A circle is shown. Secant X Z and tangent W Z intersect at point Z outside of the circle. Secant X Z goes through the center of the circle and intersects the circle at point Y. The length of W Z is k + 4, the length of Z Y is k, and the length of X Y is 12.
What is the length of line segment XZ?
Answers
Given:
Consider the below figure attached with this ques.
To find:
The length of the line segment XZ.
Solution:
According to the tangent-secant theorem, the square of tangent is equal to the product of secant and external segment of secant.
Using tangent-secant theorem, we get
[tex]WZ^2=ZX\times ZY[/tex]
[tex](k+4)^2=(k+12)k[/tex]
[tex]k^2+8k+16=k^2+12k[/tex]
[tex]8k+16=12k[/tex]
Subtract both sides by 8k.
[tex]16=12k-8k[/tex]
[tex]16=4k[/tex]
Divide both sides by 4.
[tex]4=k[/tex]
Now,
[tex]XZ=12+k[/tex]
[tex]XZ=12+4[/tex]
[tex]XZ=16[/tex]
Therefore, the measure of XZ is 16 units.
Related Questions
i need help finding the y-intercept
Answers
Answer: (0, -7)
Step-by-step explanation:
y = mx + b
Where m is slope and b is y-intercept
y = 2x + b
One point that passes through the line is (5,3), which means that x = 5 and y = 3
3 = 2(5) + b
3 = 10 + b
b = -7
(0, -7) is the y-intercept
Using this info you can find the equation of the line
:)
The bearing of a plane from an airport is 65 degress.Calculate the bearing of the airport from the plane
Answers
Answer:180+65=245, your answer is 245 degrees.
Step-by-step explanation:
Help please. I need this in a few minutes
Answers
Answer:
Step-by-step explanation:
Uriel's hiking stick is 3 2/3 feet long, and Nat's is 3 3/8 feet long. Whose walking stick is longer and by how much?
Answers
Answer:
Uriel's stick is LONGER by 7/24 feet
Step-by-step explanation:
Uriel's hiking stick is 3 2/3 feet long, and Nat's is 3 3/8 feet long. Whose walking stick is longer and by how much?
The above question is solved as
Uriel's stick - Nat's stick
= 3 2/3 feet - 3 3/8 feet
= 7/24 feet
Hence, Uriel's stick is LONGER by 7/24 feet
BICYCLES A bicycle has tires that are 24 inches in
diameter.
How many inches does the tire travel after 350 rotations?
Answers
Answer:
75.4 in. b. 7540 in. Find the diameter and radius of a circle with the.
Step-by-step explanation:
hope this helped !!!!!!
Algebra 1
help please!
Answers
Answer:
b
Step-by-step explanation:
Sorry this isn't the answer, I could give it to you but I know a website that would help you better and I don't feel like opening my laptop but desmos would be great for this if you don't already use it
Step-by-step explanation:
But you put the (2,4) in a box and the (-6,5) in another box and the answer will be where they connect like in and x
What value of x makes the equation 5(4x - 1)=4(2.5x+8) true?
need help asap ?
Answers
Answer:
37/10
( I hope this was helpful) >;D
Joseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.
A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.
8 squared + 12 squared = d squared. 64 + 24 = d squared. 88 = d squared. StartRoot 88 EndRoot = d. 9.4 almost-equals d.
She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
She did not square the 12 in the problem. She should have used 12 squared = 144.
She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 44.
She should not have taken the square root of each side when solving. She should have just divided each side by 2.
She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
Answers
For this case the distance will be given by:
d ^ 2 = (12 * 1.5) ^ 2 + (8 * 1.5) ^ 2
Rewriting we have:
d ^ 2 = (18) ^ 2 + (12) ^ 2
d ^ 2 = 324 + 144
d ^ 2 = 468
d = root (468)
d = 21.63 Km
Answer:
1) She did not find the full distance each traveled in 1.5 hours.
2) She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance.
Answer:
a and b
Step-by-step explanation:
can someone help me please ❤️
Answers
Answer:314
Step-by-step explanation:
V=pi r squared
V= 3.14x10 squared
10 squared= 100
V=3.14x 100
V= 314
Whats the answer to this?
Answers
Step-by-step explanation:
area of figure = 5x² + 3
plz mark my answer as brainlist plzzzz.hope this will be helpful to you if you find it useful ☺️
How many degrees is angle x?
Answers
Answer
127
Step-by-step explanation:
First add 42 and 85. Then do 180-(42+85) to get w. Then do 180-w to get x as a line always equals 180
NEED HELP ! PLEASE HELP ASAP !
Answers
Answer:
distance between points is 5.6568...
when you round it will be 5.7
answer is 5.7
Step-by-step explanation:
find the distance between two points using distance formula
true or false: the diagonals of a rectangle bisect opposite angles
Answers
Answer:
False
Step-by-step explanation:
diagonals don't have to be congruent or bisect each other. The diagonals of a rectangle bisect its angles.
Use your knowledge of special cases to solve the problem.
( 3a - 2b )2 = ??
a) 9a^2 + 12ab + 4b^2
b)9a^2 - 4b^2
c)9a^2 - 12ab + 4b^2
Answers
Answer:
C
Step-by-step explanation:
We want to simplify:
[tex](3a-2b)^2[/tex]
Recall the perfect square trinomial pattern:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Let a = 3a and b = -2b. Thus:
[tex](3a-2b)^2=(3a)^2+2(3a)(-2b)+(-2b)^2[/tex]
Simplify:
[tex]=9a^2-12ab+4b^2[/tex]
Our answer is C.
Part C: If HI = 7, find KL. Show your work.
Answers
Answer:
KL= 14
Step-by-step explanation:
4*2=8
5*2=10
7*2=14
Pythagorean therom HELPOP
Answers
Answer:
its 12
Step-by-step explanation:
1. Se dispara una bala de 10grbcon una velocidad de 500m/s contra un muro de 10cm de espesor. Si la resistencia del muro al avance de la bala es de 3000 N, calcula la velosidad calcula la velocidad de la bala después de atravesar el muro. 2. Un automóvil de 1000kg de masa aumenta su velosidad de 0 a 100 km/h en un tiempo mínimo de 8s calcula su potencia en watios y en caballos de vapor. Dato : 1cv = 735w. 3. Desde una altura de 10m deja caer un cuerpo de 5kg. Calcula su velocidad al llegar al suelo
Answers
Answer:
1) La velocidad de la bala después de atravesar el muro es de aproximadamente 435,890 metros por segundo.
2) La potencia del automóvil es 96438,272 watts o 131,208 caballos de vapor.
3) La velocidad del objeto al llegar al suelo es aproximadamente 14,005 metros por segundo.
Step-by-step explanation:
1) La velocidad final de la bala puede determinarse mediante el Teorema del Trabajo y la Energía, a partir del cual se tiene la siguiente fórmula:
[tex]\frac{1}{2}\cdot m\cdot v_{o}^{2} -F\cdot \Delta s = \frac{1}{2}\cdot m \cdot v_{f}^{2}[/tex] (1)
Where:
[tex]m[/tex] - Masa de la bala, en kilogramos.
[tex]v_{o}, v_{f}[/tex] - Velocidades inicial y final de la bala, en metros por segundo.
[tex]F[/tex] - Resistencia del muro al avance de la bala, en newtons.
[tex]\Delta s[/tex] - Espesor del muro, en metros.
Si sabemos que [tex]m = 0,01\,kg[/tex], [tex]v_{o} = 500\,\frac{m}{s}[/tex], [tex]F = 3000\,N[/tex] and [tex]\Delta s = 0,1\,m[/tex], entonces la velocidad final de la bala es:
[tex]v_{f}^{2}=v_{o}^{2} -\frac{2\cdot F\cdot \Delta s}{m}[/tex]
[tex]v_{f} = \sqrt{v_{o}^{2}-\frac{2\cdot F\cdot \Delta s}{m} }[/tex]
[tex]v_{f} \approx 435,890\,\frac{m}{s}[/tex]
La velocidad de la bala después de atravesar el muro es de aproximadamente 435,890 metros por segundo.
2) Asumamos que el automóvil acelera a tasa constante, significando que la fuerza neta será constante. Para un sistema cuya fuerza neta sea constante, la potencia experimentada queda descrita por la siguiente ecuación:
[tex]P = m\cdot a(t)\cdot v(t)[/tex] (2)
[tex]a(t) = a[/tex] (3)
[tex]v(t) = v_{o} + a\cdot t[/tex] (4)
Donde:
[tex]P[/tex] - Potencia, en watts.
[tex]m[/tex] - Masa del automóvil, en kilogramos.
[tex]a(t)[/tex] - Aceleración, en metros por segundo al cuadrado.
[tex]v(t)[/tex] - Velocidad, en metros por segundo.
[tex]v_{o}[/tex] - Velocidad inicial del automóvil, en metros por segundo.
Si sabemos que [tex]m = 1000\,kg[/tex], [tex]a = 3,472\,\frac{m}{s}[/tex], [tex]v_{o} = 0\,\frac{m}{s}[/tex] y [tex]t = 8\,s[/tex] entonces la potencia experimentada por el automóvil es:
[tex]P = 96438,272\,W[/tex] ([tex]131,208\,C.V.[/tex])
La potencia del automóvil es 96438,272 watts o 131,208 caballos de vapor.
3) El cuerpo experimenta un Movimiento de Caída Libre, el cual es un Movimiento Uniformemente Acelerado debido a la gravedad terrestre. La velocidad del cuerpo al llegar al suelo se determina mediante la siguiente fórmula cinemática:
[tex]v_{f} = \sqrt{v_{o}^{2}+2\cdot g\cdot h}[/tex] (5)
Donde:
[tex]v_{o}[/tex] - Velocidad inicial del cuerpo, en metros por segundo.
[tex]v_{f}[/tex] - Velocidad final del cuerpo, en metros por segundo.
[tex]g[/tex] - Aceleración gravitacional, en metros por segundo al cuadrado.
[tex]h[/tex] - Altura recorrida por el cuerpo, en metros.
Si sabemos que [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]g = 9,807\,\frac{m}{s^{2}}[/tex] y [tex]h = 10\,m[/tex], entonces la velocidad al llegar al suelo es:
[tex]v_{f} \approx 14,005\,\frac{m}{s}[/tex]
La velocidad del objeto al llegar al suelo es aproximadamente 14,005 metros por segundo.
Find the perimeter of the figure.
Answers
Answer:
24 in
Step-by-step explanation:
Perimeter = 9 + 5 + 1 + 5 + 4 = 24 in
Hope that helps!
Which angles are vertical angles?
2 and 4
1 and 5
2 and 5
2 and 3
Answers
En un estudio estadistico se van a usar unicamente variables cuantitativas discretas para ingresarlas a un programa de analisis estadistico. la variable que se debe ingresar en el programa corresponde a: a nacionalidad b nivel de escolaridad c edad d altura
Answers
Answer:
la variable que se debe ingresar en el programa corresponde a: c. edad
Step-by-step explanation:
Las variables cuantitativas son aquellas que toman valores numéricos y se clasifican en variables cuantitativas discretas que son las que sólo pueden asumir un número limitado de valores en un determinado rango, como por ejemplo, el número de carros que posee una persona y variables cuantitativas continuas que pueden tomar cualquier valor en un rango específico, como por ejemplo, el peso de un objeto. De acuerdo a estas definiciones, la respuesta es que la variable que se debe ingresar en el programa corresponde a: edad porque es una variable discreta dado que se registra en números enteros y no acepta cualquier valor en un intervalo específico.
Las otras opciones no son correctas porque la nacionalidad y el nivel de escolaridad no son variables cuantitativas y la altura es una variable cuantitativa continua.
I need help? anyone know the answer?
Answers
Answer:
the answer you are looking for is B
Lexi and Ann went shopping. Ann wondered how much tax she would have to pay on her purchase of $76. Lexi said, "They just charged me $17 in taxes when I bought these outfits for $200." How much will Ann pay in taxes?
Answers
Ann will pay in taxes on her purchase of $76, if Lexi paid a charge of $17 in taxes when she bought these outfits for $200, is $6.46.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
Lexi paid a charge of $17 in taxes when I bought these outfits for $200,
Calculate the charge in one dollar = 17 / 200
Now, calculate the charge for $76 dollar = 17 / 200 × 76
The charge for $76 dollar = $6.46
To know more about division:
https://brainly.com/question/27566440
#SPJ2
Out of the 400 students surveyed,
-how many more students chose Mr.
Crosby than Ms. Smokey?
Favorite Teacher
Answers
Answer:
60 more students
Step-by-step explanation:
400 × 0.3 (30%) = 120
400 × 0.15 (15%) = 60 = 120÷2
120 -- 60 = 60
60 more students
brainliest plz if someone else answers
Sarah drove 420 miles in 6 hours. Jonathan drove the same distance going an average of 60 miles per hour throughout the entire trip.
Who was driving faster and by how much?
Answers
Answer:
Sarah was driving faster by 10 mph.
She was driving 70 miles per hour while Jonathan was only driving 60 miles per hour.
Pls help o have to return this today
Answers
Answer:
Which part of the story's plot structure does this sentence illustrate? I think its B. Climax
Wayne types about 50 words per minute.A typical double spaced page contains 500 words.how long doe sit take Wayne to type 8 1/2 pages?
Answers
Answer:
Step-by-step explanation:
50t=500(8.5)
t=10(8.5)
t=85 minutes
Answer: 85 minutes
Step-by-step explanation:
First, find how many minutes it takes for Wayne to type a page containing 500 words. 500/50= 10 minutes
You then multiply that by 8
8(10)= 80 minutes to type 8 pages.
Now find how many words are in half a page.
500/2=250 words
Divide that by the amount of words Wayne can type per minute. 250/50= 5
Add that to the amount of minutes it took to type 8 pages. 85 minutes
Which is also 1 hour 25 minutes
If Lucas runs 5 miles in 38 minutes, what is his unit rate per minute?
Answers
Answer:
1 mile every 7.6 min
Step-by-step explanation:
Answer:
7.6 minutes per mile
Step-by-step explanation:
38 divided by 5 equals to 7.6
WILL GIVE BRAIN FIND THE UNKNOWNS TYSM!!!!
Answers
Answer:
if i'm correct you either divide the two numbers you have to get the answer or you multiply them to get the answer
Step-by-step explanation:
108 divided by 92
or
108 x 92
The graph shows a line and two similar triangles. What is the equation of the line? y = 3 x y = one-third x y = one-third x + 2 y = 3 x + 2
Answers
CONCEPTO
Una ecuación es una igualdad matemática entre dos expresiones, denominadas miembros y separadas por el signo igual, en las que aparecen elementos conocidos y datos desconocidos o incógnitas, relacionados mediante operaciones matemáticas
------------------------------------------------------------------------Igualdad entre dos expresiones que contiene una o más variables."ecuación de segundo grado"Igualdad o paralelismo entre dos o más cosas.Select the end behavior of the exponential function shown in the graph
Answers
Answer:
The x graph
Step-by-step explanation:
The x graph
Answer: D
Step-by-step explanation: