Answers
Given:
A figure of a circle. [tex]KJ=6,KL=x-2,ML=4[/tex].
To find:
The length of KJ.
Solution:
From the given figure it is clear that the number 6 is marked between K and J it means the number 6 represents the distance between the points K and j.
Therefore, the length of KJ is 6 units.
Note: In the given question we need to find KL instead of KJ because KJ is already given.
According to the tangent secant theorem:
[tex]a^2=bc[/tex]
Where,
a is the length of the tangent.b is the length of the external segment of the secant.c is the measure of the secant.Using the tangent secant theorem, we get
[tex]ML^2=KL\times JL[/tex]
[tex](4)^2=(x-2)\times (6+x-2)[/tex]
[tex]16=(x-2)\times (4+x)[/tex]
[tex]16=4x+x^2-8-2x[/tex]
On further simplification, we get
[tex]16=x^2+2x-8[/tex]
[tex]0=x^2+2x-8-16[/tex]
[tex]0=x^2+2x-24[/tex]
Splitting the middle term, we get
[tex]x^2+6x-4x-24=0[/tex]
[tex]x(x+6)-4(x+6)=0[/tex]
[tex](x+6)(x-4)=0[/tex]
[tex]x=-6,4[/tex]
For [tex]x=-6[/tex],
[tex]KJ=-6-2[/tex]
[tex]KJ=-8[/tex], which is not possible because side cannot be negative.
For [tex]x=4[/tex],
[tex]KJ=4-2[/tex]
[tex]KJ=2[/tex]
Therefore, the measure of KL is 2 units.
Related Questions
For whole numbers between 1 and 1001, inclusive, let m be the sum of odd numbers and n be the sum of even numbers. What is the value of m−n?
Answers
Answer:
m - n = 501
Step-by-step explanation:
Remark
The first thing you have to do is find the number of odd and even numbers. This is where you have to be careful because there is a danger of being out by one.
equation
l = a + (n - 1)*d
Solution even
l = 1000
a = 2
d = 2
1000 = 2 + (n - 1)*2
998/2 = (n - 1) * 2 / 2
499 = n - 1
n = 500
Solution odd
l = 1001
a = 1
d = 2
1001 = 1 + (n - 1)*2
1000 = (n - 1)*2
1000/2 = (n - 1)2/2
500 = n - 1
501 = n
Sum Even of even numbers from 1 to 1001
Givens
a = 2
n = 500
l = 1000
Equation
Sum = (a + l ) * n / 2
Solution
Sum = (2 + 1000)*500/2
Sum = 1002 * 250
Sum = 250500
Sum of Odd numbers from 1 to 1001
a = 1
l = 1001
n = 501
Equation
sum = (a + l)*n/2
sum = (1 + 1001) * 501
sum = (1002)*501 / 2
Sum = 251001
Answer
m - n = 251001 - 250500 = 501
A function y(t) satisfies the differential equation dy dt = y4 − 10y3 + 24y2. (a) What are the constant solutions of the equation? (Enter your answers as a comma-separated list.) y = (b) For what values of y is y increasing? (Enter your answer in interval notation.) y (c) For what values of y is y decreasing? (Enter your answer in interval notation.) y
Answers
Answer:
[tex](a)\ y =0\ or\ y=4\ or\ y=6[/tex]
[tex](b) \ (-\infty,4)\ u\ (6,\infty)[/tex]
[tex](c)\ (4,6)[/tex]
Step-by-step explanation:
Given
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
Solving (a): The constants
This implies that:
[tex]\frac{dy}{dt} = 0[/tex]
So, we have:
[tex]y^4 - 10y^3 + 24y^2 = 0[/tex]
Factorize:
[tex]y^2(y^2 - 10y + 24) = 0[/tex]
Expand and Factorize the expression in bracket
[tex]y^2(y^2 - 6y - 4y + 24) = 0[/tex]
[tex]y^2(y(y - 6) - 4(y - 6)) = 0[/tex]
[tex]y^2(y - 4)(y - 6) = 0[/tex]
Split
[tex]y^2 =0\ or\ y-4=0\ or\ y-6=0[/tex]
Solve for y
[tex]y =0\ or\ y=4\ or\ y=6[/tex]
The above represents the constants
Solving (b): Increasing values
Here
[tex]\frac{dy}{dx} > 0[/tex]
Follow the same process in (a) but replace all = with >
i.e.
