Given: PK and PF tangent to circle k(O) K and F points of tangency
Prove: m∠P=m∠EK
Answers
Answer:
See explanation
Step-by-step explanation:
If PK and PF are tangent to the circle, then the radii OK and OF are perpendicular to the lines PK and PF respectively.
Consider quadrilateral PFOK. The sum of the measures of all interior angles in quadrilateral PFOK is equal to 360°. Since OK and OF are perpendicular to the lines PK and PF, you have that
∠FOK+90°+∠KPF+90°=360°,
∠FOK=360°-90°-90°-∠KPF=180°-∠KPF.
Angles FOK and KOE are supplementary angles, then
∠KOE=180°-∠FOK=180°-(180°-∠KPF)=∠KPF.
Since angle KOE is central angle, the arc EK has the same measure as angle KOE and as angle KPF.
Given [tex]\(PK\) and \(PF\)[/tex] tangents to circle [tex]\(O\),[/tex] angles [tex]\( \angle P \) and \( \angle EK \)[/tex] are equal by the properties of tangents.
To prove that [tex]\( m\angle P = m\angle EK \)[/tex] given the diagram, we can use properties of tangents and circles. Here is a step-by-step proof:
1. Identify the given information:
- [tex]\( PK \) and \( PF \)[/tex] are tangents to circle [tex]\( k(O) \) at points \( K \) and \( F \),[/tex] respectively.
- [tex]\( O \)[/tex] is the center of the circle.
- [tex]\( PK \) and \( PF \)[/tex] are tangent to the circle, meaning they touch the circle at exactly one point.
2. Use properties of tangents:
- A tangent to a circle is perpendicular to the radius at the point of tangency.
- Thus, [tex]\( OK \perp PK \) and \( OF \perp PF \).[/tex]
3. Mark the right angles:
[tex]- \( \angle OKP = 90^\circ \)[/tex]
[tex]- \( \angle OFP = 90^\circ \)[/tex]
4. Connect the points to form a triangle:
- Draw the line segment [tex]\( OP \).[/tex]
5. Use the exterior angle theorem:
- In [tex]\(\triangle OKP\),[/tex] [tex]\( \angle OPK \)[/tex] is an exterior angle for [tex]\(\angle OKP\) and \(\angle PKO\).[/tex]
- Since [tex]\( \angle OKP = 90^\circ \)[/tex] and [tex]\(\angle PKO\)[/tex] is another angle in the triangle, we have:
[tex]\[ \angle OPK = 180^\circ - (\angle OKP + \angle PKO) = 180^\circ - (90^\circ + \angle PKO) = 90^\circ - \angle PKO. \][/tex]
6. Similarly, in [tex]\(\triangle OFP\):[/tex]
-[tex]\( \angle OFP = 90^\circ \) and \(\angle PFO\)[/tex] is another angle in the triangle.
- Using the same logic as before:
[tex]\[ \angle OEP = 180^\circ - (\angle OFP + \angle PFO) = 180^\circ - (90^\circ + \angle PFO) = 90^\circ - \angle PFO. \][/tex]
7. Note that [tex]\( \angle OKP = \angle P \)[/tex] and [tex]\( \angle OFP = \angle EK \):[/tex]
- By the property of the tangents from the same external point, [tex]\( PK = PF \).[/tex]
- [tex]\( \angle PKO \) and \( \angle PFO \)[/tex] are complementary to [tex]\(\angle P\)[/tex] and [tex]\(\angle EK\)[/tex] respectively.
Therefore, it follows that:
[tex]\[ m\angle P = m\angle EK \][/tex]
Thus, the proof is complete.
Related Questions
How many inches are in 35 feet?
Answers
Answer:
420 inches
Step-by-step explanation:
There are twleve inches in one foot.
(35) (12) = 420
Answer:
420 in.
Step-by-step explanation:
Going from a bigger unit to a smaller unit, you multiply 12 by 35 to get 420.
I am joyous to assist you anytime.
106,68 dm. = 35 ft. :]
Which is the value of the equation?
Answers
Answer:
A+7
Step-by-step explanation:
Pocket money is split between Paula, Alan and Henry in the ratio 7:3:2. Alan gets £3.75.
How much do the others get?
How much altogether?
Answers
➷ Writing it out like this will help:
7 : 3 : 2
? : 3.75 : ?
So, 3.75 is 3 parts as per this ratio
Divide this amount by 3 to get 1 part in the ratio
3.75 / 3 = 1.25
Now simply multiply all the other ratios by this value to find how much the others get:
1.25 x 7 = 8.75
1.25 x 2 = 2.5
Paula gets £8.75 and Henry gets £2.50
The amount altogether would be their individual amounts added together:
8.75 + 2.50 + 3.75 = 15
The total amount of money is £15.
✽➶ Hope This Helps You!
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If the formula in the picture below were used to find the r-value of the following data, what would be the value of ¥?
Answers
Answer:
option C
ȳ = 9
Step-by-step explanation:
ȳ (yBar) is used to represent mean value of y
Mean, which is the average score of the population on a given variable
It is represented by = ( Σ Xi ) / N
There are two steps to calculate mean value
Add the numberssum of all numbers = 3 + 7 + 8 + 11 + 16
= 45
2. Divide by how number of ys (there are 5 numbers)
45 / 5 = 9
So ȳ = 9
a cone and a sphere have the same volume. the height of the cone is 96 units. what would be the values for the radius of the cone and the sphere?
Answers
The volume [tex]V_c[/tex] of a cone with base radius [tex]r_c[/tex] and height [tex]h_c[/tex] is
[tex]V_c = \dfrac{1}{3}\pi r_c^2 h_c[/tex]
Similarly, the volume [tex]V_s[/tex] of a sphere with radius [tex]r_s[/tex] is
[tex]V_s = \dfrac{4}{3}\pi r_s^3[/tex]
We know that [tex]V_c=V_s[/tex] and that [tex]h_c=96[/tex]
So, we can set up the following equation:
[tex]\dfrac{96}{3}\pi r_c^2=\dfrac{4}{3}\pi r_s^3[/tex]
We can simplify the common denominator 3, and pi appearing on both sides:
[tex]96r_c^2=4r_s^3[/tex]
We can divide both sides by 4:
[tex]24r_c^2=r_s^3[/tex]
Without further information, this is all we can say: the cubed radius of the sphere is the same as 24 times the squared radius of the cone.
The values for the radius of the cone and the sphere is 24 units.
It is given that a cone and a sphere have the same volume.
It is required to find the radius of the cone and sphere if the height of the cone is 96.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
We know the volume of the cone:
[tex]\rm V_c = \pi R^2\frac{H}{3}[/tex]
Where R is the radius of the cone and H is the height of the cone.
And the volume of the sphere:
[tex]\rm V_s = \frac{4}{3} \pi r^3[/tex]
Where r is the radius of the sphere.
[tex]\rm V_c = V_s[/tex] (From the question)
[tex]\rm \pi R^2\frac{H}{3}=\rm \frac{4}{3} \pi r^3[/tex]
[tex]\rm \pi R^2\frac{96}{3}=\rm \frac{4}{3} \pi r^3[/tex] ( H = 96 units)
[tex]\rm 32R^2=\rm \frac{4}{3} r^3[/tex]
[tex]\rm 24R^2= r^3[/tex]
We are assuming that R = r
[tex]\rm 24r^2= r^3[/tex]
r = 24 units and
R = 24 units.
Thus, the values for the radius of the cone and the sphere is 24 units.
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In the diagram,AB=10 AC=2 square root 10 what is the perimeter of triangle ABC ?
Answers
20 + 2 units square root 10 units
Given two functions f(x)=2x+1 and g(x)=−13x−3 , what is the function rule for (f+g)(x)
Answers
Answer:
(f+g)(x)=5/3x−2
Step-by-step explanation:
(f+g)(x)=f(x)+g(x)
f(x)=2x+1 + g(x)=−1/3 x−3
add like terms
2x+(-1/3 x)=5/3 x
1+(-3)= -2
so...
(f+g)(x)=5/3 x−2
Write 5/3 as a mixed number in simplest form.
Answers
Step-by-step explanation:
[tex]\dfrac{5}{3}=\dfrac{3+2}{3}=\dfrac{3}{3}+\dfrac{2}{3}=1\dfrac{2}{3}[/tex]
The function y = -2(x-3)^2+4 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x ist the price of a hot dog (in dollars). Find and interpret the zeros of this function
Answers
Answer:
Option A The zeros are the hot dog prices that give $0.00 profit (no profit)
Option C. Zeros at [tex]x=3(+/-)\sqrt{2}[/tex]
Step-by-step explanation:
we know that
The zeros of the function are the values of x when the value of y is equal to zero
In this problem
The zeros of the function are the price of a hot dog (in dollars) when the daily profit (in hundreds of dollars) of a hot dog stand are zero
we have
[tex]y=-2(x-3)^{2}+4[/tex]
Find the zeros
equate the equation to zero
[tex]0=-2(x-3)^{2}+4[/tex]
[tex]2(x-3)^{2}=4[/tex]
[tex](x-3)^{2}=2[/tex]
square root both sides
[tex]x-3=(+/-)\sqrt{2}[/tex]
[tex]x=3(+/-)\sqrt{2}[/tex]
Answer:
Option A The zeros are the hot dog prices that give $0.00 profit (no profit)
Option C. Zeros at
Step-by-step explanation:
The U.S. government collects information on Americans who do not have health insurance. Here is the data, sorted by geographic region:
Region Uninsured Insured Row Totals
Northeast 6,782 47,043 53,825
Midwest 7,757 57,135 64,892
South 19,090 85,800 104,890
West 11,676 55,427 67,103
Column Totals 45,305 245,405 290,710
The percentage of people from the West that are insured is:
Answers
Do 55,427 divided by 67,103 which is 0.825998838 then multiply that by 100 to get 82.5998838 then round up to the nearest tenth to get 83 percent
The percentage of people from the West that are insured is 83%.
Given that, the U.S. government collects information on Americans who do not have health insurance.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Number people insured from west region = 55,427
Total number of people from west region = 67,103
So, percentage = 55,427/67,103 × 100
= 0.8259 × 100
= 82.59
≈ 83%
Therefore, the percentage of people from the West that are insured is 83%.
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if x=3 calculate the value of
x3+x
and if X=-3 calculate the value of X3+3
Answers
Answer:
if X =3 then X would be equal to 12
Step-by-step explanation:
x3+x
put x=3
(3)3+3
9+3
12
Answer:
Step-by-step explanation:
[tex]x=3 \\3(x)+x\\3(3)+3\\9 +3\\= 12\\ X= - 3 \\ 3(x)+x\\3(-3)+(-3)\\-9-3\\= -12[/tex]
How many apples can be purchased for $10
Answers
Answer:
Divide ten by the price of the apples.
Which sides are congruent? What is the correct answers choice(s)
Answers
I think the answer is B and C
Answer: fr and nr, rc and ro, no and nm
Step-by-step explanation: you just have to look at each of the lines and see if they are equal or not i hope this helps :))
Rewrite the expression 5(10+12) using distributive property of multiplication over addition
Answers
Answer:
50+60=110
Step-by-step explanation:
multiply 10 by 5 and 12 by 5 to get 50 and 60 add them together to get 110.
What is the value of x enter your answer in the box
Answers
Answer:
x = 25Step-by-step explanation:
Use the Pythagorean theorem:
[tex]c^2=a^2+b^2[/tex]
a,b - legs
c - hypotenuse
We have c = x, a = 7 and b = 24. Substitute:
[tex]x^2=7^2+24^2\\\\x^2=49+576\\\\x^2=625\to x=\sqrt{625}\\\\x=25[/tex]
Lucy and Ricky buy a home. They plan to make a down payment and carry an $82,500 mortgage. Closing costs are $2,000 and are added to the loan amount. What is the new amount being financed?
(A) 78,500
(B) 84,500
(C) 80,500
Answers
Answer:
B.) 84,500
Step-by-step explanation:
$82,500 is the morgage right now. but an additional $2,000 is added.
82,500 + 2,000 = 84,500
$84,500
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Marni and Mikela are playing a color-guessing game. Each player chooses two colors from a list of red (R), blue (B), green (G), purple (P), and yellow (Y). A player then has three chances to correctly guess both the colors that the other player chose. The simulation of Marni’s guesses about Mikela’s colors are shown in the table. If Mickela’s colors are red and green, what is the experimental probability that Marni’s guesses are correct? Write the answer as a fraction in simplest form.
trials
1 PRB 2 YBG 3 GPR 4 RYP 5 RYG 6 GYB 7 RGP 8 GPR 9 RPG 10 BGP
Answers
The answer should be 1/2.
Answer:
The answer is 1/2!
Step-by-step explanation:
In a survey, 250 adults and children were asked whether they know how to
swim. The survey data are shown in the relative frequency table.
What percentage of the people surveyed cannot swim?
Answers
Answer:
Step-by-step explanation:
B because .06 + .12 = .18 which is 18% out of 250 people
Hello, I'm Eric. I'll be trying my best to assist you on your question today.
0.12 is 12 percent.
We also have the 0.06 percent which would just be 6 percent
We need to add up those percentages to get 18 percent, for the people surveyed that cannot swim would be 18 percent.
Our final answer is D.
Not the right answer or confused? Reply to this question for help.
Enjoy your day - Eric
This scale factor is a ____.
Answers
Answer:
I would believe the scale factor to be 1.5:6!
Rob deposits $1000 in a savings account at New York State bank that pays 4.4% interest,compounded monthly. How much is in his account at the end of one year? What is the APY for this account to the nearest hundredth of a percent ?
Answers
Answer:
$45
Step-by-step explanation:
I used a compound interest calculator
Rob will have $1044.89 in his account at the end of one year. The APY for this account is 4.47%.
Explanation:The subject of the question is related to calculating the final balance of a savings account that earns compound interest. In Rob's case, he deposits $1000 in a bank account that pays 4.4% interest compounded monthly. In order to calculate the balance at the end of the year, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
To find Rob's account balance at the end of one year, we would substitute the values into the formula as follows: A = 1000(1 + 0.044/12)^(12*1) = $1044.89. This means Rob will have $1044.89 in his account at the end of one year. The APY (Annual Percentage Yield) for this account is closer to the nominal rate due to the effect of monthly compounding, which follows the formula APY = (1 + r/n)^(nt) - 1. Substituting the values gives us, APY = (1+ 0.044/12)^(12) - 1 = 0.044682, which is approximately 4.47 after converting to percentage and rounding to the nearest hundredth of a percent.
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Help??????? It’s precal
Answers
what does precal mean I don't understand
[tex]\frac{F}{G} ( - 1) = - \frac{ 2}{ 3}[/tex]
EXPLANATION
The given functions are:
[tex]F(x)=2x[/tex]
and
[tex]G(x)= {x}^{2} + 2[/tex]
[tex] \frac{F}{G} (x) = \frac{F(x)}{G(x)} [/tex]
[tex] \frac{F}{G} (x) = \frac{2x}{ {x}^{2} + 2 }[/tex]
Substitute x=-1
[tex] \frac{F}{G} ( - 1) = \frac{2( - 1)}{ {( - 1)}^{2} + 2 }[/tex]
[tex] \frac{F}{G} ( - 1) = \frac{ - 2}{ 1+ 2 }[/tex]
[tex]\frac{F}{G} ( - 1) = - \frac{ 2}{ 3}[/tex]
The first choice is correct.
just look at the question on the picture
Answers
Answer:
A = ½bh + lw
Step-by-step explanation:
Your composite figure is a triangle on top of a rectangle.
The formula for the area of a triangle is A = ½bh.
The formula for the area of a rectangle is A = lw.
The formula for the total area is
A = ½bh + lw.
can someone plz help me out.....
Answers
Answer: The correct answer is 3
Step-by-step explanation:
4³ = 64
The way to check your work is to multiply 4 x 4 x 4:
16 x 4 = 64
It's just 64 = 4^3
4 * 4 * 4 = 64
Find the least common multiple of 6 , 2 and 9
Answers
Answer:
18
Step-by-step explanation:
The multiples of 6 are : 6, 12, 18, 24, 30, ......
The multiples of 2 are : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ......
The multiples of 9 are : 9, 18, 27, 36, ......
The common multiple is 18
The least common multiple is 18
Write the fractions as mixed number. Answers please for each
Answers
Answer:
32/5 = 6 2/5
19/3 = 6 1/3
15/4 = 3 3/4
51/10 = 5 1/10
Step-by-step explanation:
Divide the top number and the bottom number. Example: 32 divided by 5 = 6 R2. Put the 5 under the 2. 2/5. So the total is 6 2/5.
The area of a triangle is 1,4440 cm^2. The base of the triangle is 5 times the height. What is the height of the triangle?
Answers
Answer:
h = 24 cm
Step-by-step explanation:
The formula for area of a triangle is
A = (1/2)bh where b is the base and h is the height.
We are told that the base is 5 times the height, this translates to
b = 5h, so we can rewrite our formula to
A = (1/2)(5h)(h) or
A = (1/2)5h²
We are given A = 1,440, so plug that in and solve for h...
1,440 = (1/2)5h²
2,880 = 5h² (multiply both sides by 2 to get rid of the fraction)
576 = h² (divide both sides by 5 to get the h value by itself)
24 = h (take the square root of both sides)
The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one standard deviation of the mean? 18° 19° 22° 30°
Answers
Answer:
22°
Step-by-step explanation:
If the mean is m and the standard deviation is s, then we can say that the temperatures that fall within 1 standard deviation of the mean will be:
m - s < temperatures < m + s
To we take the sum of mean and standard deviation: 24 + 4 = 28
and, the different of mean and standard deviation: 24 - 4 = 20
So, the temperature that is in between 20 and 28 is the temperature within 1 standard deviation of the mean.
This is the third answer, 22°
Answer:
The answer is C, 22
Step-by-step explanation:
I just took the test
Lois and Clark own a company that sells wagons. The amount they pay each of their sales employees (in dollars) is given by the expression 12h+30w12h+30w12, h, plus, 30, w where hhh is the number of hours worked and www is the number of wagons sold.
What is the amount paid to an employee that works 666 hours and sells 333 wagons?
Answers
Answer:
The amount paid to an employee was 162Step-by-step explanation:
The expression 12h + 30w Identifies the amount paid to an employee.Let h represent hours and let w represent the total amount of g-wagons sold. Since the question explains that an employee works 6 hours and sells 3 wagons, put h as h = 6 and w as w = 3. We would end up getting this equation. 12h + 30w = 12(6) + 30(3).Now all you need to do is solve it.left side = 72right side = 9072 + 90 = 162What is the equation in standard form of the line which passes through (-2, 6) and has a slope of -1?
Answers
Answer:
x + y = 4
Step-by-step explanation:
To write the equation of the line use the point slope form. Then convert to the standard from. Begin by substituting m = -1 and (-2,6).
[tex]y - y_1 = m(x-x_1)\\y - 6 = -1(x --2)\\y - 6 = -1(x+2)\\y - 6 = -x -2\\x + y - 6 = -2\\x + y = 4[/tex]
3 ½ – 2 ⅓
Give your answer as a improper fraction
Answers
❣ R̾e̾f̾e̾r̾ t̾h̾e̾ a̾t̾t̾a̾c̾h̾m̾e̾n̾t̾.... ❣
☺.. h̾o̾p̾e̾ i̾t̾ h̾e̾l̾p̾s̾ y̾o̾u̾.. ☺
first change them into improper fractions
(2×3)+1/2 -->7/2
(3×1)+1/2--> 7/3
7/2-7/3 now find the least common denominator (lcd) it is 6
2 goes into 6, 3 times,7×3 =21--> 21/6
3 goes into 6, 2 times, 7×2=14 --> 14/6
21/6-14/6=7/6