The points P (22, 15), Q (−13, c) and R (k, 24) all lie on a circle, centre (2, 0). Find the radius of the circle and the possible values of the constants c and k.
Answers
Answer:
r = 25c = 20k = 9 or k = -5Step-by-step explanation:
Circle of center A(2, 0) and radius r.
P (22, 15), Q(−13, c) and R (k, 24) all lie on a circle,
[tex]r=AP=\sqrt{\left( 22-2\right)^{2} +\left( 15-0\right)^{2} }[/tex]
[tex]=25[/tex]
Q(−13, c) lies on the circle then ,
[tex]AQ=r\Longrightarrow AQ^{2}=r^{2}\Longrightarrow (-13-2)^{2}+(c-0)^2=25^2=625[/tex]
[tex]\Longrightarrow 225+c^{2}=625[/tex]
[tex]\Longrightarrow c=20[/tex]
R (k, 24) lies on the circle then ,
[tex]AR=r\Longrightarrow AR^{2}=r^{2}\Longrightarrow (k-2)^{2}+(24-0)^2=25^2=625[/tex]
[tex]\Longrightarrow (k-2)^{2}+576=625[/tex]
[tex]\Longrightarrow (k-2)^{2}=49[/tex]
[tex]\Longrightarrow k-2=7\ \ or \ \ k-2=-7[/tex]
[tex]\Longrightarrow k=9\ \ or \ \ k=-5[/tex]
Related Questions
number 12 Simplify the expression. Write your answer as a power.
Answers
Answer:
(4)^5
Step-by-step explanation:
When multiplying expressions with exponents you add the exponents together so in this equation you would get -4^11/-4^6. However since both exponent have the same base (-4) you can simplify it farther. When dividing expression with exponents you subtract the exponents. So, here, you would get 4^5.
Hope that helps! :)
The circumference of a circle is 88 ft. Find the diameter to the nearest tenth. Use 227 for .
Answers
Answer:
28.0ft
Step-by-step explanation:
22/7= π= 3.142857143
circumference= πd
88= 3.142857143×d
d= 88/3.142857143
d=28.0ft
find an angle between 0 and 2\pi that is coterminal with -5pi/12
Answers
Check the picture below.
how do I make frequency table
Answers
Answer:
To make such a frequency distribution table, first, write the class intervals in one column. Next, tally the numbers in each category based on the number of times it appears. Finally, write the frequency in the final column. A frequency distribution table drawn above is called a grouped frequency distribution table.
The money in Maya’s college savings account earns 2 1/5% interest. Which value is less than 2 1/5%?
Answers
Answer:
u be mumu go ask ur father that one
Select the correct answer. A company offers its employees free recreational activities and gym memberships. Of the 200 employees, 95 employees registered for recreational activities, 80 employees registered for gym memberships, and 30 employees did not register at all. If an employee is chosen at random, what is the probability that the employee has registered for both recreational activities AND gym memberships?
Answers
Answer:
1/40
Step-by-step explanation:
95 + 80 + 30 = 205
205 - 200 = 5
5/200 = 1/40
Took the test and got it right.
Hope this helped!
By using Venn Diagram, one can easily visualize that 5 people out of 200 chose both the activities(or whatever)
So.
[tex] \frac{5}{200} = \boxed{\frac{1}{40}} = 2.5percent[/tex]
(sorry for the s t u p i d handwriting)
Which graph represents the solution set of the system of inequalities?
y < 3x – 1
y ≤ –2 x
Answers
Answer:
The #4 graph represents
Step-by-step explanation:
i plugged the inequalitites into desmos.
(see below)
What is this word phrase as a math expression?
11 times the sum of a number and 15
11y + 15
11+(y+15)
11y + 15y
11(y+15)
Answers
11 times the sun of a number and 15
11(y+15)
the answer is d
have great day and I hope you make a good grade
Answer:
D
11(y+15)
Step-by-step explanation:
i really you get this right!
do good on your test!!
35-12+6×36÷4 simplify it
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{35 - 12 + 6 \times 36 \div 4 }[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{35 - 12 + 6 \times 36 \div 4 }[/tex]
[tex]\mathsf{= 35 - 12 + \dfrac{6\times36}{4}}[/tex]
[tex]\mathsf{= 23 + \dfrac{6\times36}{4}}[/tex]
[tex]\mathsf{= 23 + \dfrac{216}{4}}[/tex]
[tex]\mathsf{= 23 + 54}[/tex]
[tex]\mathsf{= 77}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{77}}\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]The circle is rotated around the horizontal dashed line. Which type of geometrical figure will be generated?
A.
cylinder
B.
sphere
C.
ring
D.
cylindrical shell
Answers
When the circle is rotated around the horizontal dashed line, the resultant figure is a sphere.
What is a circle?A circle is a round figure. The sum of angles in a circle is 360 degrees. The circle could be rotated to yield another figure.
Thus, when a circle such as the one here is rotated around the horizontal dashed line, the resultant figure is a sphere.
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Answer:
Sphere
Step-by-step explanation:
I got it right on Edmentum
Hook me up with a 5 star and a thanks :)
Find the Nth term of this number sequnce
7,10,13,16
Answers
[tex]\text{It is an arithmetic series.}\\\\\text{First term,}~ a = 7\\\\\text{Common difference,}~ d=10 -7 = 3\\\\\text{Nth term} = a + (n -1) d\\\\~~~~~~~~~~~~~=7+(n-1)3\\\\~~~~~~~~~~~~~=7+3n-3\\\\~~~~~~~~~~~~~=4+3n[/tex]
5. A moving car has kinetic energy. If the mass is doubled what happens to the
amount of kinetic energy? If the speed is doubled what happens to the amount
of kinetic energy?
Answers
Answer:
See below ~
Step-by-step explanation:
Change in KE if mass is doubled
KE (original) = 1/2mv²KE (new) = 1/2 x (2m) x v²KE (new) = mv²⇒ KE is doubledChange in KE if speed is doubled
KE (new) = 1/2 x m x (2v)²KE (new) = 1/2 x 4 x mv²KE (new) = 2mv²⇒ KE is quadrupledWhen completely filled, a spherical storage tank
holds 7,240 A of propane. What is the radius of
the tank?
Answers
Answer:
radius: 12
Given the following:
Volume of sphere: 7,240
Formula of volume of sphere:
Volume = 4/3 π (radius)³
Find radius:
4/3 π (radius)³ = 7,240change sides
(radius)³ = 7,240/(4π/3)simplify
(radius)³ = 1728.422682cube root on both sides
radius = ∛1728.422682simplify
radius = 12Need help in math ASAP
Answers
Answer:
Step-by-step explanation:
Givens
Plastic Bag with 3000 cm^3 of sand
Bottle
radius = 7
height = 15 cm
Formula for cylinder
V = pi * r^2 * h
Solution for the Volume of the bottle
V = pi r^2 h
r = 7 cmh = 15 cmpi = 3.14V = 3.14*7*7*15
V = 2307.9
Answer
A
The bottle is too small.
The model represents the factorization of 2x2 5x 3. an algebra tile configuration. 4 tiles are in the factor 1 spot: 2 x tiles, 2 tiles. 2 tiles are in the factor 2 spot.: 1 x tile, 1 tile. 10 tiles are in the product spot in 4 columns with 2 rows. first row: 2 x squared tiles, 3 x tiles. second row: 2 x tiles, 3 tiles. what are the factors of the polynomial? (2x 3)(x 1) (2x−3)(x−1) (3x 2)(x 1) (3x−2)(x−1)
Answers
The algebra tile configuration that represents the factors of 2x² + 5x + 3 must have a product of (2x + 3) and (x + 1)
How to model the factor?The expression is given as:
2x² + 5x + 3
Expand the expression
2x² + 5x + 3 = 2x² + 2x + 3x + 3
Factorize the expression
2x² + 5x + 3 = 2x(x + 1) + 3(x + 1)
Factor out x + 1
2x² + 5x + 3 = (2x + 3)(x + 1)
The above means that the algebra tile configuration that represents the factors of 2x² + 5x + 3 must have a product of (2x + 3) and (x + 1)
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Answer:
(A) (2x+3)(x+1)
Step-by-step explanation:
got it right on edge 2022
. The initial cost for Travis and his band to record their first CD was $1500. Each CD will cost $4 to produce.
If they sell their CDs for $10 each, how many must they sell before they make a profit?
Answers
10x > 1500 + 4x
6x > 1500
x > 250
Since x cannot equal 250, they must sell 251 CD's before they can make a profit.
Proof:
[tex]1500+4(250)=2500[/tex]
[tex]10(250)=2500[/tex]
No net profit
[tex]1500+4(251)=2504[/tex]
[tex]10(251)=2510[/tex]
Net profit of $6
A and B are independent events. If P(A) = 0.50 and P(A and B) = 0.20, find P(B).
