what is the volume of a cylinder with the base radius of 10 units and a height of nine units?

Which would mean that 540 people died or left the town.

I hope that this helps! :D

Answer:

2a² + 5a - 3 = (2a - 1)(a + 3)

2a² - a - 3 = (2a - 3)(a + 1)

2a² - 5a - 3 = (2a + 1)(a - 3)

2a² + a - 3 = (2a + 3)(a - 1)

Step-by-step explanation:

* To factor a trinomial in the form ax² ± bx ± c:

- Look at the c term

# If the c term is positive

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will have the same sign (sign of b)

∵ a = h × k ⇒ h , k are the factors of a

∴ rk + hs = b

∴ (hx + r)(kx + s) ⇒ if b +ve  OR  (hx - r)(kx - s) ⇒ if b -ve

# If the c term is negative

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will not have the same sign

∵ a = h × k ⇒ h and k are the factors of a

∴ rk - hs = b OR hs - rk = b

(hx + r)(kx - s) OR (hx - r)(kx + s)

* Now lets solve the problem

∵ 2a² + 5a - 3

∴ c = -3 ⇒ -ve term

∴ r , s have different sign

∵ 3 = 1 × 3 then r = 1 , s = 3

∵ a = 2

∵ a = h × k

∵ 2 = 2 × 1 then h = 2 , k = 1

∵ rk = 1

∵ sh = 6

∴ sh - rk = 5 ⇒ same value of b

∵ (hx - r)(kx + s)

∴ 2a² + 5a - 3 = (2a - 1)(a + 3)

∵ 2a² - a - 3

∴ c = -3 ⇒ -ve term

∴ r , s have different sign

∵ 3 = 3 × 1 then r = 3 , s = 1

∵ a = 2

∵ a = h × k

∵ 2 = 2 × 1 then h = 2 , k = 1

∵ rk = 3

∵ sh = 2

∴ sh - rk = -1 ⇒ same value of b

∵ (hx - r)(kx + s)

∴ 2a² - a - 3 = (2a - 3)(a + 1)

∵ 2a² - 5a - 3

∴ c = -3 ⇒ -ve term

∴ r , s have different sign

∵ 3 = 1 × 3 then r = 1 , s = 3

∵ a = 2

∵ a = h × k

∵ 2 = 2 × 1 then h = 2 , k = 1

∵ rk = 1

∵ sh = 6

∴ rk - hs = -5 ⇒ same value of b

∵ (hx + r)(kx - s)

∴ 2a² - 5a - 3 = (2a + 1)(a - 3)

∵ 2a² + a - 3

∴ c = -3 ⇒ -ve term

∴ r , s have different sign

∵ 3 = 3 × 1 then r = 3 , s = 1

∵ a = 2

∵ a = h × k

∵ 2 = 2 × 1 then h = 2 , k = 1

∵ rk = 3

∵ sh = 2

∴ rk - sh = 1 ⇒ same value of b

∵ (hx + r)(kx - s)

∴ 2a² + a - 3 = (2a + 3)(a - 1)

Answer:

43.75 inches or 43 and 3/4 inches.

Step-by-step explanation:

Ok, thanks for the complement of information.

So, to find the volume of that step, which is a rectangular prism, we would use the simple formula:

V = length *  width * height

In this case, we have the total volume (3,500 cu in), we have the width (10 inches)  and we have the height (8 inches).  But we need to find out the new length in order for him to use all 3,500 cu in of cement.

So, we transform the formula above into:

length = V / (width * height)

then we plug-in the numbers:

length = 3,500 / (8 x 10) = 3,500 / 80 = 43.75

So, the new length of the step would be 43.75 inches or 43 and 3/4 inches.

ax - 5 = b

ax = b + 5

a = [tex]\frac{b+5}{x}[/tex]

Answer:

[tex]a=\frac{b+5}{x},x\ne0[/tex]

Step-by-step explanation:

The given equation is:

[tex]ax-5=b[/tex]

We want to solve this equation for a.

We add 5 to both sides of the equation to get:

[tex]ax=b+5[/tex]

We divide both sides by x to get:

[tex]a=\frac{b+5}{x},x\ne0[/tex]

We must restrict the domain because a is not defined for all values of x.

Answer:

Exponential function.

[tex]y = - 6( {3}^{x - 1} ) = - 2( {3}^{x} )[/tex]

As the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.

Answer:

4153. Read the explanation please. There is no point in just reading the answer because the same type of problem can come up in the RSM homework or in a test and you will have no idea how to solve it.

Step-by-step explanation:

Form an equation with the information you know.

1. Moving the last digit, 3, to the first position is the same as doing (x-3)/10 +3000, where x is the original 4-digit number.

    Why it works: This expression works because first, you subtract 3 from the original number. This removes 3 from the last digit, but leaves a zero there. To remove the zero, you divide by 10. Finally, to put the 3 at the first position, you add 3000.

2. Since you know that the number will decrease by 738, you can do the second part of forming the equation. Make the expression equal to x - 738, like so --> (x-3)/10 + 3000 = x - 738

Solve the equation.

3. (x-3)/10 + 3000 = x-73

   (x-3)/10 = x - 3738

   x-3 = 10x - 37380

   x = 10x - 37377

   -9x = -37377

   x = 4153

Well, I've got to get back to my RSM homework. I hope this helped!

P.S.- The next time you have a question, email your RSM teacher (I'm assuming you go to RSM) because he/she is much more qualified then me (I'm only 12) and you don't really know if you can trust people giving you answers on Brainly.com.

Answer:

[tex]y=-1,869.5x+27,995[/tex]

Step-by-step explanation:

Let

x-----> the time in years

y----> value of Zachary’s car in dollars

[tex]A(0,27,995), B(10,9,300)[/tex]

step 1

Calculate the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{9,300-27,995}{10-0}=-1,869.50[/tex]

step 2

Find the equation of the line

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=-1,869.50[/tex]

[tex]b=27,995[/tex]  -----> the y-intercept is the point A

substitute

[tex]y=-1,869.5x+27,995[/tex]

The linear equation to represent the value of Zachary's car after x years since its purchase is y = -1869.5x + 27995.

To write a linear equation to represent the value of Zachary's car after x years since its purchase, we need to determine the slope and y-intercept. The initial value of the car is $27,995, and after 10 years it depreciates to $9,300. The slope (m) can be calculated as (9300 - 27995) / (10 - 0) = -1869.5. The y-intercept (b) is the initial value, which is $27,995. Therefore, the linear equation that represents the value of Zachary's car is y = -1869.5x + 27995.

https://brainly.com/question/32634451

#SPJ3

Answer:

centre = (2, 4)

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 4x - 8y - 5 = 0

Rearrange the x/y terms together and add 5 to both sides

x² - 4x + y² - 8y = 5

Use the method of completing the square on both the x/y terms

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(- 2)x + 4 + y² + 2(- 4)y + 16 = 5 + 4 + 16

(x - 2)² + (y - 4)² = 25 ← in standard form

with centre (2, 4) and r = [tex]\sqrt{25}[/tex] = 5

Answer:

The slope of the line is 77

Explanation:

We know the speed is constant and that the mile-marker location over time can be represented by a line. This means that the equation is linear.

The slope can, therefore, be calculated as follows:

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

where (x₁ , y₁) and (x₂ , y₂) are two points on the line

We are given that the two points (1, 123) and (3, 277) are two points in the line

Substitute with them in the above equation to get the slope as follows:

[tex]slope = \frac{277-123}{3-2}=77[/tex]

Hope this helps :)

The slope of a line represents the rate of change between two variables. The value of the slope in this scenario is 77/2.

The slope of a line represents the rate of change between two variables. In this case, the slope can be calculated using the formula:

slope = (change in y) / (change in x).

Given the points (1,123) and (3,277), the slope can be calculated as follows:

slope = (277 - 123) / (3 - 1).

Therefore, the value of the slope of the line representing the Morales family's mile-marker locations over time is 77/2.

Answer:

2, 6, 12, 20, 30

Step-by-step explanation:

To find the first 5 terms, substitute n = 1, 2, 3, 4, 5 into the rule

a₁ = 1² + 1 = 1 + 1 = 2

a₂ = 2² + 2 = 4 + 2 = 6

a₃ = 3² + 3 = 9 + 3 = 12

a₄ = 4² + 4 = 16 + 4 = 20

a₅ = 5² + 5 = 25 + 5 = 30

Answer: 68%

Step-by-step explanation:

Answer: Hope this helps, and hopefully this is what you needed!

1 7/16 = 23/16

11 5/9 = 104/9

30 5/9 = 275/9

10 10/13 = 140/13

24 3/5 = 123/5

129 1/2 = 259/2

Step-by-step explanation:

Answer:

25 ft

Step-by-step explanation:

a² + b² = c²

7² + 24² = c²

49 + 576 = c²

c² = 625

c = √625

c= 25

Answer:

D. 25 ft.

Step-by-step explanation:

To find the missing length of any right triangle, you can use the Pythagorean Theorem (A^2+B^2=C^2) to solve. A and B represent the legs (which we do have) and C represents the hypotenuse (which we are trying to find). Insert our known values into the theorem, and we will get 24^2+7^2=C^2. Now we just do the basic math for the numbers that we have (24^2 is 576; 7^2 is 49), and that added up would equal to 625. Now, since C is being squared on the other side, we now have to root both sides. On the side where C is, the radical and the square will cancel out each other, leaving us with just C. But, on the side where 625 is, it should root to 25. Since C is by itself now, the number on the other side (25) will be our answer. Therefore, the missing side is 25 feet long.

Answer:

The other two other representation are (6 , -4π/3) and (-6 , -π/3)

Step-by-step explanation:

* Lets revise some important facts about the polar form of a point

- In polar coordinates there is an infinite number of coordinates for a

 given point

- The point (r , θ) can be represented by any of the following coordinate

  pairs (r , θ+2πn) , (-r , θ + [2n+1]π) , where n is any integer

* Now lets solve the problem

∵ A point has polar coordinates (6 , 2π/3)

- We can find many points as the same with this point

- The point (r , θ) can be represented by any of the following coordinate

  pairs(r , θ + 2πn) and (-r , θ + (2n + 1)π), where n is any integer.

∵ The angle in [-2π , 2π]

∵ r = 6 and Ф = 2π/3

- Let n = -1

∴ (r , Ф + 2πn) = (6 , 2π/3 + 2π(-1)) = (6 , 2π/3 - 2π) = (6 , -4π/3)

* One point is (6 , -4π/3)

∴ (-r , θ + (2n + 1)π) = (-6 , 2π/3 + (2(-1) + 1)π) = (-6 , 2π/3 + (-2 + 1)π)

∴ (-r , θ + (2n + 1)π) = (-6 , 2π/3 + (-1)π) = (-6 , 2π/3 - π)

∴ (-r , θ + (2n + 1)π) = (-6 , -π/3)

* One point is (-6 , -π/3)

Final answer:

To find two additional polar representations of a point, you can add or subtract 2π radians (or 360° if using degrees) from the original angle, while keeping the radius the same.

Explanation:

A student has asked for two additional polar representations of a point. Polar coordinates specify the location of a point in a plane by a distance from the origin (r) and an angle (φ) with respect to the positive x-axis. To find additional representations, we can add 2π radians to the angle for each full rotation around the circle, keeping the same distance 'r'. For example, if a point has polar coordinates (r, φ), two other representations could be (r, φ + 2π) and (r, φ - 2π), or if in degrees, (r, φ + 360°) and (r, φ - 360°).

20.00 + 4.00 + 00.50 + 00.08

To write expanded from take each number from left to right and turn all the numbers that are after it into zeros (if there is a decimal then turn the numbers  before it into zeros as well)

2 has 4 numbers after it so it gets 4 zeros: 20.00

4  has 2 numbers after it so it gets 2 zeros: 4.00

5 is a decimal that has two numbers before it and one after, so before the decimal there are two zeros, then after the decimal comes the five, then there is one number after the 5 so one zero after the five.

8 is a decimal that has three numbers before it , so before the decimal there are two zeros, then after the decimal is a number that becomes zero then the 8

Hopefully that made sense to you and was helpful! Let me know!

Step-by-step explanation:

the curves intersect at approcx=0.46

Answer:

Step-by-step explanation:

The given function is

[tex]log(6x+10)=log_{\frac{1}{2} }x[/tex]

If we graph this function, the result is like the image attached. There you can observe that the intersection point is at (0.464, 1.107).

If we round this points to the nearest hundred, they would be

x = 0.46 and y = 1.11.

Therefore, the right answer is

a. the curves intersect at approx. x=0.46

It's the second one because each means one or single and a singular subject has a singular verb...

Answer:

[tex]\large\boxed{a=\dfrac{58}{25},\ b=0}[/tex]

Step-by-step explanation:

[tex]\dfrac{3\sqrt3+\sqrt2}{3\sqrt3-\sqrt2}+\dfrac{3\sqrt3-\sqrt2}{3\sqrt3+\sqrt2}\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\dfrac{(3\sqrt3+\sqrt2)(3\sqrt3+\sqrt2)}{(3\sqrt3-\sqrt2)(3\sqrt3+\sqrt2)}+\dfrac{(3\sqrt3-\sqrt2)(3\sqrt3-\sqrt2)}{(3\sqrt3+\sqrt2)(3\sqrt3-\sqrt2)}\\\\=\dfrac{(3\sqrt3+\sqrt2)^2}{(3\sqrt3)^2-(\sqrt2)^2}+\dfrac{(3\sqrt3-\sqrt2)^2}{(3\sqrt3)^2-(\sqrt2)^2}\qquad\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]=\dfrac{(3\sqrt3)^2+2(3\sqrt3)(\sqrt2)+(\sqrt2)^2}{3^2(\sqrt3)^2-2}+\dfrac{(3\sqrt3)^2-2(3\sqrt3)(\sqrt2)+(\sqrt2)^2}{3^2(\sqrt3)^2-2}\\\\=\dfrac{3^2(\sqrt3)^2+6\sqrt6+2}{9\cdot3-2}+\dfrac{3^2(\sqrt3)^2-6\sqrt6+2}{9\cdot3-2}\\\\=\dfrac{9\cdot3+6\sqrt6+2}{27-2}+\dfrac{9\cdot3-6\sqrt6+2}{27-2}\\\\=\dfrac{27+6\sqrt6+2}{25}+\dfrac{27-6\sqrt6+2}{25}\\\\=\dfrac{29+6\sqrt6}{25}+\dfrac{29-6\sqrt6}{25}\\\\=\dfrac{29+6\sqrt6+29-6\sqrt6}{25}\\\\=\dfrac{58}{25}[/tex]

Answer: 1206.37

Step-by-step explanation:

Multiply the pie times the radius and height

3.14 * 8^2 * 6

Answer:

V =384 pi  units ^3  

or

V =1205.76 units ^3

Step-by-step explanation:

Volume of a cylinder is given by

V = pi r^2 h

where r is the radius and h is the height

V = pi (8)^2 *6

V = pi (64)*6

V =384 pi  units ^3  (exact answer)

or is we used 3.14 for pi

V = (3.14) * 384

V =1205.76 units ^3

Answer:

Mean: 7.1, median: 7, mode: 4

Step-by-step explanation:

The mean, also known as the average, is equal to the sum of all the numbers divided by how many numbers there are.

4 + 8 + 11 + 6 + 4 + 5 + 9 + 10 + 10 + 4 = 71

10 numbers

71/10 = 7.1

The median is the number in the middle of the set.

4, 4, 4, 5, 6, 8, 9, 10 ,10 ,11

6 and 8 are in the middle, and the number between 6 and 8 is 7.

The mode of a set of numbers is the most common number. In this case, the number is 4 as it appears 3 times.

Answer:

the answer is C.5

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

15 divided by 20 = .75 then convert to a percentage is 75%

Answer: The answer to your question is 20

Step-by-step explanation: We know that 3 out of every 5 picks are oranges. And if the next 12 picks are orange, what is the total number of oranges in all?

