The graph of f(x) with the graph of w(x)=(x-6)^2

Answer:

Step-by-step explanation:

There are 2 different ways to do this: calculus and by completing the square. In this particular instance, calculus is WAY easier, and since I don't know for what class you are doing this, I'll do both ways. First the calculus way. We know the position equation, and the first derivative of the position is velocity. We also know that when the velocity is equal to 0 is when the object is at its max height. So we'll find the derivative first, then solve it for t:

If [tex]s(t)=-3t^2+20t+2[/tex] then the first derivative is

v(t) = -6t + 20 Solving for t requires that we set the velocity equal to 0 (again, this is where the object is at its max height), so

0 = -6t + 20 and

-20 = -6t so

t = 3.3 seconds. Now that we know that at 3.3 seconds the object is at its highest point, we sub that time into the position function to see where it is at that time:

s(3.3) = [tex]-3(3.3)^2+20(3.3)+2[/tex] and

s(3.3) = 35.3 meters.

Now onto the more difficult way...completing the square. Begin by setting the position function equal to 0 and then move over the constant to get:

[tex]-3t^2+20t=-2[/tex] Since the leading coefficient is not a 1 (it's a 3), we have to factor out the 3, leaving us with:

[tex]-3(t^2-\frac{20}{3}t)=-2[/tex] Now the rule is to take half the linear term, square it, and add it to both sides. Our linear term is [tex]\frac{20}{3}[/tex] and half of that is [tex]\frac{20}{6}[/tex]. Squaring that:

[tex](\frac{20}{6})^2=\frac{400}{36}=\frac{100}{9}[/tex]. We will add that in to both sides. On the left it's easy, but on the right we have to take into account that we still have that -3 sitting out front, refusing to be ignored. So we have to multiply it in when we add it to the right. Doing that gives us:

[tex]-3(t^2-\frac{20}{3}t+\frac{100}{9})=-2-\frac{100}{3}[/tex] We will clean this up a bit now. The reason we do this is because on the left we have created a perfect square binomial which will give us the time we are looking for to answer this question. Simplifying the right and at the same time writing the perfect square binomial  gives us:

[tex]-3(t-\frac{20}{6})^2=-\frac{106}{3}[/tex] Now the last step is to move the constant back over and set the quadratic back equal to y:

[tex]y=-3(t-\frac{20}{6})^2+\frac{106}{3}[/tex].  The vertex of this quadratic is

[tex](\frac{20}{6},\frac{106}{3})[/tex] where

[tex]\frac{20}{6}=3.3[/tex] as the time it takes for the ball to reach its max height of

[tex]\frac{106}{3}=35.3[/tex] meters.

I'd say if you plan on taking calculus cuz you're not there yet, you'll see that many of these types of problems become much simpler when you know it!

Answer:

Let June's sweets be 5x.

Then Gavyn's sweets will be 5x.

And Alex's sweets will be 3x.

5x = 3x + 22

2x = 22

x = 11

So June has 5 x 11 = 55 sweets

Gavyn has 5 x 11 = 55 sweets

And Alex have 3 x 11 = 33 sweets

Total

= 55 + 55 + 33

= 143 sweets

Answer:

If rounded to the nearest 10 bacteria, then it would be 500 bacteria.

Step-by-step explanation:

First multiply 150 by two in order to get 300, that leaves 4 hours to figure out. From there you can figure out the rest by seeing that 4 is 2/3 of 6. I converted it into the decimal number .66. Multiply 300 by .66 to get 198 and then add it to 300 to get 498. Then just round it up to the nearest 10 bacteria which leaves you with the final answer of 500 bacteria.

The limit of the difference quotient of the above function [tex]f(x)[/tex] at [tex]x=3[/tex] is [tex]3[/tex] such that [tex]f(x)=x^{3} - 4x^{2} + 2[/tex].

The difference quotient of a function [tex]f(x)[/tex] is [tex]\frac{f(x+h)-f(x)}{h}[/tex].

