]³

t -5 = [p(t)]³

[tex]\sqrt[3]{t-5}=p(t)[/tex]

Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

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Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

im sorry but the thing is i cant translate these words but the answer is D

Answer:

number of nickel = 60

number of dimes  = 20

Step-by-step explanation:

1 nickel = 5 cents

1 dimes = 10 cents

$1 = 100 cents

we will use these value to solve the questions

_______________________________

Total no of coins = 80

let the number of nickels be x

let the number of dimes be y

thus,

x+y = 80

y = 80-x   equation 2

value of x nickels = 5x

value of y dimes = 10y

Total value of x nickels and y dimes = 5x+10y

The total value of the coins is $5.00

total value of the coins in cents = 5*100 = 500

thus

5x+10y = 500

using y = 80-x   from equation 2

5x + 10(80 - x) = 500

5x + 800 - 10x = 500

-5x = 500 - 800 = -300

x = -300/-5 = 60

Thus,

number of nickel = 60

number of dimes = 80-60 = 20

Answer:

Lori will pay $12 more if she makes monthly payments

Step-by-step explanation:

to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72

subtracting the amount she would pay as a down payment

$72 - $60 is $12

Lori will pay $12 more if she makes monthly payments

Answer:

(1, -9)  yes

(7,3)  no

(-9,4)  no

(0, -9) yes

Step-by-step explanation:

The y value must be -9

The x value can be any value to satisfy   the equation y = -9