So first, you would set up a proportion, which would look like this:

3 oranges/ 5 picks = 12 oranges/ x picks

Let the number of picks be known as x, our variable, since we don't know how many oranges are there total.

Next, when you have a proportion that you are trying to solve, the best thing to do is cross multiply, which will look this:

3x = 12(5)

3x = 60

3x/3 = 60/3

x=20 picks

Therefore, the answer is 20 picks

Answer:

Parent function: [tex]x^{5}[/tex]

Step-by-step explanation:

Parent function is the simplest form of the type of function given

for equation: [tex]\frac{2}{5} (-x -5)^{5} +2[/tex]

the simplest form is: [tex]x^{5}[/tex]

Answer:

b = - 3

Step-by-step explanation:

Given

- 11b + 7 = 40 ( subtract 7 from both sides )

- 11b = 33 ( divide both sides by - 11 )

b = - 3

Answer:

-3

Step-by-step explanation:

-11b + 7 = 40

-11b = 40 - 7

-11b = 33

b = 33/-11

b = -1

Happy to help

Pls mark as Brainliest

Answer:

139 and 59, respectively

Step-by-step explanation:

By definition, supplementary means that the angles all add up to equal 180 degrees.  Therefore, 180 - 41 = 139.

By definition, complementary means that the angles all add up to equal 90 degrees.  Therefore, 90 - 31 = 59.

Answer:

Here you go! 8x+10-5x!

Just kidding. here you go. x=1.66

Step-by-step explanation:

you can simplifiy the x´s by making it 3x by subtracting. You can also subract 10 from both sides. That leaves you with 3x=5.

x=1.66

Answer:

[tex]\large\boxed{x=\dfrac{5}{3}=1\dfrac{2}{3}}[/tex]

Step-by-step explanation:

[tex]8x+10-5x=15\qquad\text{subtract 10 from both sides}\\\\8x+10-10-5x=15-10\qquad\text{combine like terms}\\\\3x=5\qquad\text{divide both sides by 3}\\\\x=\dfrac{5}{3}[/tex]

Slope equation: y2-y1/x2-x1

7-9/-12-(-10)

-2/-2 = 1

Answer:

Slope = 1

Step-by-step explanation:

(y2 - y1) ÷ (x2 - x1) = (7 - 9) ÷ (-12 - [-10]) = -2 ÷ (-2) = 1

ANSWER

[tex]{f}^{ - 1} (x) = 7x - 2[/tex]

EXPLANATION

The given function is:

[tex]f(x) = \frac{x + 2}{7} [/tex]

Let

[tex]y = \frac{x + 2}{7} [/tex]

Interchange x and y.

[tex]x= \frac{y + 2}{7} [/tex]

Solve for y by first multiplying through by 7.

[tex]7x = y + 2[/tex]

Add -2 to both sides of the equation.

[tex]7x - 2 = y[/tex]

Or

[tex]y = 7x - 2[/tex]

Hence the inverse function is:

[tex]{f}^{ - 1} (x) = 7x - 2[/tex]

Answer:

p(x) = 7x - 2

The answer is g(x)=(x-6)(2x-1).hope this helps please add brainlist

Answer:

[tex]\boxed{g(x) = (x - 6)(2x - 1)}[/tex]

Step-by-step explanation:

An x-intercept is the value of x when g(x) = 0. So, for each function, we must set g(x) = 0 and solve for x.

(a) g(x) = 2(x + 1)(x +  6) = 0

x + 1 = 0     x + 6 = 0

    x = -1           x = -6

Wrong.

(b) g(x) = (x - 6)(2x - 1)

x - 6 = 0     2x – 1 = 0

    x = 6            2x = 1

                          x = ½

Right.

(c) g(x) = 2(x - 2)(x - 6)

x - 2 = 0     x - 6 = 0

    x = 2           x = 6

Wrong.

(d) g(x) = (x + 6)(x + 2)

x + 6 = 0     x +2 = 0

    x = -6          x = -2

Wrong.

The only function that has x-intercepts at (½, 0) and (6, 0) is

[tex]\boxed{g(x) = (x - 6)(2x - 1)}[/tex]