AB is tangent to circle O at B. Find the length of the radius, r, for AB = 5 and AO = 13.

Answers

Answer 1

ΔABO is a right triangle with AB⊥BO. The radius of the circle is BO. The Pythagorean theorem applies.
AO² = AB² + BO²
13² = 5² + r²
169 -25 = r²
r = √144 = 12

The radius (r) is 12.

Answer 2

the radius is twelve

Related Questions

A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2

10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft

Answers

A(s) equals 1/2 s square root of 144 minus s squared.. As s and r are the sides and the area of the triangle are 1/2(s)(r)

Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft

Step-by-step explanation: Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]

where:

b is base of a triangle

h is height of a triangle

For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:

hypotenuse² = side² + side²

[tex]12^{2} = s^{2} + x^{2}[/tex]

[tex]x^{2} = 12^{2} - s^{2}[/tex]

[tex]x^{2} = 144 - s^{2}[/tex]

x = [tex]\sqrt{144 - s^{2} }[/tex]

To determine the Area of the right triangle as function of s:

A = [tex]\frac{b.h}{2}[/tex]

A = [tex]\frac{1}{2}[/tex](s.x)

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

Therefore, the area of the right triangle is:

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:

hypotenuse² = side² + side²

h² = 13² + 5²

h² = 169 + 25

h = [tex]\sqrt{194}[/tex]

h = 14

The minimum length the ladder has to have to reach the top is 14 ft.

Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2

Answers

A function is its own inverse if it is symmetrical about the line y=x. This is the case for functions t, y, w. Function d(x) = 1/x^2 is symmetrical about the line x=0, but is not symmetrical about the line y=x.

The appropriate choices are ...
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y

Answer:

a,b and c.

Step-by-step explanation:

We have to find the the functions that are their own inverses.

a.t(p)=p

Then the inverse function of given function is

[tex]p=t^{-1}(p)[/tex]

Therefore, the given function is inverse function of itself.

Hence, option a is true.

b.y(j)=[tex]-\frac{1}{j}

Let y(j)=y then we get

[tex]y=-\frac{1}{j}[/tex]

[tex]j=-\frac{1}{y}[/tex]

[tex]j=-\frac{1}{y(j)}[/tex]

[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]

[tex]j=j[/tex]

Hence, the function is inverse of itself.Therefore, option b is true.

c.[tex]w(y)=-\frac{2}{y}[/tex]

Suppose that w(y)=w

Then [tex]w=-\frac{2}{y}[/tex]

[tex]y=-\frac{2}{w}[/tex]

[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]

[tex]w(y)=w[/tex]

[tex]w(y)=-\frac{2}{y}[/tex]

Hence, the function is inverse function of itself.Therefore, option c is true.

d.[tex]d(p)=\frac{1}{x^2}[/tex]

Let d(p)=d

If we replace [tex]\frac{1}{x^2}by p then we get

[tex]d=\frac{1}{x^2}[/tex]

[tex]x^2=\frac{1}{d}[/tex]

[tex]x=\sqrt{\frac{1}{d}}[/tex]

[tex]x=\sqrt{\frac{1}{d(p)}[/tex]

Hence, the function is not self inverse function.Therefore, option d is false.

What is the area of sector GPH?

Answers

The area of the entire circle = pi r^2
The area of the shaded area = (40/360) * pi r^2
r = 9 cm

Area of the shaded area = 1/9 * 3.14 * 9^2
Area of the shaded area = 3.14 * 9
Area of the shaded area = 28.26

Notice one of the 9s disappeared. Where did it go?
You could begin the problem by writing out 9^2
Area = 1/9 * 3.14 * 9 * 9 Notice that 1/9 will cancel out 1 of the nines.

28.26 yds = Shaded area.

The area of sector GPH is [tex]$\frac{1}{4}\pi r^2$.[/tex]

To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]$\frac{\theta}{360^\circ} \times \pi r^2$[/tex], where [tex]$\theta$[/tex] is the central angle of the sector in degrees, and [tex]$r$[/tex] is the radius of the circle.

Given that the central angle of sector GPH is [tex]$90^\circ$ (or $\frac{\pi}{2}$[/tex] radians, since[tex]$180^\circ$ is $\pi$ radians)[/tex], and the radius [tex]$r$[/tex] is unspecified, we can express the area of the sector in terms of [tex]$r$.[/tex]

Using the formula for the area of a sector:

[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]

Substituting [tex]$\theta = 90^\circ$:[/tex]

[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]

Simplifying the fraction:

[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]

So, the area of sector GPH is [tex]$\frac{1}{4}\pi r^2$[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]$90^\circ$[/tex] central angle.

function that has the same domain as y=2√x

Answers

The rest of the question;
A.y= [tex] \sqrt{2x} [/tex]
B.y=[tex] \sqrt[3]{ x^{2} } [/tex]
C.y=[tex] \sqrt{x-2} [/tex]
D.y=[tex] \sqrt[3]{x-2} [/tex]
====================================================

We are given the function
y = 2 √x

The domain for the given function is this
{ x | x ≥ 0 }

The answer is A. y = √2x

In general any function that has a domain of x that is equal to or greater than 0. Some examples:
f(x) = √x - 2
f(x) = 5 √x

Answer:

The answer is A. y = √2x

Step-by-step explanation:

which transformations are needed to change the parent some function to the sine function below?

Answers

Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.

The first choice is the answer:

Solution:
the function y = sin x, which would have range from -1 to 1 and period of 2pi:

So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2

To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?

Answers

Asked and answered elsewhere.
https://brainly.com/question/10013755

We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.

The formula for the combination is given by

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be

[tex]^{50}C_6[/tex]

Using the above formula, the number of different selections are

[tex]^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700[/tex]

Therefore, 15890700 different selections are possible.

The circle belowis centered at the point (-2 ,1) and has a radiusof length 3

Answers

Answer:
Option A, (x + 2)² + (y - 1) = 9

Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.

From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9

The equation for the given circle is (x + 2)² + (y - 1)² = 9

ln(x+2)-ln(4x+3)=ln(1/2*x)

Answers

ln(x+2)-ln(4x+3)=ln(1/2*x)

Using properties of logarithms

[tex] \frac{ln(x+2)}{ln(4x+3)} = ln \frac{x}{2} \\ \\ \frac{x+2}{4x+3} = \frac{x}{2} \\ \\2(x+2)=x(4x+3) 2x+4=4x^2+3x \\ \\ 4 x^{2} +x-4=0 \\ \\ x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} \\ \\ x= \frac{ -1+/-\sqrt{1+64} }{8} \\ \\ x_{1} = \frac{-1+ \sqrt{65} }{8} \\ \\ x_{2} = \frac{-1- \sqrt{65} }{8} Check: When you substitute x_{2} into \\ \\ ln(4x+3)=ln(4* \frac{-1- \sqrt{65} }{8} ) =ln( \frac{-1- \sqrt{65} }{2} ) you will get negative number under ln, that is impossible , [/tex]

so x2 is not a solution of this logarithmic equation.

Only x1 is a solution.

What is the number of social security credits a worker needs to earn over his or her working lifetime to collect Social security benefits?

Answers

According to the Social Security Administration website, the number of work credits you need to get benefits depends on when you were born. If you were born in 1929 or afterward, you need 40 credits. If you were born before 1929, you don't need 40: 39 credits are required if you were born in 1928, 38 credits if you were born in 1927, etc.

PLz help!

Write the equation of the line that passes through (3, −2) and has a slope of 4 in point-slope form. (2 points)

1 y + 2 = 4(x − 3)

2 y − 3 = 4(x + 2)

3 x − 3 = 4(y + 2)

4 x + 2 = 4(y − 3)

Answers

[tex]y+2=4(x-3)[/tex]

It's the first answer.

[tex]\text{Slope} = \dfrac{Y_2 - Y_1}{X_2 - X_1} [/tex]

Given that the slope = 4 and the coordinate is (3, -2),

[tex]4 = \dfrac{y + 2}{x + 3} [/tex]

[tex] y + 2 = 4(x - 3) [/tex]

Answer : y + 2 = 4(x - 3) (Answer A)

Help ASAP PLEASE!!! match the term with the appropriate definition.

Answers

1) x-1>5→x-1+1>5+1→x>6: Option F. x>6, open dot at 6 and shaded to the right

2) 5x+1>=11→5x+1-1>=11-1→5x>=10→5x/5>=10/5→x>=2: Option J. x>=2, closed dot at 2 and shaded to the right

3) x-7>-4→x-7+7>-4+7→x>3: Option H. x>3, open dot at 3 and shaded to the right

4) -2x<6→(-1/2)(-2x<6)→(-1/2)(-2x)>(-1/2)(6)→x>-3: Option G. x>-3, open dot at -3 and shaded to the right

5) 4<-4x→(-1/4)(4<-4x)→(-1/4)(4)>(-1/4)(-4x)→-1>x→x<-1: Option B. x<-1, open dot at -1 and shaded to the left

6) -2x+3<-7→-2x+3-3<-7-3→-2x<-10→(-1/2)(-2x<-10)→
(-1/2)(-2x)>(-1/2)(-10)→x>5: Option A. x>5, open dot at 5 and shaded to the right

7) 2x<=6→2x/2<=6/2→x<=3: Option I. x<=3, closed dot at 3 and shaded to the left

8) 3(x+4)>8x-6→3x+12>8x-6→3x+12-3x+6>8x-6-3x+6→18>5x→
18/5>5x/5→18/5>x→x<18/5: Option E. x<18/5, open dot at 18/5 and shaded to the left

9) -3x+4<-x+2→-3x+4+3x-2<-x+2+3x-2→2<2x→2x>2→2x/2>2/2→x>1: Option C. x>1, open dot at 1 and shaded to the right

10) -2(x-4)>5-(x+2)→-2x+8>5-x-2→-2x+8>3-x→-2x+8+2x-3>3-x+2x-3→
5>x→x<5: Option D. x<5, open dot at 5 and shaded to the left

The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?

Answers

The vertex of the graph y=|x| is at (0,0)

After transformation the vertex becomes at (-3,-2)
Apply axes transformation from (0,0) to (h,k)
So, the transformation rule is (x,y) → (x-h, y-k)
(h,k) will be equal (-3,-2)

∴ y=|x| ⇒ (y-(-2)) = |x-(-3)|
∴(y+2) = |x+3|
∴ y = |x+3|-2

So, the correct answer is option 2

we have that

the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]

The transformed function has the vertex at point [tex](-3,-2)[/tex]

the rule of the translation is equal to

[tex](x,y)------> (x-3,y-2)[/tex]

That means

The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down

therefore

the answer is

the transformed function is [tex]y=\left|x+3\right|-2[/tex]

What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)

Answers

good day ~_~ /////////////

Answer: (5, -9)

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

on a game show that are 10 keys in the bag and three of the key start a car and contest in randomly choosing the key it doesn't not start the car she returned to the bag the host mixed up the back she randomly selects another key this key does not start the car either what is the probability of this no start no start outcome

Answers

What are the answers

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$450\\ P=\textit{original amount deposited}\to& \$3000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &3 \end{cases} \\\\\\ 450=(3000)(r)(3)\implies \cfrac{450}{(3000)(3)}=r\implies \cfrac{1}{20}=r \\\\\\ 0.05=r\implies r\%=0.05\cdot 100\implies r=\stackrel{\%}{5}[/tex]

HELP
______________________

Answers

The answer is the third one, since it goes up between the two by 50.
x*50 = y

Answer:

The answer is the third option/choice.

Factor \2x^2-11x+5=0

Answers

2x² - 11x + 5
2x² - x - 10x + 5
x(2x - 1) - 5(2x - 1)

(2x - 1)(x- 5) is your answer.

Final answer:

The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.

Explanation:

The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.

We rewrite the middle term using these two numbers and then group the terms to factor by grouping:

[tex]2x^2[/tex]- 10x - x + 5 = 0
([tex]2x^2[/tex]- 10x) - (x - 5) = 0
2x(x - 5) - 1(x - 5) = 0
(2x - 1)(x - 5) = 0

The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.

Which ordered pair is the vertex of y = [x - 3]+ 2?

A.(2, –3)

B.(–3, 2)

C.(3, 2)

D.(2, 3)

Answers

An absolute value function without transformations, [tex]y = |x|[/tex], has a vertex at (0, 0). The transformations here are to shift the function right 3 and up 2. The vertex would then be at (3, 2). Your answer should be C.

kaelyn has 14 coins that have a vaule of $ 1.20. she only has dimes and nickles. how many nickles does kaely have

Answers

Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.

The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:

D + N = 14 (since there are 14 coins in total)0.10D + 0.05N = 1.20 (representing the total value of the coins in dollars)

Multiply the second equation by 100 to deal with whole numbers:

10D + 5N = 120

From the first equation, we can express D as:

D = 14 - N

Substitute this into the second equation:

10(14 - N) + 5N = 120140 - 10N + 5N = 120-5N = -20N = 4

So, Kaelyn has 4 nickels and the rest are dimes.

Q # 15 in the diagrams a || b a. Use the fiagrama o answer the question(diagrama not to scale.)

Answers

The interior angel to ∠7 is the angel ∠4

because ∠7 + ∠4 = 180°

The correct choice is number 1

I’m pretty sure its <4 angle four...
///EAGLEPAW

hey can you please help me posted picture of question

Answers

The correct answer is D. Graph D

Find the Vertex of   y = 3x2+7x+2

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 3 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -1.1667

Plugging into the parabola formula  -1.1667  for  x  we can calculate the  y -coordinate :
  y = 3.0 * -1.17 * -1.17 + 7.0 * -1.17 + 2.0
or   y = -2.083
Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 3x2+7x+2
Axis of Symmetry (dashed)  {x}={-1.17}
Vertex at  {x,y} = {-1.17,-2.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = {-0.33, 0.00}

We can find the roots of the given equation to determine its graph.

3x²+7x+2=0

Solving using factorization.

3x²+6x+x+2=0

3x(x+2)+1(x+2)=0

(3x+1)(x+2)=0

This means the roots of the equation are x = -2 and x = -1/3

Now from the graphs determine which one has the roots at these two points. We can observe that Graph D has the roots at x=-2 and x=-1/3

So the answer to this question is option D

This is incredibly frustrating. PLEASE HELP ME

Answers

The correct option is: Option (C)

Explanation:
Given expression:
[tex]\sum_{i=1}^{25} 2^{2i}[/tex]

When i = 1: The answer is [tex]2^{2*1}[/tex] = 4
When i = 2: The answer is [tex]2^{2*2}[/tex] = 16
When i = 3: The answer is [tex]2^{2*3}[/tex] = 64
.
.
When i = 25: The answer is [tex]2^{2*25}[/tex] = [tex]2^{50}[/tex]

Which is the series mentioned in Option C

Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?

Answers

127/4 = 31.75 = 31
85/2 = 42.5 = 43

She can only make 31 full gift baskets with the amount of soap she has.

Therefore, Chloe can make 31 gift baskets.

Amy has 5 yards of border to put around a garden. She uses all the border to make four sections that are the same length. Which expession does not equal the length of one these sections in yards?

Answers

I added a screenshot of the question along with the given choices

Answer:
F. 4 ÷ 5

Explanation:
We know that Amy has 5 yards of boarders and that she will use them to make 4 equal borders.
This means that:
she will divide 5 yards by 4 to know the length of each border

Among the given choices, choices G, H and J show the division of 5 by 4 which is correct representation of the length
On the other hand. choice F shows the division of 4 by 5 which is an incorrect representation of the length.

Hope this helps :)

Answer:

4 ÷ 5

Step-by-step explanation: becuz i said so

What is the equivalent of pi over 3 radians in degrees?

Answers

(π/3)x(180/π)=60 degrees

[tex] \frac{ \pi }{3} [/tex] is equivalent to 60°

Two thirds of the families in smithville own their own homes. The total number of home owning families there is 480. How many families live in smithville?

Answers

x- the total number of families in Smithville.
(2/3)x - the number of home owning families.
At the same time, the number of home owning families is 480.

(2/3)x=480
x=480*3/2=720.

720 families live in Smithville.

Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years? A. $48,000 B. $44,237 C. $45,082 D. $43,270

Answers

Given that the value of $50000 car decreases by 4% per year, the value after 3 years will be given by exponential form:
y=abˣ
where:
a=initial value
b=decreasing rate
x=time in years
from the information:
a=50000, b=0.96, x=3
thus
y=50000(0.96)³
simplifying we get:
y=$44, 236.8
~$44237

Answer:
B. $44,237

Solve the equation 3x+5y=4
for y

Answers

Answer:

y = (4 -3x)/5

Step-by-step explanation:

Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.

3x +5y = 4

5y = 4 - 3x . . . . . non-y term subtracted

y = (4 -3x)/5 . . . . divide by the coefficient of y

_____

If you like, you can rearrange this to slope-intercept form:

... y = -3/5x +4/5

graph of this ellipse

x^2 + y^2 =1
_ _
4 16

Answers

check the picture below.

Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN

Answers

The trapezoid is shown in the picture attached.

We know:
LK // MF
KF = 10
A(KLMF) = A(FMN)

Since LM // KF (because they are bases of the trapezoid) and LK // MF because is given in the hypothesis, KLMF is a parallelogram.
The area of a parallelogram is given by the base times the height.
A(KLMF) = b × h
= 10 × h

The area of a triangle is given by the formula:
A(FMN) = (b × h) / 2
= (FN × h) / 2

We know that the two areas are congruent, therefore:
A(KLMF) = A(FMN)
10 × h = FN × h / 2

The two "h" cancel out because they are the same and we can solve for FN:
10 = FN / 2
FN = 20

Now we can calculate:
KN = KF + FN = 10 + 20 = 30

Hence, KN is 30 units long.

Final answer:

In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.

Explanation:

In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.

Since KF and LM are parallel, KF = LM. Therefore, LM = 10.

Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.

Hence, KN = KL + LM = AN + LM = AN + 10.

Therefore, KN = AN + 10.

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