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
If (x²- 4) = (x + 2) = x - 2, which polynomial should fill in the blank below?
(x + 2)x____= x² - 4
O x² – 4
OX-2
O x + 2
O x²-2
Answers
Answer:
x-2
Step-by-step explanation:
(x+2)× ___=(x+2)(x-2)
___=(x+2)(x-2)/(x+2)
___=x-2
The polynomial which should be filled in the blank is (x - 2).
What are Polynomials?Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
Given that,
x² - 4 = (x + 2) (x - 2).
We have to find the blank space.
By commutative property, the other side is also equal.
That is,
(x + 2) (x - 2) = x² - 4
Hence the correct option is (x - 2).
Learn more about polynomials here :
https://brainly.com/question/11536910
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Find the distance between (8,5)(-1,3). Round your answer to the nearest tenth.
Answers
Answer: 9.2
Step-by-step explanation:
d = sqrt ((x2-x1)^2 (y2-y1)^2)
d = sqrt (85)
d = 9.219544
need help ASAP !!!
[tex] \sqrt{88 \times 11 \times 2 \times 4} [/tex]
Answers
Answer:
√(88×11×2×4}=√88²=±88 is your answer
Answer:
[tex]±88.[/tex]
Step-by-step explanation:
[tex]= \sqrt{88 \times 88} [/tex]
[tex] = \sqrt{ {88}^{2} } [/tex]
[tex]±88[/tex]
Determine the slope of the line.
Answers
Answer:
what line?
Step-by-step explanation:
Make the Fraction into a Decimal square route 81 over 100
Answers
Answer: 0.9
Step-by-step explanation:
Sqrt 81 is 9
over 10 is 9/10
which is 0.9
Please Help ill mark as brainiest
Answers
Answer:
Step-by-step explanation:
Price at the end of 1 month = $59 ⋅ 1.03 = $60.77
The temperature of chicken soup is 192.7°F. As it cools, the temperature of the soup decreases 2.3°F per minute. What is the temperature in degrees Fahrenheit of the soup after 25 minutes?
Answers
Answer: 135.2 °F
Step-by-step explanation:
The temperature decreases at a rate of 2.3 °F per minute.
This means that in 25 minutes, the temperature would have reduced by:
= 2.3 * 25
= 57.5°F
If the original temperature was 192.7 °F, the temperature after 25 minutes will be:
= 192.7 - 57.5
= 135.2 °F
NEED HELP ASAP WILL GIVE BRAINLY
Answers
Answer:
B = 240/h
Step-by-step explanation:
5 is what percentage of 10 question: now do I divide 5 divided by 10 equals 0.5 then do I multiply 0.5 by 100 or divide 0.5 by 100?
Answers
Answer:
50%
Step-by-step explanation:
5 question is what percentage of 10 question
Step 1: Divide 5 by 10
5/10 = 0.5
Step 2: multiply 0.5 by 100
0.5 × 100
= 50%
Therefore, percentage of 5 questions out of 10 questions is 50%
Answer:
50%
Step-by-step explanation:
5 is half of 10
50 is half of 100
HELP HELP PLEASE!! D:
Find the length of the missing side of the trapezoid below:
PLEASE NO CAP!!
Answers
both sum of three consecutive integers is 108 what are the three integers
Answers
Answer:
35 , 36 , 37
Step-by-step explanation:
Let the consecutive integers be x, (x + 1) , (x +2)
x + x + 1 + x +2 = 108
x + x + x + 1 + 2 = 108 {Combine like terms}
3x + 3 = 108 {Subtract 3 from both sides}
3x = 108 - 3
3x = 105 {Divide both sides by 3}
x = 105/3
x = 35
The three integers are, 35 , 36 , 37
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
Solve for n. -4(n+5)=8
Answers
Answer:
Simplify first:
-4n - 20 = 8
Add 20 to both sides:
-4n = 28
Divide by -4:
Therefore you will get:
n = -7
Answer:
n = -7.
Step-by-step explanation:
-4(n + 5) = 8
-4n - 20 = 8
-4n = 28
n = -7.
I WILL GIVE BRAINLIEST!!!
NO SENDING ME LINKS!!!
Answers
5.) Find the area of the triangle in bold.
Answers
Answer:
the answer is 0.98
Step-by-step explanation:
if it not correct plz correct me
Answer:
.975 mi²
Step-by-step explanation:
Hello There!
Formula for area of a triangle [tex]A =\frac{1}{2}bh[/tex]
where b = base and h = height
the dimensions of the triangle shown are b = 1.5 and h = 1.3
given the dimensions all we have to do is plug in the values into the formula
so
[tex]A=\frac{1}{2} 1.3*1.5\\1.3*1.5=1.95\\\\\frac{1.95}{2} =0.975[/tex]
so we can conclude that the area of the triangle is
.975 mi²
Can someone please answer this question. If I get it right this is hopefully the last question I’ll be posting for the rest of the day
Answers
Answer:
53°
Step-by-step explanation:
not sure what you mean by nearest degree but use the cosine ratio to get the answer.
in ΔCDE we have the hypotenuse and adjacent side so use cosine ratio : cos C= 45/75
<C=cos^1 (45/75)
<C= 53°
7/12 minus 1/6 gggggggggggggggggggg
Answers
Answer:
[tex] \frac{5}{12} [/tex]
Step-by-step explanation:
[tex] \frac{7}{12} - \frac{1}{6} \\ \\ = \frac{7}{12} - \frac{2}{12} \\ \\ = \frac{7 - 2}{12} \\ \\ = \frac{5}{12} [/tex]
Answer:
0.41666666666
or
5/12
Step-by-step explanation:
The vertex form of the equation of a parabola is y = (x+ 3)2 + 53.
What is the standard form of the equation?
Answers
Answer:
y = 2x² + 12x + 71
Step-by-step explanation:
Help pls and thank you :)
Answers
As a first step in developing a new drug to treat cancer in humans, an initial study of the drug is undertaken in rats. Three hundred rats with cancer are studied, and each is assigned to one of three treatments. One hundred rats are randomly assigned to a high dose of the new drug, 100 are randomly assigned to a low dose, and 100 are randomly assigned to a control group (no drug). After six months, each rat is examined and classified as having developed no tumors, one tumor, or two or more tumors.Which of the following would be an appropriate alternative hypothesis in this study for a chi-square test for homogeneity of tumor response across treatments?A. Ha :Ha : There is no difference in the distribution of tumor status across the three treatments.B. Ha :Ha : There is a difference in the distribution of tumor status across the three treatments.C. Ha :Ha : There is no association between tumor status and treatment.D. Ha :Ha : There is an association between tumor status and treatment.E. Ha :Ha : The proportion of rats with no tumors is the same for each treatment group.
Answers
Solution :
Here, we are interested to study if the treatments have any effect on going tumor or not. Actually, this is model is an ANOVA one way layout with a treatment 'drug'.
In this kind of model or ANOVA model, we take the negative statement as our null hypothesis i.e.,
[tex]$H_0:$[/tex] There is no difference in the distribution of tumors states across the three statements.
Therefore, alternative hypothesis would be :
[tex]$H_a:$[/tex] There is a difference in the distribution of tumor states across the three treatments.
So the correct option is (B).
f(x)=9x+3 find f(5).
Answers
Answer:
48
Step-by-step explanation:
f(x)=9x+3
f(5)=9(5)+3
f(5)=45+3
f(5)=48
b) Select all expressions that can be used to find 85% of 280.
A.
8.5
10
280
B.
0.85
100
280
C.
85
100
280
Answers
Answer:
238
85%of 280 is 238
Step-by-step explanation:
hope this helps
3) A 24 foot wire is attached to an electrical pole. If the pole is 20 feet tall, how
far is the wire sitting from the base of the pole? Round answers to the nearest
tenth of a foot.
9ned
WIRE
SASE
A) 312
B) 133
C) 176
OD) 132
HELLPP PLEASEEE
Answers
Answer:
13.3 feet
Step-by-step explanation:
This question can be solved using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length = 20
b = base
c = diagonal = 24
24^2 = 20^2 + b^2
576 = 400 + b^2
b^2 = 176
b = 13.3
11) Nick & John ordered burritos & tacos for lunch. Nick
ordered 3 burritos & 4 tacos for $11.33. John ordered 9
burritos & 5 tacos for $23.56. Find the cost of one
burrito & one taco.
Answers
Answer:
taco: $1.49 each
burrito: $1.79 each
Step-by-step explanation:
Let b = cost of one burrito
t = cost of one taco
(1) 3b + 4t = 11.33 (2) 9b + 5t = 23.56
Multiply (1) by -3 and add to (2) -9b - 12t = 33.99
- 7t = - 10.43
t = 1.49
3b + 4(1.49) = 11.33
3b + 5.96 = 11.33
3b = 5.37
b = 1.79
Select all the values of x that make x + 3 > 5 true.
Answers
Answer:
D AND E
Step-by-step explanation:
The value of a bank account, B, after x years is represented by the equation B = 1000(1+.014)x. To the nearest penny, how much is the account worth after 15 years?
Answers
Answer:
your mom
Step-by-step explanation:
you mom
Please its really urgent, step by step working out
Answers
Answer:
70.99
Step-by-step explanation:
Use Pythagorean Theorem to find the shortest distance.
80^2-50^2=3900
Square rt= 62.44
Subtract by 15
47.44
Next find half of the circular path it is (3.14 x 15)/2
23.55
Add 47.44+23.55=70.99
Hope this is correct
PLEASE HELP DUE AT MIDNIGHT!
Answers
Answer:
60 i think
Step-by-step explanation:
109-180= 71
u=71
71+49=120
120-180=60
109 is on a straight line with an interior angle of a triangle, so 180 - 109 = 71 degrees.
Add two known interior angles (71 + 49) together and you get 120 degrees.
Subtract 120 from 180 (since 180 is the sum of all three interior angles of a triangle) and you get 60 degrees.
Answer: ∠ULE is 60 degreesSolve the equation.
2t – 5 = -10
t
Answers
Answer: (2t - 5) • (t - 1) - 2 = 0
t=3
Step-by-step explanation:
2t-5=-10t
T=5/12
In decimal 0.416
Hope this helps
24 less than the number of snakes is 35.