Find domain and range of
f(x) = -x2 - 4x + 2

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 1330.4644 cm³.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

Given the height of the cylinder is 14 cm, while the diameter of the cylinder is 11 cm. Therefore, the volume of the cylinder can be written as,

The volume of the cylinder = (π/4)×(D²) × H

                                               = (π/4)×(11)² × 14

                                               = 1330.5 cm³

Hence, the volume of the cylinder is 1330.5cm³.

Learn more about Cylinder:

https://brainly.com/question/12248187

#SPJ1

The difference in the given functions is 2x^3 + 6x^2 -8x + 1

Given the following function a shown

f(x)= 2x^3 + 6x^2 -5x - 3

g(x)= 3x-4

Take the difference

(f-g)(x) = f(x) - g(x)

Substitute

(f-g)(x)  = 2x^3 + 6x^2 -5x - 3 - (3x - 4)

Expand

(f-g)(x)  = 2x^3 + 6x^2 -5x - 3 - 3x + 4

(f-g)(x) = 2x^3 + 6x^2 -8x + 1

Hence the difference in the given functions is 2x^3 + 6x^2 -8x + 1

Learn more on polynomials here: https://brainly.com/question/2833285

#SPJ1

Answer:

55

Step-by-step explanation:

1+1 = 2

1+2 = 3

2+3 = 5

3+5 = 8

5+8 = 13

8+13 = 21

13+21 = 34

21 +34 = 55

PLEASE GIVE BRAINLIEST

Let x be multiple-choice questions
Let y be short-answer questions

x + y = 28

3x + 5y = 100

The quotient [tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex] is [tex]x^3 + 2x - 3[/tex]

The quotient can be represented as:

[tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex]

Start by expanding the dividend

[tex]x^5 + 2x^3 - 5x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex]

Rewrite as:

[tex]x^5 + 2x^3 - 3x^2 - 5x^3 - 10x + 15 \div x^2 - 5[/tex]

Factorize the dividend

[tex]x^2(x^3 + 2x - 3) - 5(x^3 + 2x - 3) \div x^2 - 5[/tex]

Factor out x^3 + 2x - 3

[tex](x^2- 5)(x^3 + 2x - 3) \div x^2 - 5[/tex]

Cancel out the common factor

[tex]x^3 + 2x - 3[/tex]

Hence, the quotient [tex]x^5 - 3x^3 - 3x^2 - 10x + 15 \div x^2 - 5[/tex] is [tex]x^3 + 2x - 3[/tex]

Read more about polynomials at:

https://brainly.com/question/1498111

#SPJ1

Answer: x3 + 2x – 3

Step-by-step explanation:

The x intercept of the linear equation is -4 and y intercept is 8.

The intercept of the linear equation is calculated as follows;

x - y/2 = -4

make y the subject of the formula;

y/2 = x + 4

y = 2x + 8

y = 0 + 8

y = 8

0 = 2x + 8

2x = -8

x = -4

Thus, the x intercept of the linear equation is -4 and y intercept is 8.

Learn more about x and y intercept here: https://brainly.com/question/24363347

#SPJ1

Answer:

The x intercept of the linear equation is -4 and y intercept is 8

Step-by-step explanation:

(a) X ≈ N (0.10 , 0.02²)

(b) The probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.

(c) The 60th percentile is 11%.

A. X ~ N( , )  

B. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11%.

C. Find the 60th percentile for this distribution.

According to the question,

The random variable X is defined as the THC content for a bag of marijuana that is sold on the street.

(a)The random variable X is Normally distributed with mean, μ = 0.10 and standard deviation, σ = 0.02.

Therefore, X ≈ N (0.10 , 0.02²)

(b) The value of P (X > 0.11) as follows:

P (X > o.11_ = P(X -μ/a > [tex]\frac{0.11-0.10}{0.02} \\[/tex])

= P(Z > 0.50)

= 1 -P (Z <0.50)

= 1- 0.69146

= 0.30854 ≈ 0.31

Hence,

the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.

(c)Let x represent the 60th percentile value.

Then, P (X < x) = 0.60.

⇒ P (Z < z) = 0.60

The value of z is,

z = 0.26.

Now put the value of x as follows:

z = x - μσ

0.26 = x - 0.100.02

x = 0.10+ ( 0.26 x 0.02)

x = 0.1052

x ≈ 0.11

Therefore,

The 60th percentile is 11%

Learn more about Probability here:

https://brainly.com/question/23345093

#SPJ1

The solution will be x= -10

Simplifying the given expression

[tex]1.8(1.1x - 1.3) - 1.88 = - 24.02[/tex]

Step1: Convert decimal to fraction

[tex]1.8( \frac{11x}{10} - 1.3) - 1.88 = - 24.02[/tex]

[tex]1.8( \frac{11x}{10} - \frac{13}{10} ) - 1.88 = - 24.02[/tex]

[tex]\frac{18}{10} ( \frac{11x}{10} - \frac{13}{10} ) - 1.88 = - 24.02[/tex]

Step2: Make denominator common

[tex]\frac{18}{10} ( \frac{11x - 13}{10}) - 1.88 = - 24.02[/tex]

Step3: Simplifying the fraction

[tex]\frac{9}{5} ( \frac{11x - 13}{10}) - 1.88 = - 24.02[/tex]

Step4: Make denominator common

[tex] \frac{9(11x - 13)}{5 \times 10} - \frac{1.88 \times 50}{50} = - 24.02[/tex]

[tex] \frac{9(11x - 13)}{50} - \frac{94}{50} = - 24.02[/tex]

[tex] \frac{9(11x - 13 - 94)}{50} = - 24.02[/tex]

[tex] \frac{99x - 117 - 94}{50} = - 24.02[/tex]

Step5: Simplifying

[tex] \frac{99x - 211}{50} = - 24.02[/tex]

[tex] 99x - 211 = - 24.02 \times 50[/tex]

[tex] 99x - 211 = - 1201[/tex]

[tex] 99x = - 1201 + 211[/tex]

[tex] 99x = - 990[/tex]

[tex] x = \frac{ - 990}{99} [/tex]

[tex]x = - 10[/tex]

Hence, the solution x=-10

Learn more about simplification here:

https://brainly.in/question/49393260

#SPJ10

Answer

T-axis of his graph should go from 0 to at least 720, and the h-axis of his graph should go from 0 to at least 40.

Explanation

We know form our problem that  is the total pay,  is the number of hours, and $18 is the rate per hour, so putting it all into an equation we get:

We also know that James works between 25 and 40 hours each week, so we can replace the number of hours in our equation to get how much he can make per week:

- For

- For

Now we know that he can make between $450 and $720 working between 25 and 40 hours per week. So, to best show this information the T-axis should go from 0 to at least 720; otherwise, we won't be able to show values between $450 and $720. Similarly, the h-axis should go form 0 to at least 40; otherwise, we wont be able to show values between 25 and 40 hours.

The mean and standard deviation of the x sampling distribution for each of the following sample sizes will be [tex]N(100,10/\sqrt{41} ), N(100,10/\sqrt{130} )[/tex].

Suppose X has a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma,[/tex]then,

the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with a mean equal to the mean of X, and a standard deviation equal to [tex]\sigma/\sqrt{n}[/tex]

Symbolically, we write it as:

[tex]X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )[/tex]

A random sample is selected from a population with a mean = of 100 and a standard deviation = of 10.

The mean and standard deviation of the x sampling distribution for each of the following sample sizes.

If N=41

[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{41} )[/tex]

If N=130

[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{130} )[/tex]

Learn more about standard normal distribution here:

https://brainly.com/question/10984889

#SPJ1

Answer:

(-5, -6)

Step-by-step explanation:

The smaller integer is x.

The larger integer is x + 1.

x + 1 = 7 + 2x

-x = 6

x = -6

x + 1 = -6 + 1 = -5

Answer: (-5, -6)

The quadratic equation in standard form is:

[tex]y = 2x^2 - 8x + 6[/tex]

Here we have the quadratic equation:

[tex]y = 2*(x - 2)^2 - 2[/tex]

Here we need to expand the right side, remember:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

Using that, we get:

[tex]y = 2*(x - 2)^2 - 2 = 2*(x^2 - 4x + 4) - 2\\\\y = 2x^2 - 8x + 8 - 2\\\\y = 2x^2 - 8x + 6[/tex]

This is the quadratic equation in standard form.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

The answer to the question on Parallelograms being rectangles is that; No; the diagonals may not be congruent

1) We cannot conclude that the parallelogram is a rectangle but we can say that all rectangles are parallelograms.

2) The explanation for number 1 above is that the parallelogram's diagonals may not be equal or congruent but in rectangles diagonals are always equal and bisect each other.

Read more about Parallelogram Properties at; https://brainly.com/question/970600

#SPJ1

a) When x = -2, g(x) = 5.

b) When x = -4, g(x) = 7.

c) When g(x) = 6, x = -3

d) When g(x) = -1, x = 4

Answer:

it is 2 spaces away. a positive number from zero would be +2 and a negative number would be -2

Step-by-step explanation:

Answer:

740

Step-by-step explanation:

$415-$230=$185

$185×0.25=740 max miles

Answer:

The correct option is;

B. Rolling a die; 1 or 2 represents door A, 3 or 4 represents door B, and 5 or 6 represents door C

Answer: [tex]5\frac{1}{4}[/tex] gallons are left

Step-by-step explanation:

convert to mixed number...

[tex]8\frac{3}{4} = \frac{35}{4}[/tex]

[tex]3 \frac{1}{2} = \frac{7}{2}[/tex] or [tex]\frac{14}{4}[/tex]

[tex]\frac{35}{4} -\frac{14}{4}=\frac{21}{4}[/tex]

[tex]\frac{21}{4} =5\frac{1}{4}[/tex]

therefore, [tex]5\frac{1}{4}[/tex] gallons are left in Ms. Mather's fuel tank

Answer:

5 1/4 gallons are left... correct

C and A

X = at least 45 and more

This means we need to have a full closed dot.

It's A because the question says more than 75 ft meaning only open dots.

Answer:

The very last one is a function

Step-by-step explanation:

The last one is a function because there are no y values that repeat. For example, If the points on one graph are like this; (1, 3) (2, 3); then it cannot be a function, the y values cannot repeat if it is a function.

To make things easier, just try to imagine vertical drawing lines through each point in every graph, if this imaginary vertical line passes more than one point in any graph, then that graph is not a function.

I hope this helps!! :D

Answer:

The last graph represents a function.

Explanation:

A function cannot be one-to-many, i.e., one value of x cannot produce multiple values of y.

In the first graph, when x = 1, y = 3 and y= -2, so it is not a function.

In the second graph, when x = 2, y = 2 and y = -2, so it's not a function.

In the third graph, when x = -3, y = 2 and y = -2, so it's not a function.

∴ In all the graphs except the last, single values of x give multiple values of y on the graph, so they are not functions.

Answer:

3.5 km

Step-by-step explanation:

The answer to this question is (A) left.

Jessica sells = 240 books,

Josh sells = 16 books.

The price of one book is = $15

Jessica sold 15 times more books than Josh.

In total, they have sold 256 books.

We can easily find the answer using variables.

Let,

Josh sold a total of x books whereas Jessica sold a total number of 15x books.

together they sold 16x books.

So we can form the equation

16x= 256

by solving this equation we will get x=16

So, Josh sold 16 books and Jessica sold 16×15=240 books in total.

Answer:

Jessica=240

Josh=15

Step-by-step explanation:

The result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.

Here, given fraction

 [tex]\frac{9}{\sqrt{x+3} }[/tex]

Multiply and divide by [tex]\sqrt{x+3}[/tex], we get

[tex]\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }[/tex]  =  [tex]\frac{9\sqrt{x+3} }{x+3}[/tex]

Thus, the result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

Learn more about Rationalization from:

https://brainly.com/question/15837135

#SPJ1

Answer:

First Image:         Option D

Second Image:   Option D

Third Image:       Option C

Fourth Image:     Option B

Fifth Image:         Option B

Step-by-step explanation:

First Image:

Second Image:

Third Image:

Fourth Image:

Fifth Image:

Learn more about Triangles here: https://brainly.com/question/4186813

The formula for the area of the shaded region in the figure.

x² = 4py is mathematically given as

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

Parameters

[tex]$x^{2}=4 p y$[/tex]

[tex]$y=h$[/tex]

[tex]\therefore x^{2}=4 p h \Rightarrow x=2 \sqrt{p h} \\[/tex]

Generally, the equation for the Area is mathematically given as

[tex]& A=2 \int_{0}^{2 \sqrt{p h}}\left(h-\frac{x^{2}}{4 p}\right) d x \\\\& A=2\left(h x-\frac{x^{3}}{12 p}\right]_{0}^{2 \sqrt{p h}} \\\\& A=2\left[\left[h 2 \sqrt{p h}-\frac{1}{12 p} \cdot(2 \sqrt{p h})^{3}-0\right]\right. \\[/tex]

[tex]&A=2\left[2 h^{3 / 2} \sqrt{p}-\frac{8(\sqrt{p})^{3}(\sqrt{h})^{3}}{12 p}-0\right] \\\\&A=2\left[2 h^{k / 2} \sqrt{p}-\frac{2}{3} \sqrt{p} \cdot h^{3 / 2}\right] \\\\&A=2 \times \frac{4 \sqrt{p} \cdot h^{3 / 2}}{3} \\\\&A=\frac{8}{3} \cdot \sqrt{p} \cdot \sqrt{h} \cdot h \\\\&A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

In conclusion,  the equation for the Area is

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

Read more about Area

https://brainly.com/question/27683633

#SPJ1

Answer:

14.30

Step-by-step explanation:

6.50/5=1.3

so one ice cream is 1.30 pounds

1.30X11=14.3

so 11 ice creams is 14.30 pounds

Step-by-step explanation:

10 that's what my teacher told me

There is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.  

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

There is a 50% chance of rain here and a 25% chance of rain on Mars. Therefore, there is a 75% chance that it will rain here or on Mars.

The probability that it will rain here:

P(rain here) = 50%

P(rain on mars) 50%

P(not rain here) = 100 - 50 = 50%

P(not rain on mars) = 100 - 50 = 50%

P(rain here and not on mars) = 0.5×0.5 = 0.25 or 25%

Thus, there is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.  

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

Answer:

4 inches

Step-by-step explanation:

In a regular pentagon, all sides are equal in length