The given equation is, [tex]f(x)=x^{3} -4x^{2} +2[/tex]

So, [tex]f(x+h)=(x+h)^{3} -4(x+h)^{2} +2= x^{3} +h^{3}+3x^{2} h+3xh^{2} -4x^{2} -4h^{2} -8xh+2[/tex]

Now, [tex]f(x+h)-f(x)[/tex]

[tex]=x^{3}+h^{3}+3x^{2}h+3xh^{2}-4x^{2}-4h^{2}-8xh+2-x^{3}+4x^{2}-2[/tex]

[tex]=h^{3}+3x^{2}h+3xh^{2}-4h^{2}-8xh[/tex]

So, [tex]\frac{f(x+h)-f(x)}{h} =\frac{h^{3}+3x^{2}h+3xh^{2} -4h^{2}-8xh }{h}[/tex]

[tex]=h^{2}+3x^{2}+3xh-4h-8x[/tex]

Now, at [tex]x=3[/tex],

[tex]h^{2}+3x^{2}+3xh-4h-8x=h^{2}+27+9h-4h-24=h^{2}+5h+3[/tex]

If   [tex]h[/tex]→[tex]0[/tex], the value of [tex]h^{2}+5h+3=3[/tex]

Thus, the limit of the difference quotient of the above function [tex]f(x)[/tex] at [tex]x=3[/tex] is [tex]3[/tex].

Learn more about the limit of the difference quotient here- https://brainly.com/question/17008881

#SPJ2

The null hypothesis is [tex]\mu = 39.09[/tex]  

The symbol [tex]\mu[/tex] is the Greek letter mu

The alternate hypothesis is [tex]\mu \ne 39.09[/tex] telling us we have a two-tailed test here. The "not equal" is directly tied to the keyword "different" given in the instructions. In other words, mu being different from 39.09 directly leads to [tex]\mu \ne 39.09[/tex]

So either mu is 39.09 or it's not 39.09

You can use H0 and H1 to represent the null and alternate hypotheses respectively.  

----------------------

Summary:

The two hypotheses are

H0: [tex]\mu = 39.09[/tex]

H1: [tex]\mu \ne 39.09[/tex]

This is a two tailed test.

Answer:

7/4

Step-by-step explanation:

(4/7)^-1

We know a^-b = 1/a^b

1/ (4/7)^1

7/4

Answer:

(4/7)^-1

=1/(4/7)^1

=1÷4/7

=1×7/4

=7/4

Therefore 7/4 is equal to 1.75 as a rational number

Step-by-step explanation:

Area of a square = s x s

(4x-7)x(4x-7)

Open brackets

4x(4x-7)-7(4x-7)

16x^2-28-28x+49

16x^2-28x+21

Answer:

B. Pie chart.

Step-by-step explanation:

In this question, the students are asked what political party they belong. The best display format would be one in which the graph can be divided into parts, or percents, according to the percentage of students belonging to each political party. The graph that best describes this, distributing a group into parts, is a pie chart, and thus, the correct answer is given by option b.

Scatterplot is used when two variables correlate together, that is, there is a relationship between them, which we don't have between the number, or proportion of students belonging to each political party. Stemplot are used when there is a high number of quantitative data, which we do not have here.

Answer:

volume=length×width×height

v=15×20×20

v=6000

Answer:

$325.50

Step-by-step explanation:

1) 210÷100 = 2.1

  2.1×55 = 115.5

  210 + 115.5 = 325.5

2) 210×55 = 11550

   11550÷100 = 115.5

   210 + 115.5 = 325.5

Answer:

The warranty period should be of 30 months.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months.

This means that [tex]\mu = 37, \sigma = 5[/tex]

What should be the warranty period, in months, so that the manufacturer will not have more than 7% of the blenders returned?

The warranty period should be the 7th percentile, which is X when Z has a p-value if 0.07, so X when Z = -1.475.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.475 = \frac{X - 37}{5}[/tex]

[tex]X - 37 = -1.475*5[/tex]

[tex]X = 29.6[/tex]

Rounding to the nearest whole number, 30.

The warranty period should be of 30 months.

Answer:

900 at 12%

2100 at 10%

Step-by-step explanation:

Let x= amount invested at 12%

let y= amount invested at 10%

with that being said we can write the two equation

Equation 1: x+y=3000

Equation 2: 3000*.106=.12x+.1y

isolte x from equation 1

x= 3000-y

plug this into equation 2

318=.12(3000-y)+.1y

318=360-.12y+.1y

-42= -.02y

y= 2100

Plug this into equation 1

x+2100=3000

x=900

she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

Let's denote the amount of money Hattie invests at 12% as \(x\) dollars, and the amount she invests at 10% as \(\$3000 - x\) dollars.

The formula for calculating interest is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\).

For the 12% account:

Interest_12% = \(x \times 0.12 \times 1\) (1 year)

For the 10% account:

Interest_10% = \((3000 - x) \times 0.10 \times 1\) (1 year)

Hattie wants to earn 10.6% interest on the total investment, so we can set up the equation:

\(\text{Total Interest} = \text{Interest}_12% + \text{Interest}_10%\)

\(3000 \times 0.106 = x \times 0.12 + (3000 - x) \times 0.10\)

Now, solve for \(x\):

\(318 = 0.12x + 300 - 0.10x\)

\(318 = 0.02x + 300\)

\(18 = 0.02x\)

\(x = 900\)

Hattie should invest $900 at 12% and \(3000 - 900 = 2100\) at 10%.

Therefore, she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

Learn more about interest at https://brainly.com/question/29451175

#SPJ3

Answer:

b. 28[tex]\pi[/tex] in.

Step-by-step explanation:

circumference of a circle = 2 [tex]\pi[/tex] r

whrere r is the radius of rhe circle

= 2 × [tex]\pi[/tex] × 14 in.

= 28 [tex]\pi[/tex] in.

that is option b

We have to find,

The circumference of the given circle in terms of the π.

The formula we use,

→ C = 2πr

Then we can find the circumference,

→ 2 × π × r

→ 2 × π × 14

→ 28π in.

Hence, option (b) is correct answer.

Answer:

c is answer

Step-by-step explanation:

yes

Answer:

C

Step-by-step explanation:

took test

Answer:

a. The friend is incorrect.

2(x) is the same as x(2). PEMDAS does not apply to the same order of operation under normal conditions and both are directly proportional functions.

b. The parentheses are the only thing making the functions different. After you simplify from the parentheses, both values have the same priority.

Step-by-step explanation:

Answer:

369 cm^3

Step-by-step explanation:

you just multiply all the numbers together

Answer:

369 cm³.

Step-by-step explanation:

Volume of a rectangular prism is just length × width × height. So:

2.25 × 8 = 18

18 × 20.5 = 369

So, the volume is 369 cm³.

Step-by-step explanation:

y=k/x

Answer:

C. 15.6

Step-by-step explanation:

Perimeter of WXYZ = WX + XY + YZ + ZW

Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.

✔️Distance between W(-1, 1) and X(1, 2):

Let,

[tex] W(-1, 1) = (x_1, y_1) [/tex]

[tex] X(1, 2) = (x_2, y_2) [/tex]

Plug in the values

[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]

[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]

[tex] WX = \sqrt{4 + 1} [/tex]

[tex] WX = \sqrt{5} [/tex]

[tex] WX = 2.24 [/tex]

✔️Distance between X(1, 2) and Y(2, -4)

Let,

[tex] X(1, 2) = (x_1, y_1) [/tex]

[tex] Y(2, -4) = (x_2, y_2) [/tex]

Plug in the values

[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]

[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]

[tex] XY = \sqrt{1 + 36} [/tex]

[tex] XY = \sqrt{37} [/tex]

[tex] XY = 6.08 [/tex]

✔️Distance between Y(2, -4) and Z(-2, -1)

Let,

[tex] Y(2, -4) = (x_1, y_1) [/tex]

[tex] Z(-2, -1) = (x_2, y_2) [/tex]

Plug in the values

[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]

[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]

[tex] YZ = \sqrt{16 + 9} [/tex]

[tex] YZ = \sqrt{25} [/tex]

[tex] YZ = 5 [/tex]

✔️Distance between Z(-2, -1) and W(-1, 1)

Let,

[tex] Z(-2, -1) = (x_1, y_1) [/tex]

[tex] W(-1, 1) = (x_2, y_2) [/tex]

Plug in the values

[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]

[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]

[tex] ZW = \sqrt{1 + 4} [/tex]

[tex] ZW = \sqrt{5} [/tex]

[tex] ZW = 2.24 [/tex]

✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56

≈ 15.6

Answer:CCCCCCCCCCCCCCCCC

Step-by-step explanation:

Answer: Movies Average around 1 hour to 2 hours long. 1:30 to 2:30 so id say somewhere around 4-5 pm. Which leaves time for dinner after

Step-by-step explanation:

Answer:

503.75, 504.75, 505.75, 506.75

Step-by-step explanation:

x+(x+1)+(x+2)+(x+3)=2021

4x+6=2021

4x=2015

x=503.75

so it would be

503.75+504.75+505.75+506.75= 2021

Answer:

x2-4

Step-by-step explanation:

Answer:

hope it helps

Answer:

B. h = 7.4 inches

Step-by-step explanation:

height of the laptop screen = h

d = 12.1 in.

w = 9.6 in.

We are given the formula,

d = √(w² + h²)

Plug in the values and solve for h

12.1 = √(9.6² + h²)

Square both sides

12.1² = 9.6² + h²

146.41 = 92.16 + h²

146.41 - 92.16 = h²

54.25 = h²

√54.25 = h

7.4 = h (nearest tenth)

h = 7.4 inches

Answer:

[tex]f(x) = \frac{5}{x}[/tex]

[tex]g(x) = x - 4[/tex]

Step-by-step explanation:

Composite function:

[tex]h(x) = f(g(x)) = (f \circ g)(x)[/tex]

h(x) = 5/x-4

We have x on the denominator and not the numerator, so the outer function is given by:

[tex]f(x) = \frac{5}{x}[/tex]

The denominator is x - 4, so this is the inner function, so:

[tex]g(x) = x - 4[/tex]

Answer:

y - 2 = 2/3 (x-1)

y - 4 = 2/3(x-4)

Step-by-step explanation:

With this graph,the equation can be found on a straight line as the graph is .

So the formula is

[tex]y - y1 = m(x - x1)[/tex]

where your m is your gradient or slope as already said,the equation can be used by this formula (note;after finding your normal slope (not on a straight line ) firstly)

When you are done take any of the points connecting to the x axis and y axis directly as in (4,-4) or (2,1)

Let your first number be x1 and second y1 and place it in the formula .

where m is still your normal slope.

9514 1404 393

Answer:

Step-by-step explanation:

One way to write the relationship between time, speed, and distance is ...

  time = distance/speed

For the first part of the trip, the time is ...

  t1 = 240/r

For the second part of the trip, the time is ...

  t2 = 72/(r+10)

The total time is 6 hours, so we have ...

  t1 +t2 = 6

  240/r +72/(r+10) = 6

We can simplify this a bit by multiplying by (r)(r+10)/6 to get ...

   40(r+10) +12(r) = r(r+10)

  r² -42r -400 = 0 . . . . . . . . subtract the left side and collect terms

  (r -50)(r +8) = 0 . . . . . . . . factor

  r = 50 . . . . . the positive solution of interest.

The two average speeds were 50 mph and 60 mph.

Answer:

expected profit is  - $0.50

Step-by-step explanation:

1  $(7.00) 0.166666667  $(1.17)

2  $(7.00) 0.166666667  $(1.17)

3  $1.00  0.166666667  $0.17  

4  $1.00  0.166666667  $0.17  

5  $1.00  0.166666667  $0.17  

6  $8.00  0.166666667  $1.33  

   $(0.50)

9514 1404 393

Answer:

  10 minutes

Step-by-step explanation:

The current legal tender conversion rate is 50 kobo = 0.50 naira. Then the airtime balance is ...

  (300 NGN)/(0.50 NGN/s) × (1 min)/(60 s) = 300/(0.50×60) min = 10 min