What is an equation of the line, in POINT-SLOPE FORM, that passes through the given point and has the given slope?

point: (5,6); slope: 2/5

A. y-6=2/5(x-5)
B. y+6=2/5(x-5)
C. y-5=2/5(x-6)
D. y-5=2/5(x-6)​

Answer:

1. f= 7 1/2

2. f= 9/10

3. f= -2 1/2

Answer:

Step-by-step explanation:

its C

Answer:

(12m+10)(2m-2)

hope this helps

Step-by-step explanation:

I don't have a calculator with me right now but I can give you the equation to work out your answer.

cos-1(35/38)

There should be a function of "cos-1" on you're calculator, not just "cos"

hope it helps :)

To calculate the total amount of liquid in all the containers, we need to add up the volumes of liquid in each container.

Since three 1-liter containers are filled, each containing 1000 milliliters, the total volume from these containers is 3 liters or 3000 milliliters.

The fourth container has 200 milliliters of liquid, and the fifth container has 800 milliliters. Adding these volumes, we get 200 milliliters + 800 milliliters = 1000 milliliters.

To find the total amount of liquid in all the containers, we add the volume from the three 1-liter containers (3000 milliliters) to the volume from the fourth and fifth containers (1000 milliliters). Thus, the total amount of liquid in the containers is 3000 milliliters + 1000 milliliters = 4000 milliliters.

Therefore, the combined volume of liquid in all the containers is 4000 milliliters.

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Answer:

x^2+y^2-32x+24y+375=0

Step-by-step explanation:

Equation of circle with given centre (h,k) and radius=r is

(x-h)^2+(y-k)^2=r^2

Given centre are=(16, - 12) and radius= 5

So equation of circle=

(x-16)^2+(y- -12)^2=5^2

x^2-32x+256+y^2+24y+144=25

x^2+y^2-32x+24y+375=0

Answer

Answer:

5.24m

Step-by-step explanation:

volume of a cone = (1/3)πr²h

= (1/3)×(22/7)×1²×5

= 5.24m

The area of the surface generated by rotating the parametric curve about the x-axis is π/8.

To find the area of the surface generated by rotating the parametric curve about the x-axis, we can use the formula for the surface area of revolution:

\(A = \int\limits^a_b {2\pi y} \sqrt{(\frac{dx}{d\theta})^2+ (\frac{dy}{d\theta})^2} \, dx\)

In this case, the given parametric equations are:

\(x = cos^3\theta\\\\y = sin^3\theta\)

Let's calculate the derivatives of x and y with respect to θ:

\(\frac{dx}{d\theta} = -3cos^2\theta sin\theta\\\\\frac{dy}{d\theta} = 3sin^2\theta cos\theta\\\)

Now we can substitute these values into the surface area formula:

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{(-3cos^2\theta sin\theta)^2+ (3sin^2\theta cos\theta)^2} \, d\theta\)

Simplifying the expression inside the square root:

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^4\theta sin^2\theta+ 9sin^4\theta cos^2\theta} \, d\theta\)

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^2\theta sin^2\theta(cos^2\theta +sin^2\theta)} \, d\theta\)

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^2\theta sin^2\theta} \, d\theta\)

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \quad 3cos^2\theta sin^2\theta \, d\theta\)

\(A = 6\pi \int_{0}^{\pi /2} {sin^4\theta} \quad cos^2\theta d\theta\)

Now, we can use a trigonometric identity to simplify the integral. The identity is:

\(Sin^2\theta = \frac{1-cos2\theta}{2}\)

Using this identity, we can rewrite the integral as:

\(A = 6\pi \int_{0}^{\pi /2} {(\frac{1-cos2\theta}{2})^2 } \quad cos^2\theta d\theta\)

Simplifying further:

\(A = 6\pi \int_{0}^{\pi /2} {(\frac{1+cos^22\theta-2cos2\theta}{4}) } \quad cos^2\theta d\theta\)

\(A = 3\pi /2\int_{0}^{\pi /2} {cos\theta-2cos2\theta cos\theta+\frac{1}{4} cos^3\theta} d\theta\)

Evaluating the limits of integration:

\(A = 3\pi /2[\frac{1}{2} sin\theta-\frac{1}{3} cos^3\theta+\frac{1}{12} cos^32\theta]^{\pi /2}_0\)

Evaluating =

A = π/8

Therefore, the area of the surface generated by rotating the parametric curve about the x-axis is π/8.

