Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?

Using linear approximation, the expression √125.2 can be approximated as approximately 10.02.

To find the equation of the tangent line to the function f(x) = √x at x = 125, determine the slope (m) and the y-intercept (b) of the tangent line.

First, find the slope (m) using the derivative of the function f(x) = √x:

f'(x) = 1 / (2√x)

Evaluate the derivative at x = 125:

f'(125) = 1 / (2√125) = 1 / (2 × 5) = 1/10

Now, find the y-coordinate of the point on the function f(x) at x = 125:

f(125) = √125 = 5

So, the tangent line at x = 125 passes through the point (125, 5) and has a slope of 1/10.

Using the point-slope form of a linear equation, the equation of the tangent line can be written as:

y - 5 = (1/10)(x - 125)

To simplify, multiply through by 10:

10y - 50 = x - 125

Rearranging the equation, express it in the form y = mx + b:

y = (1/10)x - 75/10 + 5

Simplifying further:

y = (1/10)x - 75/10 + 50/10

Combining the terms:

y = (1/10)x - 25/10

Therefore, the equation of the tangent line to f(x) = √x at x = 125 is y = (1/10)x - 25/10.

Now, use this tangent line to approximate the value of √125.2:

Substitute x = 125.2 into the equation:

y = (1/10)(125.2) - 25/10

y = 12.52 - 2.5

y ≈ 10.02

So, using linear approximation, approximate √125.2 as approximately 10.02.

Find out more on linear approximation here: https://brainly.com/question/30403460

#SPJ1

Answer:

Required probability = 2 / 11

Step-by-step explanation:

Sample space of 5 person = 11!

One woman one man arrangement = 2!

Arrangement without woman = 10!

Required probability = [2!][10!] / [11!]

Required probability = 2 / 11

The probability that the parents will be standing next to each​ other is 2/11

Probability is the likelihood or chance that an event will occur.

Given a woman, man and their four children, if their parents will be standing next to each other, that makes it 5 people. The sample space for 5 people is 11!

Pr(parents standing next to each other) =  2!10!/11!

Pr(parents standing next to each other) = 2*10!/11*10!

Pr(parents standing next to each other) = 2/11

Therefore the probability that the parents will be standing next to each​ other is 2/11

Learn more on probability here: https://brainly.com/question/25870256

The expression with the correct coefficients in each block is given as follows:

20x³ + 0x² - 7x.

The functions in the context of this problem are defined as follows:

The operation is given as follows:

f(x)g(x) + h(x).

Hence, to obtain the resultant function, we apply the definitions into the operation and the simplify, applying the distributive property and combining the like terms, as follows:

4x(5x² - 4) + 9x = 20x³ - 16x + 9x = 20x³ - 7x.

As there is no x² term, the coefficient of zero multiplies the term x².

More can be learned about functions at https://brainly.com/question/31895757

#SPJ1

Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.

A rectangular array of numbers or even other mathematical objects that can perform actions like addition and multiplication is known as a matrix. Matrices are widely used to describe systems of equations, transformations, and data in mathematics, physics, engineering, computer science, and many other disciplines. The individual matrix components are frequently identified by their row and column positions, and matrices have a predetermined number of rows and columns. There are numerous actions that can be carried out on matrices, including addition, subtraction, and multiplication by other matrices.

given

We can write the equations in matrix form as follows to answer the simultaneous equations 1x + 4y = 9 and 2x - 3y = 7 using the matrix method:

Then, on the left side of the equation, we can locate the inverse of the coefficient matrix:

| 1 4 |^-1 = 1/(-11) | -3 -4 |

|-2 -1 |

When we multiply both sides of the equation by the coefficient matrix's inverse, we obtain:

| x | | 1 4 |^-1 | 9 |

| x | | -3/11 -4/11 | | 9 |

| y | = | -2/11 -1/11 | x | 7 |

If we simplify, we get:

x = (-3/11)*9 + (-4/11)*7 = -1

y = (-2/11)

*9 + (-1/11)

*7 = 1

Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.

To know more about matrix visit :-

https://brainly.com/question/28180105

#SPJ1

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

The perimeter of the triangle is 30 units

The vertices are (−7,−1), (5,−1), and (5,4).

Start by calculating the distance between the vertices using:

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2\)

So, we have:

\(d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2\)

d1 = 12

\(d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2\)

d2 =5

\(d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2\)

d3 = 13

The perimeter is then calculated as:

P = d1 + d2 + d3

This gives

P = 12 + 5 + 13

Evaluate

P = 30

Hence, the perimeter of the triangle is 30 units

Read more about perimeter at:

https://brainly.com/question/6465134

#SPJ1

Answer:

c) 113°

Step-by-step explanation:

Exterior angle is equal to the sum or the "remote" interior angles, that is the two angles that are not just next to the exterior angle. See image.

So the answer, quickly:

exterior angle

= 65° + 48°

= 113°

This is why:

(skip if you don't care)

The three angles in a triangle add up to 180° But also, a linear pair of angles also add up to 180°

So

x + 65° + 48° = 180°

x + y = 180°

y = 65° + 48°

See image.

Answer:

25 minutes

Step-by-step explanation:

First you subtract the original amount on the card from the remaining amount left.

So you can get the amount of money spent on that call.

$15 - $13.50 = $1.50

Then you divide that number by how much it cost per minute.