[tex]y^2(y - 4)(y - 6) > 0[/tex]
[tex]y >0\ or\ y>4\ or\ y>6[/tex]
Test the values of each inequality
For [tex]y > 6[/tex]; say [tex]y = 7[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 7^4 - 10*7^3 + 24*7^2[/tex]
[tex]\frac{dy}{dt} = 147[/tex]
[tex]147 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]; This implies that: [tex](6, \infty)[/tex]
For [tex]y > 4[/tex] Say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is false:
Say [tex]y = 3[/tex] i.e. [tex]y < 4[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
[tex]27 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that: [tex](0,4)[/tex]
For [tex]y > 0[/tex]
[tex]y > 0[/tex] implies that: [tex]y < 4[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that [tex](-\infty, 0)[/tex]
We have: [tex](-\infty,0), (0,4)\ and\ (6,\infty)[/tex]
[tex](-\infty,0)\ and\ (0,4)[/tex] can be combined to give: [tex](-\infty,4)[/tex]
So, the interval is: [tex](-\infty,4)\ u\ (6,\infty)[/tex]
Solving (c): Decreasing values
Here
[tex]\frac{dy}{dx} < 0[/tex]
i.e.
[tex]y^2(y - 4)(y - 6) < 0[/tex]
[tex]y <0\ or\ y<4\ or\ y<6[/tex]
Test the values of each inequality
For [tex]y < 6[/tex]; say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is true for [tex]\frac{dy}{dx} < 0[/tex]; This implies that: [tex](\infty,6)[/tex]
For [tex]y < 4[/tex]; say [tex]y = 3[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
This is false
Say [tex]y = 5[/tex] i.e. [tex]y > 4[/tex]
This is the same as: [tex]y < 6[/tex]
So, we have the interval to be: [tex](4,\infty)[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is false
Say [tex]y = 2[/tex] i.e [tex]y > 0[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 2^4 - 10*2^3 + 24*2^2[/tex]
[tex]\frac{dy}{dt} = 32[/tex]
This is also false
So, the intervals are: [tex](4,\infty)[/tex] and [tex](\infty,6)[/tex].
This can be merged as: [tex](4,6)[/tex]
Hence, the interval for [tex]\frac{dy}{dt} < 0[/tex] is [tex](4,6)[/tex]
Six years ago Matt was four times as old as Brown, and in 3 years the sum of their
ages will be 43 years. Find their present ages.
Answers
Answer:
Matt=26
Brown=11
Step-by-step explanation:
Just trust me!!!
The present age of Matt given the information in the question is 26.
The present age of Brown given the information in the question is 8.
What are the linear equations that represent the question?4y - 6 = x equation 1
x + y + 6 = 43 equation 2
Where:
x = Matt's agey = Brown's ageWhat is Brown's age?Subsistute for x in equation 2
4y - 6 + y + 3 = 43
Combine similar terms
5y = 40
y = 8
What is Matt's age?
Subsitute for y in equation 1
4(8) - 6 = x
32 - 6 = 26
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
twenty subtract from 28
Answers
Answer:
8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
20-28= -8
MUST HELP!!!! (+50 POINTS +BRANILEST +5 STARS +THANKS ON PROFILE)
Answers
Answer:
Personification is your answer.
Hope it helps!!!
PLEASE HELp ME U GET ALOT OF POINTS 97points
circumference and Area of circles
7. Demi measured the wheels on her brother's wagon. The diameter of each
wheel is 15 inches. To the nearest inch, how far will the wagon travel each
time the wheels make a complete turn?
8.The radius of circle A is 6 ft. The diameter of circle B is 6 ft. To the nearest
foot, how much greater is the circumference of circle A as compared to the circumference of circle B?
9. The larger circle in the design at the right has a radius of 40 in.
What is the area of the shaded part of the design?
30 in.
10. Max knows that the circumference of a circular pool is 12 ft.
He estimates that the diameter of the pool is between 3 ft and 4 ft. Is this reasonable? Explain.
Answers
Answer:
#7
C = πd = 3.14*15 in = 47 in (rounded)#8
C₁ = 2πr = 2*3..14*6 ft = 37.68 ftC₂ = πd = 3.14*6 ft = 18.84 ftThe difference:
C₁ - C₂ = 37.68 - 18.84 = 19 ft (rounded)#9
No picture attached#10
C = 12 ftd = C/πd = 12/3.14 = 3.82 ft3 ft < 3.82 ft < 4 ftMax is right
The cost of an item is $75. What will the total cost be with 9% tax?
Answers
Answer:
81.75
Step-by-step explanation:
75*1.09 = 81.75
Answer:$81.75
Step-by-step explanation:
9% of 75 is 6.15, add that to 75 and the answer is 81.75
You are constructing a concrete landing pad for a helicopter. You have 4704 cubic feet of concrete
If the landing pad is a square that is 56 feet on each side, how thick will the pad be
The pad will be feet thick
If you want to use the concrete to build a circular landing pad with the same thickness as the square landing pad, what would the diameter of that landing pad be?
The diameter will be feet
(Use 3.14 for pi Round the answer to the nearest hundredth)
Answers
Answer:
Round it to the nearest hundredth
Step-by-step explanation:
PLEASE HURRY! FIRST PERSON GETS BRAINLIST!!!!!!
Hank is throwing a surprise party. The party costs $20 per person. Create an equation and graph to represent the relationship between the cost of the party and the number of friends attending.
The independent variable is ____.
A. Number of friends (f)
B. Cost of party (c)
Answers
Answer:
B
Step-by-step explanation:
I NEED HELP PLEASE ASAP!
Answers
Answer:
Step-by-step explanation:
David invests $7000 in two different accounts. The first account paid 2 %, the second account paid 5
% in interest. At the end of the first year he had earned $182 in interest. How much was in each
account?
Answers
Answer:
3,990
Step-by-step explanation:
Choose the THREE expressions that represent quadratic functions.
Answers
Answer:
3 / 5 and 6 options
Step-by-step explanation:
A quadratic function has the form
an² + bn + c ( a ≠ 0 )
From the given table
n² + 1 ← is in this form ( 3rd option )
n(n + 4)
= n² + 4n ← is in this form ( 5th option )
n(n + 6) + 2
= n² + 6n + 2 ← is in this form ( 6th option )
Solve for the following by
FACTORING:
x2 + 15x + 56 = 0
Answers
Answer:
17x + 56 = 0
Step-by-step explanation:
add 2x and 15x
1. Find the slope of the graph. Slope:
Answers
Answer:
I think the answer is 5 down and over to the left 3.
Step-by-step explanation:
I just counted from the point on the (4,3) and counted down until it was line up with the other point. Next, I counted from there to the other point.
A box contains 3 black pens, 7 blue pens and 5 red pens. Without replacing the first pen,
what is the probability of pulling a red or blue pen?
Answers
Answer:12/15
Step-by-step explanation: first you add 7+5=12
then add 12+3=15
Which of the following is NOT an example of a right angle?
Ο Α.The corner of a door
O B.The corner of a book
C.The point of a pencil
D.The corner of a piece of notebook paper
Answers
Answer:
The point of a pencil
Step-by-step explanation:
all other three mesure 90 the point of pencil is not square shape in order for it to be right angle its gotta be square shape hope this helps! may i be marked brainliest?
Can you help me thanks!
Answers
Can someoneee please help me
Answers
9514 1404 393
Answer:
37°
Step-by-step explanation:
The diagonals of a rhombus are angle bisectors. Angle 1 matches the other half of angle L.
∠1 = 37°
__
Angle 2 is the complement, 53°, and angle 3 is the same as angle 2, 53°.
The diagonals of a rhombus are perpendicular bisectors of each other, so angle 4 is 90°.
Pls help me solve this
Answers
−8≤2/5(k−2) negative 8 is greater than/equal to 2/ fifths (k minus 2)
Answers
Answer:60
Step-by-step explanation:
You moved 7 units left, 8 units up, and ended at point W
Where did you begin?
OA) (1.8)
OB) (9.1)
OC) (81)
OD) (9.8)
Please help me I’m tired
Answers
Answer:
C. (8,1)
Step-by-step explanation:
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9 What is the confidence interval for the population mean μ? <μ
Answers
Answer:
Confidence Interval = ( 5.6 < μ < 8.2 )
The interval shows that the mean attractiveness is Above average on a scale of 1 to 10
Step-by-step explanation:
Data Given : 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9
a) construct a confidence interval at a 95% confidence level
confidence interval = x ± tcritical ( s / √ n ) ------ ( 1 )
n = 12
μ (mean) = ( 5+8+2+8+7+6+6+8+9+9+6+9 ) / 12 ≈ 6.92
std ( s ) = √ 1/11 *∑( xi- X )^2
= √ 1/11 * ( 5 - 6.92)^2 + ( 8 - 6.92)^2 + ( 2 - 6.92)^2 + ( 8 - 6.92)^2 + ( 7-6.92)^2 + ( 6 - 6.92)^2 + (6 - 6.92 )^2 + ( 8 - 6.92 )^2 + ( 9 - 6.92)^2 + ( 9 - 6.92)^2 + ( 6 - 6.92 )^2 + ( 9 - 6.92 )^2
= √ 1/11 * 46.92 = 2.07
tcritical at ∝ 0.05 , df = 11 = 2.20
Back to equation 1
6.92 ± 2.2 ( 2.07 / √ 12 )
( 6.92 ± 1.31 )
Confidence Interval = ( 5.6 < μ < 8.2 )
Jamie placed $2800 in a savings account which earns 4.3% interest, compounded continuously. How much will she have in the account after 9 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answers
Answer:
4123
Step-by-step explanation:
A=Pert,
where A is the balance of the account, P is the principal, r is the annual interest rate (as a decimal), and t is the time (in years). We are given that P=2800, r=0.043, and t=9. Substituting the values into the formula and using a calculator to evaluate, we find
A=Pert=2800e(0.043)(9)≈4123.16
find the HCF of 12;28 and 32
Answers
Answer:
4
Step-by-step explanation:
28 = 22 • 7
12 = 22 • 3
32 = 25
The measure of angle ABC is 84, find the measure of angle ADC.
Answers
Answer:
Step-by-step explanation:
uhhh i think so its 84 is abc but adc is missing try 48 i dont know but i try
What is the range of the function on the graph?
Answers
Range is the output values which are the y values.
The dot is at y = 2 and the line moves upward to the right off the graph. This means the line will continue to infinity.
The range would be 2 to infinity.
(2, infinity)
Find the derivative of f(x) = -12x2 + 9x at x = 6.
a) -112.5
b)-135
c)90
d)108
Answers
hi
f(x) = -12x²+9x
So
f'(x) = -24x +9
if x = 6 then f'(6) = -24 (6) +9 = -135
Carl paid $40 for 12.5 gallons of gas.After calculating,he said that the cost per gallon was about 31 cents per gallon.Is there anything wrong with Carl's thinking?.
Answers
Answer:
Well yes, because it should have cost $3.2 PER gallon
Step-by-step explanation:
Divide 40 by 12.5 to find out how much of a per gallon costs! Hope it helps.
Answer Choices
A. -0.01
B. 2
C. 0.01
D. 10,000
Answers
Answer:I hink its B if its not im sorry
Step-by-step explanation:
9.3+b=−42 , you would subtract 9.3 to isolate the variable.
Answers
Answer:
yeh you are correct so it will be b is equal to minus 42 minus 9.3 that will be equal to -51.3 so that is the value of b