15-2x=6x+20, solve for x

For the problem, we have a cosine function.

5 rev per minute implies:

Since we are considering the time 3 seconds after the stopwatch is started, we have:

The distance d, of point p from the surface of the water, is:

The correct option is D

Answer:

Maximum absolute value of f=61/2 at (\(3/2\sqrt{7},-1/2\)) and (\(-3/2\sqrt{7},-1/2\))

Minimum absolute value of f=-10 at (0,-5)

Step-by-step explanation:

We are given that

\(f(x,y)=2x^2+2y\)

Let

\(g(x,y)=x^2+2y+y^2-15=0\)

\(\nabla f(x,y)=<4x,2>\)

\(\nabla g(x,y)=<2x,2+2y>\)

Using Lagrange multipliers

\(f_x(x,y)=\lambda g_x(x,y)\)

\(4x=2x\lambda\)

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

x=0 or

\(\lambda=2\)

If x=0

Then,

\(y^2+2y-15=0\)

\(y^2+5y-3y-15=0\)

\(y(y+5)-3(y+5)=0\)

\((y+5)(y-3)=0\)

\(y=-5,3\)

\(2=(2+2y)\lambda\)

If \(\lambda=2\)

\(2=2(2+2y)\)

\(2/2=2+2y\)

\(1=2+2y\)

\(2y=1-2=-1\)

\(y=-\frac{1}{2}\)

If y=-1/2

Then,

\(x^2-1+1/4=15\)

\(x^2+(\frac{-4+1}{4})=15\)

\(x^2-\frac{3}{4}=15\)

\(x^2=15+3/4=\frac{60+3}{4}=\frac{63}{4}\)

\(x=\pm\frac{3\sqrt{7}}{2}\)

Therefore, possible extreme points are

(0,-5),(0,3),(\(3/2\sqrt{7},-1/2\)) and (\(-3/2\sqrt{7},-1/2\))

\(f(0,-5)=2(0)+2(-5)=-10\)

\(f(0,3)=2(3)=6\)

\(f(3/2\sqrt{7},-1/2)=\frac{63}{2}-1=\frac{61}{2}\)

\(f(-3/2\sqrt{7},-1/2)=\frac{63}{2}-1=\frac{61}{2}\)

Therefore, maximum absolute value of f=61/2 at (\(3/2\sqrt{7},-1/2\)) and (\(-3/2\sqrt{7},-1/2\))

Minimum absolute value of f=-10 at (0,-5)

Answer:

\( -0.2 \)

Step-by-step explanation:

Given:

(-3, 3.6);

(5, 2)

Required:

Rate of change

SOLUTION:

Rate of change for the function is given as \( \frac{y_2 - y_1}{x_2 - x_1} \).

Let,

\( (-3, 3.6) = (x_1, y_1) \)

\( (5, 2) = (x_2, y_2) \)

Rate of change = \( \frac{2 - 3.6}{5 - (-3)} \)

\( = \frac{-1.6}{8} \)

\( = -0.2 \)

The rate of change of y with respect to x for this function is -0.2

Given :

The graph of a linear function is shown on the grid

To find the rate of change of y with respect to x , we need to pick two points from the graph

Two points are (-3,3.6)  and (5,2)

Lets apply slope formula to find out rate of change

\(slope =\frac{y_2-y_1}{x_2-x_1}\\slope =\frac{2-3.6}{5+3} \\slope = -0.2\)

The rate of change of y with respect to x for this function is -0.2

Learn more :  brainly.com/question/24930128

Answer:

(10, -29)

Step-by-step explanation:

I assume you are looking for the solution to this system of equations.

Plug them both into a graphing calculator. The point where they cross is:

(10, -29)

Answer:(10, -29)

Step-by-step explanation:

The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

Learn more about equations on:

https://brainly.com/question/14201243

#SPJ1

The types of rotation are:

In this case:

 ⇒ it is reflection since the graph is inverted and each point is the same distance from the line of reflection

Answer: reflection

Hope that helps!

Answer:

Given function:

a)

Find x when p(t) = 200:

b)

Find p(t) when t = 4:

Step-by-step explanation:

If you are talking about an inverse function f-1(x) of the function f(x), you must remember that, by definition,

f(f-1(x)) = x

So given f(x) = x/4 if I apply an arbitrary K which is equal to f-1(x), then

f(K) = x

K/4 = x

K = 4x

But I want to recover f-1(x), so replace it back.

f-1(x) = 4x

Done

Step-by-step explanation:

y=kx

25= k(-5)

k= -5

y= -5x

y = -5 ×3 = -15

Answer:66 hours of video games in three weeks!

Step-by-step explanation:First you would multiply 6 by 2 because the weekend refers to Saturday and Sunday which are two days,when you multiply 6 by 2 you get 12.Next you would multiply 2 by 5 because the problem says  2 hours each day of the week,when you multiply 2 by 5 you get 10.Then you add 10 and 12 which gets you to 22.Last but not least you multiply 22 by 3 because the question says  how many hours does mr.danie spend playing video games over 3 weeks,which bring you to 66!

I hope I helped!

Answer:

Step-by-step explanation:

1271 = 31 *41

31 and 41 are prime number.

Answer: 165 miles

Step-by-step explanation: In order to figure out the answer, you must do 55 x 3 because he drove for 3 hours at 55 mph so you could break it up and go 50 x 3 to equal 150 and 5 x 3 to equal 15 and add those to get 165.

Answer:

The answer is 165miles

Step-by-step explanation:

\(distance = speed \times time\)

d=55×3

d=165 miles

Answer:

16.2

Step-by-step explanation:

By geometric mean theorem:

\( {9}^{2} = 5(x) \\ \\ \implies \: 81 = 5x \\ \\ \implies \: x= \frac{81}{5} \\ \\ \implies \: x=16.2\)

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

um i love ur key bored

A) The equations consistent and independent because they are y=mx+b form. And the equations are two completely different lines.

B) After you solve for the equation and put in it y=mx+b, you see that both of the equations are the same. These means that the lines are consistent and dependent.

leave the variable alone Y

-y=-2x-7

divide the negative one that the Y has with the other numbers that are in the other side of the equal sign

y=2x+7

hope i helped

Answer:

Step-by-step explanation:

2x-y=-7

leave the variable alone Y

-y=-2x-7

divide the negative one that the Y has with the other numbers that are in the other side of the equal sign

y=2x+7

Answer:

One: D

Two: D

Step-by-step explanation:

One

The trick here is to get rid of the cube root and the square root.

Step One

Cube both sides of the given equation.

(m^3)^3 = (∛√n)^3

m^9 = √n

Step Two

Square both sides

(m^9)^2 = (√n)^2

m^18 = n

So the answer is D.    

Two

There is no way to get any kind of answer out a linear equation that transforms itself into an expression of divided powers. It is just impossible.

D again

The area of the face of a nickel 353.14 \(mm^{2}\) (nearest hundredth)

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.

As the surface of nickel is in shape of 2-D circle.

radius of circle = \(\frac{21.21}{2}\) = 10.605 mm

Area of circle= \(\pi r^{2}\)

                      = 3.14* 21.21*21.21

                      = 353.143 \(mm^{2}\)

                      = 353.14 \(mm^{2}\) (nearest hundredth)

Thus, the area of the face of a nickel 353.14 \(mm^{2}\) (nearest hundredth)

Learn more about area of circle here:

brainly.com/question/11952845

#SPJ1

Answer:

x = -7

Step-by-step explanation:

2x+2-x+5=0

x+2+5=0

x+7=0

x = -7

So the answer is -7

Given:

\(\to \bold{ (2x+2)-(x+5)=0}\)

To find:

x=?

Solution:

\(\to \bold{ (2x+2)-(x+5)=0}\\\\\to \bold{ (2x+2-x-5)=0}\\\\\to \bold{ (x-3)=0}\\\\\to \bold{ x-3=0}\\\\\to \bold{ x=3}\\\\\)

Learn more:

brainly.com/question/75616

i think a is the answer but am not sure

Answer:

D) 55.8

Step-by-step explanation:

The volume of the cylindrical water cooler is 211.38 gallons. Therefore, option C is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall.

Now, radius = 3/2 =1.5 feet

We know that, the formula to find the volume of a cylinder is πr²h.

Here, 3.14×1.5²×4

= 28.26 cubic feet

In gallons = 28.26×7.48

= 211.38 gallons

Therefore, option C is the correct answer.

To learn more about the volume visit:

https://brainly.com/question/13338592.

#SPJ1

The correct option is C, 211.38. Hope this helps :)

Answer:

B (middle one)

Step-by-step explanation:

Given:

A fair die is rolled.

It pays off $10 for 6, $7 for a 5, $4  for a 4 and no payoff otherwise.

To find:

The expected winning for this game.

Solution:

If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.

The probability of getting a 6 is:

\(P(6)=\dfrac{1}{6}\)

The probability of getting a 5 is:

\(P(5)=\dfrac{1}{6}\)

The probability of getting a 4 is:

\(P(4)=\dfrac{1}{6}\)

The probability of getting other numbers (1,2,3) is:

\(P(\text{Otherwise})=\dfrac{3}{6}\)

\(P(\text{Otherwise})=\dfrac{1}{2}\)

We need to find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.

\(E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})\)

\(E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}\)

\(E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0\)

\(E(x)=\dfrac{10+7+4}{6}\)

\(E(x)=\dfrac{21}{6}\)

\(E(x)=3.5\)

Therefore, the expected winnings for this game are $3.50.

Answer:

Step-by-step explanation:

a = $

3.00

b = $

10.00

Answer:

B.) -2.5 z + 5 y - 8

Step-by-step explanation:

- 6 z + ( - 5.5 ) + 3.5 z + 5 y - 2.5

combine like terms

- 6 z + 3.5 z + 5 y -5.5 - 2.5

- 2.5 z + 5 y - 8

Answer:

0.0907

Step-by-step explanation:

There are 12 picture cards

There are 4 9's

There are 52-12-4 = 36 cards that are not 9's and not picture cards

(5*58905)/(52C5)

Both the domain and range of the transformed function are the same as those of the parent function.

What are Range and Domain?

The collection of all potential output values that a function can generate given its domain is known as its range.

The set of all potential input values for which a function is specified is referred to as its domain.

The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.

Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.

A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.

Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.

A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well

So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.

Learn more about Range from the given link.

https://brainly.com/question/2264373

#SPJ1