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The statement that , "The set Span{u,v} is always visualized as a plane through the origin" is False because if vectors are scalar multiples of each other, then set Span{u,v} is a line through origin .

The set Span{u,v} is defined as the set of all linear combinations of vectors "u" and "v" . This set can be visualized as a plane in three-dimensional space if the vectors are not scalar multiples of each other.

The plane may not necessarily pass through the origin, unless one of the vectors is the zero vector .

If the vectors are scalar multiples of each other, then the set Span{u,v} is a line through the origin, and if one of the vectors is the zero vector, then the set Span{u,v} is a plane through the origin.

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The nurse should run the pump at 111.1 ml/hr.

To infuse a 1000ml bag of lactated ringers over 9 hours, the nurse must determine the hourly rate at which the fluid should be infused. This can be done by dividing the total volume of the fluid (1000 ml) by the number of hours it will take to infuse it (9 hours).

So, the hourly rate would be:

1000 ml ÷ 9 hours = 111.1 ml/hr.

Therefore, the nurse should run the pump at 111.1 ml/hr in order to infuse the 1000ml bag of lactated ringers over 9 hours.

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Answer:

there were rivalries between African leaders.

Step-by-step explanation:

Answer:

X+14=y

Step-by-step explanation:

Considering the density curve, the percent of the area under the

density curve where x is less than 2 is 375.5%

The total area under the curve is by the formula of a trapezoid

= 1/2 (sum of parallel lines) * height

= 1/2 * (0.25 + 0.75) * 2

= 0.5 * 1 * 2

= 1

Area of the curve where x < 2

= 1/2 (sum of parallel lines) * height

= 1/2 * (0.25 + 0.5) * 1

= 0.5 * 0.75 * 1

= 0.375

the percent area

= area of area where x is less than 2

= 0.375 / 1 * 100

= 37.5%

the percent area is 37.5

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Answer:

4^8.

Step-by-step explanation:

4^6 ÷ 4^-2     when dividing we subtract exponents , so we have:

4^(6- (-2))

= 4^8.

Answer:

X= - 6/20

Step-by-step explanation:

Find the lcm in both sides,,,

Do a cross multiple of the sides,

Using the volume for rectangular prisms, the volume of the chimney is: 216 in.³.

The volume of a rectangular prism = (length)(width)(height).

The Chimney in Emily's house is a composite solid consisting of two rectangular prism. To find the volume, we have to decompose the figure into two rectangular prisms. Then solve for the volume of each before finding the total volume.

Volume of the bigger rectangular prism = (length)(width)(height) = (4)(4)(12)

Volume of the bigger rectangular prism = 192 in.³

Volume of the smaller rectangular prism = (length)(width)(height) = (4)(2)(3)

Volume of the smaller rectangular prism = 24 in.³

The volume of the chimney = volume of the two rectangular prism

The volume of the chimney = 192 + 24

The volume of the chimney = 216 in.³

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The average rate of change of f(x) over -6≤x-4 is -70.

The average rate of change of g(x) over -6≤x-4 is -140.

The average rate of change of g(x) is 2 times that of f(x)

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information, f(x) = 7x², g(x) = 7x² and  x₁ = -6, x₂ = -4

For f(x) = 7x²:

average rate of change =  ([7(-4)²] - [7(-6)²]) / (-4-(-6))

                                       = (112-252)/2

                                      = -70

For g(x) = 14x²:

average rate of change =  ([14(-4)²] - [14(-6)²]) / (-4-(-6))

                                       = (224-504)/2

                                      = -140

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

The answer is 48a-6b-14

Step-by-step explantion:

simplify by combining liketerms:

-6- 2b•3 -6a+ 10a• 3-16÷ 2- 4 • -6a

-6-6b-6a+30a -8+24a

48a-6b-14

Good luck!

Answer: 14

Explanation:

(3, -20)    (5, 8)

x1   y1       x2   y2

\(\frac{y2 - y1}{x2 -x1}\)

\(\frac{8 - -20}{5-3}\)  = \(\frac{8+20}{5-3} = \frac{28}{2} = 14\)

Answer: 12

Step-by-step explanation:

add

In respοnse tο the given questiοn, we can state that As a result, the functiοn turning pοints are ((4/3), -4/(3(4/3))) and (-(4/3), 4/(3(4/3))). With this data, we can draw the graph οf y = x³ - 4x shοwn in οptiοn (D).

Mathematicians examine numbers and cοmplex variatiοns, equatiοns and assοciated structures, fοrms and their lοcatiοns, and prοspective pοsitiοns fοr these things. The term "functiοning" signifies the cοnnectiοn between a cοllectiοn οf inputs, each οf which has a cοrrespοnding οutput.

A functiοn is a cοnnectiοn οf inputs and results in which each input leads tο a single, identifiable οutcοme. Each functiοn is assigned a dοmain, a cοdοmain, οr a scοpe. The letter f is widely used this tο denοte functiοns (x). The symbοl fοr admissiοn is an x. The fοur primary types οf usable functiοns are οn οperatiοns, οne-tο-οne capabilities, sο multiple functiοnality, in capabilities, and then οn functiοns.

Optiοn (D) is a design that might depict the graph οf y = x³ - 4x since it cοntains a single hump with a rοοt at x = 0 and intersects the y-axis at y = 0.

We may use the fοllοwing prοcedures tο sοlve the functiοn y = x³ - 4x:

The value οf the y-intercept is (0, 0).

We set y = 0 and sοlve fοr x tο determine the x-intercepts:

\(x^3 - 4x = 0\)

\(x( x^2 -4) = 0\)

\(x = 0 , x = -2 , x = 2\)

As a result, the x-intercepts are (-2, 0), (0, 0), and (2, 0).

\(3x^2 - 4 = 0\)

x = ±√(4/3)

As a result, the turning pοints are ((4/3), -4/(3(4/3))) and (-(4/3), 4/(3(4/3))).

With this data, we can draw the graph οf y = x³ - 4x shοwn in οptiοn (D).

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Answer:

I think the answers are 1 to 1 ,9 to 8 , 10 to7

The monthly Cost C (in dollars) as a function of the number of minutes x used will be a C=$45 when less than 600 minutes are used and C= $45 + 0.1(x -600)  when more than 600 minutes are used.

It is given that, The charge of the plan is $45, so our function of Cost C must include this price. Now, the plan includes 600 minutes of usage for free, So our definition of function should include this information as well.

Now, There will be 2 cases, Case 1 : when the minutes of usage is less than or equal to 600 and Case 2 : when the minutes of usage is greater than 600.

For the first case, the equation will be a simple constant function as no other additional cost is required :

⇒ C = 45

For the 2nd case, there is a 10 cent charge for every extra minute of usage + the plan charge of $45 and to find the number of extra minutes of usage we simply subtract 600 from 'x' (total minutes used). Therefore, our equation will be :

⇒C = 45 + 0.1 (x-600)

In conclusion, we can write our equation with proper format like this :

\(C = \left \{ {{45}\atop {45 + 0.1(x-600)}} \right.\)

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Answer:

10/11

Step-by-step explanation:

count how many cups and then what ones have water and milk

Answer:

The liability is his mortgage.

Answer:

The mortgage

Step-by-step explanation:

The mortgage is a liability. A liability is something that you have to pay for. Bills, fees, mortgages, etc are all liabilities.

The yearly salary- asset

The commission- asset

The mortgage- liability

The rental property- asset

Answer:

10. 3 musicians

11. a) 10 feet

   b) can't read all of it

Step-by-step explanation:

Answer:

#10 should be 3

Step-by-step explanation:

Answer:

$130.00

Step-by-step explanation:

674-284=390

390/3=130

what that person said :(

John's investment will thus be worth $2098.56 after a year. A = 2000 * 1.0120264 A = 2000 * 1.04928125 A = 2098.56

what is expression ?

It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.

After a set amount of time, we can apply the compound interest calculation to determine the future worth of John's investment:

\(A = P * (r/n + 1)^{n*t}\)

In this instance, John invests $2,000 in a bond fund paying 4.75% quarterly compounded. This implies:

(Annual interest rate) r = 0.0475

(Compounded quarterly) n = 4

We can set t = 1 to determine the future worth of John's investment after a year:

A = \(2000 * (1 + 0.0475/4)^{4*1}\)

A =\(2000 * 1.01202643^4\) A = 2000 * 1.04928125 A = 2098.56

John's investment will thus be worth $2098.56 after a year.

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Complete question : John invests $2000 in a bond fund that pays 4. 75% compounded quarterly. What will be his investment after a year?

Answer:

Parallel

Step-by-step explanation

Put into y=mx+b

Equation 1:

14x=2y-6

add 6

14x+6=2y

Divide by 2

7x+3=y

Equation 2:

8/7=y-7x

add 7x

7x+8/7=y

Look at the slope of each equation (the x)

1: 7x    and     2. 7x

The slopes are the same so the lines are parallel

Hope this helped!