$1.50 ÷ 6 = 0.25

Then you get your answer!

She was on the phone for 25 minutes

Answer:

(6, -5)

Explanation:

9514 1404 393

Answer:

  (11/24)x^6

Step-by-step explanation:

 \(\dfrac{1}{8}x^5\cdot3\dfrac{2}{3}x=\dfrac{1}{8}\cdot\dfrac{11}{3}\cdot x^5\cdot x=\boxed{\dfrac{11}{24}x^6}\)

__

The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(3v + 8 \geq 22\)

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

\(\boxed{\text{Breaking down the phrase...}}\\\\\text{Three times a number, v, added to eight is greater than or equal to twenty-two. }\\------------------\\\rightarrow \text{"Three times a number, v..."} - 3v \text{ This expresses the product of '3' and 'v'.}\\\\\rightarrow \text{"added to eight..."} - + 8 \text{ The product gets added to eight.}\\\\--------------\\\text{The First Part Is:}}\\\\3v + 8\\---------------\\\rightarrow \text{is greater than or equal to twenty-two. } - \geq 22\)

\(\text{The value of '3v + 8' is greater than or equal to 22.}\\---------------\\\text{\underline{Putting it together, we would have:}}\\\\\boxed{3v + 8 \geq 22}}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

42,40,58

Step-by-step explanation:

Answer:

250000

Step-by-step explanation:

20% of x is 50000

----------------------------

50000=20x/100

50000= x/5

5(50000) = x

250000 = x

Step-by-step explanation:

See image below

Answer: 37cm²

Step-by-step explanation:

Answer:

no justified

Step-by-step explanation:

If to approximate the length of a marsh, a surveyor walks x = 420 meters. The Approximate the length AC of the marsh is 420.7m.

Using this formula to find the length of Ac of the march

b² = a²+c² -2ac Cos B

Where:

a²=220

c²= 420

Cos B = 180°  - 75° = 105°

Let plug in the formula

b² = 220² + 420² - 2(220)( 420) Cos  105°

b² = 220² + 420² - 2(220)( 420) (-0.258819045)

b² = 48,400 + 176,400 - 47,829.76

b² = 224,800 -  47,829.76

b = √176,970.24

b = 420.7m

Therefore the length is 420.7m

Learn more about length here:https://brainly.com/question/2217700

#SPJ1

Answer:

its 24

Step-by-step explanation:

all the sides are equal.... btw dont download the link its a virus he is a bot

Answer:

24

Step-by-step explanation:

0.25 * 16 = 4

40 - 4 = 36

36 divided by 1.5 = 24

\(\\ \rm\hookrightarrow c=\dfrac{40-1.5r}{0.25}\)

\(\\ \rm\hookrightarrow 16=\dfrac{40-1.5r}{0.25}\)

\(\\ \rm\hookrightarrow 40-1.5r=16(0.25)=4\)

\(\\ \rm\hookrightarrow 1.5r=36\)

\(\\ \rm\hookrightarrow r=36/1.5\)

\(\\ \rm\hookrightarrow r=24\)

Answer:

Step-by-step explanation:

Slope= y2-y1/x2-x1

7- -11=18

-20 - -8= -12

Slope= 18/-12

The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.

Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.

The graph that represent this data using the points is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The x and y values

Where

x = stars

y = price

To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph

Read more about functions at:

brainly.com/question/4138300

#SPJ1

The total number of different possible outcomes is 40.

Hannah is designing a new board game and is trying to figure out all the possible outcomes. Hannah spins a spinner with five equal-sized sections labelled Monday, Tuesday, Wednesday, Thursday, and Friday. Hannah spins a spinner with four equal-sized sections labelled Red, Green, Blue, and Orange. Hannah also flips a coin at the end.

The number of possible outcomes for the first spinner is 5.

The number of possible outcomes for the second spinner is 4.

The number of possible outcomes from flipping the coin is 2.

The total number of different possible outcomes is the product of all the possibilities.

N = 5*4*2

N = 40

To learn more about product, visit :

https://brainly.com/question/22852400

#SPJ9

Y=2x-1

Step-by-step explanation:

I am big brain

Answer:

y=2x-1

Step-by-step explanation:

You add 2x to the other side, then rearrange

Angle JKL has a measure of 24 degrees while angle LKM has a measure of 12 degrees

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following angles

From the attached figure, we can see that:

Angle 1 is twice the measure of angle 2

This is so because, the angle 1 is the vertex angle of an isosceles triangle

While the angle 2 is half of it

So, we have

Angle 1 = 2 * Angle 2

Substitute the known values in the above equation

So, we have

2 * 3x = 5x + 4

Evaluate the product

So, we have

6x = 5x + 4

Evaluate the like terms

x = 4

Substitute x = 4 in the equations JKL=5x+4 and LKM=3x

So, we have

JKL= 5 x 4 + 4

LKM = 3 x 4

Evaluate the equations

So, we have

JKL= 24

LKM = 12

Hence, the measures of the angles are JKL= 24 and LKM = 12, respectively

Read more about angles at

brainly.com/question/7620723

#SPJ1

Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

The solutions to the nearest tenth are x = -0.1 and x = 1.3

From the question, we have the following parameters that can be used in our computation:

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

Read more about quadratic functions at

https://brainly.com/question/1214333

#SPJ1

Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

Answer:hello I'm from Philippines

Step-by-step explanation: