n
The graph of which function has a minimum located at (4, -3)?
O f(x) = - 5x2 + 4x - 11
f(x) = -2x? + 16x -35
O f(x) = 4x2 - 4x + 5
O f(x) = 2x2 - 16x + 35

Answers

Answer 1

9514 1404 393

Answer:

  (d)   f(x) = 2x^2 - 16x + 35

Step-by-step explanation:

The x-coordinate of the extreme will be found at ...

  x = -b/(2a)

where the function is f(x) = ax²+bx+c.

The extreme will be a minimum when a > 0. (eliminates choices A and B)

The x-coordinates of the extremes are ...

  C: -(-4)/(2(4)) = 1/2

  D: -(-16)/(2(2)) = 4 . . . . . matches the requirement

The appropriate choice is ...

  f(x) = 2x^2 - 16x + 35


Related Questions

1. Consider a lottery with three possible outcomes:-$125 will be received with probability 0.2-$100 will be received with probability 0.3-$50 will be received with probability 0.5a. What is the expected value of the lottery

Answers

Answer:

The expected value of the lottery is $80

Step-by-step explanation:

To get the expected value, we have to multiply each outcome by its probability

Then we proceed to add up all of these to get the expected value of the lottery

we have this as ;;

125(0.2) + 100(0.3) + 50(0.5)

= 25 + 30 + 25 = $80

what are the zeros of this function?

Answers

Answer:

the Ans is c

Step-by-step explanation:

actually I don't know how to explain

Evaluate z^2−3 z+4 , when z=−4

Answers

Answer:

8

Step-by-step explanation:

=z²-3z+4 when z is 4

=4²-3(4)+4

=16-12+4

=8

It should be -19

I got the answer by plugging it into Desmos scientific calculator.

Help please guys thanks

Answers

Answer:

5

Step-by-step explanation:

(625 ^2)^(1/8)

Rewriting 625 as 5^4

(5^4 ^2)^(1/8)

We know that a^b^c = a^(b*c)

5^(4*2)^1/8

5^8 ^1/8

5^(8*1/8)

5^1

5

Answer:

[tex]5[/tex]

Step-by-step explanation:

[tex] { {(625}^{2} )}^{ \frac{1}{8} } \\ { ({25}^{2 \times 2} )}^{ \frac{1}{8} } \\ {25}^{4 \times \frac{1}{8} } \\ {5}^{2 \times 4 \times \frac{1}{8} } \\ {5}^{ \frac{8}{8} } \\ {5}^{1} \\ = 5[/tex]

Find the missing length indicated

Answers

Answer:

x = 175

Step-by-step explanation:

What is the degree of the monomial 4x7y3

Answers

Answer:

degree 10

Step-by-step explanation:

The degree of the monomial is the sum of the exponents of the variables, so

4[tex]x^{7}[/tex]y³ ← is of degree 10 ( 7 + 3)

If all possible random samples of size N are drawn from a population with a mean of mu and a standard deviation of sigma, then as N becomes larger, the sampling distribution of sample means becomes approximately normal with a mean of muy(bar) and a standard deviation of sigmay(bar). This statement is known as the:

Answers

Answer:

"Central limit theorem" is the right answer.

Step-by-step explanation:

A hypothesis essentially claims that whenever there seems to be a small variance throughout the big confidence intervals, the sampling is based on averages as well as the sampling distribution (mean) usually nearly the same as the public's median.

When,

Mean = [tex]\mu_y[/tex]Standard deviation = [tex]\sigma_y[/tex]Sample size = N

is sufficiently larger than [tex]\bar Y \sim N(\mu_y, \sigma_y)[/tex]

Thus, the above is the right answer.

If 800g of a radioactive substance are present initially and 8 years later only 450g remain, how much of the substance will be present after 16 years? (Round answer to a whole number)

Answers

A=Pe^(rt)

P = 800g

t = 8 years

A = 450g

r = This is what we will try and find to start with

450=800e^(r*8)

After running the math through a calculator, we end with r = -0.07192

Now we just re-input this information into our equation: A=800e^(-0.07192*16)

A=800e^(1.15072)

Now we will re-write the equation using the negative exponent rule:

A = 800 1/e^1.15072

Combine right side:

A = 800/e^1.15072

Then do the math:

A = 253.12709836......

That will give us A = 253 (rounded to the whole number)

I hope this helps! :)

The substance that should be presented after 16 years is 253.

Given that,

If 800g of a radioactive substance are present initially and 8 years later only 450g remain.

Based on the above information, the calculation is as follows:

We know that

[tex]A=Pe^{rt}[/tex]

Here

P = 800g

t = 8 years

A = 450g

[tex]450=800e^{r\times 8}\\\\A=800e^{-0.07192\times 16}\\\\A=800e^{1.15072}\\\\A = 800 \ 1 \div e^{1.15072}\\\\A = 800\div e^{1.15072}[/tex]

A = 253

Therefore we can conclude that the substance that should be presented after 16 years is 253.

Learn more: brainly.com/question/16115373

Jean threw a disc in the air. The height of the disc can be modelled by the function
h = -5t^2 + 31.5t + 2, where h is the height in metres after t seconds.
Patrick fired a paintball at the disc. The path of the paintball is modelled by the function h = 30t + 1, with the same units. How long will it take the paint ball to hit the disc?

Answers

Answer:

It will take 0.62 seconds for the paint ball to hit the disc.

Step-by-step explanation:

Height of the disk:

[tex]H_d = -5t^2 + 31.5t + 2[/tex]

Height of the paintball:

[tex]H_p = 30t + 1[/tex]

When the paintball will hit the disk?

When they are at the same height, so:

[tex]H_d = H_p[/tex]

[tex]-5t^2 + 31.5t + 2 = 30t + 1[/tex]

[tex]5t^2 - 1.5t - 1 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

Quadratic equation with [tex]a = 5, b = -1.5, c = -1[/tex]

So

[tex]\Delta = (-1.5)^2 - 4(5)(-1) = 22.25[/tex]

[tex]t_{1} = \frac{-(-1.5) + \sqrt{22.25}}{2(5)} = 0.62[/tex]

[tex]t_{2} = \frac{-(-1.5) - \sqrt{22.25}}{2(5)} = -0.32[/tex]

Time is a positive measure, so 0.62.

It will take 0.62 seconds for the paint ball to hit the disc.

Rate of change or rate of change

A farmer has 80 feet of wire mesh to surround a rectangular pen.
A) Express the area A of the pen as a function of x, also draw the figure of A indicating the admissible values ​​of x for this problem.
B) What are the dimensions of the maximum area pen?

Answers

Answer:

Step-by-step explanation:

A). Let the dimensions of the rectangular pen are,

Length = l

Width = x

Since, farmer has the wire measuring 80 feet to surround the the pen.

Perimeter of the pen = 80 feet

2(l + x) = 80

l + x = 40

l = 40 - x ------(1)

Area of the rectangular pen = Length × width

                                               = lx

By substituting the value of l from equation (1),

Area (A) of the pen will be modeled by the expression,

A = (40 - x)

A = 40x - x²

B). For maximum area of the pen,

Derivative of the area = 0

[tex]\frac{d}{dx}(A)=0[/tex]

[tex]\frac{d}{dx}(A)=\frac{d}{dx}(40x-x^2)[/tex]

         = 40 - 2x

And (40 - 2x) = 0

x = 20

Therefore, width of the pen = 20 feet

And length of the pen = 40 - 20

                                     = 20 feet

Dimensions of the pen should be 20 feet by 20 feet.

A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.

Answers

Answer:

48, 6

Step-by-step explanation:

The ratio of the pieces is 6 to 1

Add them together to get the total

6+1 = 7

Divide the total length by 7

56/7 = 8

Multiply the ratios by 8

6*8 = 48

 1*8 = 6

The peices are 48 and 6


15. Find the x- and y-intercepts for the lineal equation - 3x + 4y = 24

Please explain steps! ❤️

Answers

Answer:

x (-8,0)

y (0,6)

Step-by-step explanation:

at the x-intercept, y = 0

at the y-intercept x=0

sub those values into your equation!

for the x-intercept,

-3x = 24

x = -8

for the y-intercept,

4y = 24

y = 6

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean

Answers

Answer:

expected value is the mean : 10.5

Standard error for the sampling distribution : 0.375

it has a bell-shaped curve  with 99.7%  of the values between  9.375  and 11.625

Step-by-step explanation:

The answer would be to 10.5

Game consoles: A poll surveyed 341 video gamers, and 95 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that the proportion of gamers who prefer consoles differs from . Does the poll provide convincing evidence that the claim is true

Answers

Answer:

proportion of gamers who prefer console does not differ from 29%

Step-by-step explanation:

Given :

n = 341 ; x = 95 ; Phat = x / n = 95/341 = 0.279

H0 : p = 0.29

H1 : p ≠ 0.29

The test statistic :

T = (phat - p) ÷ √[(p(1 - p)) / n]

T = (0.279 - 0.29) ÷ √[(0.29(1 - 0.29)) / 341]

T = (-0.011) ÷ √[(0.29 * 0.71) / 341]

T = -0.011 ÷ 0.0245725

T = - 0.4476532

Using the Pvalue calculator from test statistic score :

df = 341 - 1 = 340

Pvalue(-0.447, 340) ; two tailed = 0.654

At α = 0.01

Pvalue > α ; We fail to reject the null and conclude that there is no significant evidence that proportion of gamers who prefer console differs from 29%

If f(x) = negative 3X -2, what if f(-5)?

Answers

Answer:

f(- 5) = 13

Step-by-step explanation:

Substitute x = - 5 into f(x)

f(x) = - 3x - 2 , then

f(- 5) = - 3(- 5) - 2 = 15 - 2 = 13

Approximately 5% of calculators coming out of the production lines have a defect. Fifty calculators are randomly selected from the production line and tested for defects. What is the probability that exactly 2 calculators are defective?

Answers

Answer:

0.2611 = 26.11% probability that exactly 2 calculators are defective.

Step-by-step explanation:

For each calculator, there are only two possible outcomes. Either it is defective, or it is not. The probability of a calculator being defective is independent of any other calculator, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

5% of calculators coming out of the production lines have a defect.

This means that [tex]p = 0.05[/tex]

Fifty calculators are randomly selected from the production line and tested for defects.

This means that [tex]n = 50[/tex]

What is the probability that exactly 2 calculators are defective?

This is P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{50,2}.(0.05)^{2}.(0.95)^{48} = 0.2611[/tex]

0.2611 = 26.11% probability that exactly 2 calculators are defective.

what is the value of tan 0 in the unit circle below

Answers

Tangent = opposite / adjacent, or in this case Tangent = y / x.

Tan = (1/2) / ([tex]\sqrt{3}[/tex] / 2)

1 / [tex]\sqrt{3}[/tex]

[tex]\sqrt{3}[/tex] / 3

Hope this helps!

The following data represents the age of 30 lottery winners.

22 30 30 35 36 37 37
37 39 39 41 51 51 54
54 55 57 57 58 58 61
64 68 69 72 74 75 78 79 80

Complete the frequency distribution for the data.

Age Frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89

Answers

Door key nhfsssrtgfrtgbkoooo your name and number of your name on the card number for you and the name is your
Ages. ==> Frequencies
20-29 ==> 1
30-39 ==> 9
40-49 ==> 1
50-59 ==> 9
60-69 ==> 4
70-79 ==> 5
80-89 ==> 1
(Total 30)

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height 5h. Use cylindrical shells to compute the volume V of a napkin ring of height 5 h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h .

Answers

Answer:

V = 1/6 π ( 5h)^3

Step-by-step explanation:

Height of napkin rings = 5h

Compute the volume V of a napkin ring

let a = 5

radius = r

express answer in terms of h

attached below is the detailed solution

cho f(x)= sign x và g(x) = x(1-x^2). tìm f(g(x))

Answers

Answer:

[tex]f(g(x))= sign(x(1-x^{2})) = sign(x-x^{3})[/tex]

Step-by-step explanation:

what 30 + 30+60+(56)-82=?

Answers

94 is the correct answer for that question

Step-by-step explanation:

30+30+60+56-82=94

The graph shows the functior f(x) = 2X
What is the value of x when f(x) = 8?

Answers

Answer: b

Step-by-step explanation:

What’s the equation?

Answers

Answer:

The answer is D.

Step-by-step explanation:

what’s the missing side of the polygons

Answers

Answer:

the missing side is 21!!!!!!!!

i got 21 but i may be wrong :)

Please help on this initial amount problem

Answers

Initial amount: 27,500
Growth
Value of car change 28% each year

find x in this similar triangles

Answers

Answer:

6. x = 4

8. x = 13

Step-by-step explanation:

Using similar triangles theorem,

6. (5+4)/5 = (4x + 2)/(4x + 2 - 8)

9/5 = (4x + 2)/(4x - 6)

Cross multiply

9(4x - 6) = 5(4x + 2)

36x - 54 = 20x + 10

Collect like terms

36x - 20x = 54 + 10

16x = 64

16x/16 = 64/16

x = 4

8. (4x + 13)/20 = 52/16

(4x + 13)/20 = 13/4

Cross multiply

4(4x + 13) = 13(20)

16x + 52 = 260

16x = 260 - 52

16x = 208

x = 208/16

x = 13

If the recipe takes 60 minutes to cook at a temperature of 350 degrees, how many minutes would it take at 200degrees

Answers

Answer:

The temperature has to be inversely proportional to the time therefore the solution will be:

60minutes/200degrees=x/350degrees

200x/200=21000/200

x=105minutes

I hope this helps

Answer:

105 minutes.

Step-by-step explanation:

As 200 degrees is less than 350 it will take longer at 200.

By proportion that would be (350/200) * 60

= 60 * 7/4

= 105 minutes.

PLEASE HELP I REALLY NEED THIS

How is an inequality different from an equation?
What are four ways inequality can be written?
What would the graph of each inequality look like on a number line? (use an example)
What would the graph of an equation look like on a number line(use an example)


Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and a balance scale.

Explain the Golden Rule for solving equations
using an example.


What does it mean if a situation has a condition or constraint? Give an example.


Give an example of a situation that contains an independent and dependent variable. Explain if your data is continuous or discrete.

Answers

Answer:

inequality is mostly represented on a number line but equation is not.

Help please!! Based on Pythagorean identities, which equation is true ??

Answers

Answer:

Last answer: [tex]cot^{2} \alpha - csc^{2} \alpha = -1[/tex]

sorry couldn't find theata so I just used alpha.

When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?

Answers

Answer:

55000×100/90

61,111.111

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