Answers
The independent events are illustrations of probability, and the value of P(B) is 0.40
How to determine the value of P(B)?The given parameters are:
P(A) = 0.50
P(A and B) = 0.20
Two events A and B are independent, if
P(A and B) = P(A) * P(B)
So, we have:
0.50 * P(B) = 0.20
Divide both sides by 0.50
P(B) = 0.40
Hence, the value of P(B) is 0.40
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Given: ΔDFE is isosceles with base FE; FB ≅ EC.
Prove: ΔDFB ≅ ΔDEC
Triangle D F E is shown. 2 lines drawn down from point D to points C and B on the base of the triangle to form 3 triangles.
Complete the missing parts of the paragraph proof.
We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because
. Segment DF is congruent to segment
by the definition of isosceles triangle. Since these segments are congruent, the base angles, angles
, are congruent by the isosceles triangle theorem. Therefore, triangles
are congruent by SAS.
Answers
Answer:
Step-by-step explanation:
Explain how to prove a theorem with the axiomatic system?
Answers
Answer:
my answer is in the picture just tap it
Step-by-step explanation:
pleas heart my answer
rate my answer 5 stars
follow me
and brainliest me
pleas
8. Find the surface area of the regular hexagonal prism shown below.
Show Work
1.7 in.-
2 in.
8 in.
Answers
Melody need 155 bags of 140 cu. inches to fill the vegetable garden.
What is Volume of Cuboid?The volume of the cuboid is the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height.
Here, Length of vegetable garden = 48 inch
breadth of garden = 30 inches
height of garden = 15 inches
Volume of garden = Length X width X height
= 48 X 30 X 15
= 21600 cu. inches
Volume of each bag = 140 cu. inches
Number of Bags required = Volume of garden/Volume of each bag
= 21600 / 140
≈ 155
Thus, Melody need 155 bags of 140 cu. inches to fill the vegetable garden.
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2(4x + 1) - 3(5x - 1)
expand and simplify
Answers
Answer:
-7x + 5
Step-by-step explanation:
2(4x + 1) - 3(5x - 1)
8x + 2 - 3(5x-1)
8x + 2 - 15x + 3
8x + 5 - 15x
-7x + 5
Hope it helped !
Adriel
In the following problem solve for X
Answers
Answer:
x = 6
Step-by-step explanation:
4 is to 12 as x is to 18
4/12 = x/18
4/12 * 18 = x = 6
please help me I will give brainliest
Answers
B
because it starts at the rarefraction.
The circumference of a circular garden is approximately 20 feet. What is the approximate area inside the circular garden?
Answers
Answer:
31.85 square feet
Step-by-step explanation:
Finding the radius :
C = 2πr20 = 2πrr = 20/2πr = 10/πSubstituting in the area formula :
A = πr²A = π × 10/π x 10/πA = 100/πA = 100/3.14A = 31.85 square feetSo
2πr=20πr=10r=10/πNow
Area
πr²πr(r)10r10(10/π)100/π31.8ft²8 is not more than m
Answers
Answer: It is the 2nd one
Step-by-step explanation: 8≤m
Not only would I like the value of x, but also I wonder how I’d go about solving this problem?
Answers
Answer:
x = 58
Step-by-step explanation:
This question can be solved by using the exterior angle property, which states that the exterior angle of a triangle = the sum of the two opposite interior angles.
62 lies on a line, so the exterior angle is 180 - 62, or 118 degrees.
Using the EAP, we can conclude the following:
(x + 2) + (x) = 118
2x + 2 = 118
2x = 116
x = 58
Hope this helps
Answer:
X=58
Step-by-step explanation:
1.) 62+2+2x=180
2) 64+2x=180 (add 62 and 2)
3) 2x=116 (subtract 64 from 180)
4)x=58 (divide 116 by 2 =58
Which picture shows 2/4?
Answers
Answer:
d) last bottom picture
Step-by-step explanation:
This shape has 4 boxes and two are shaded. So, it means the fraction of 2/4. Hence, option (d) is the correct answer.
- - - - -- - - - - - - - - - - - - - -- - - - - - - - - - - - - - -- - - - - - - - - - - - -- - - - -- -
[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Which picture shows 2/4?
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
Remember, fractions should be equal parts.
The first one shows 2/5, so it's not Option A.
The second one doesn't have equal parts, so this is not a fraction.
Henceforth, it's not Option B either.
The third option shows 1/3, so it's not Option C.
However, the fourth option does show 2/4, and the parts are equal.
[tex]\dashrightarrow\bigstar\boxed{\boxed{\bold{Option\:D\:is\:correct}}}\dashleftarrow[/tex]
Good luck.- - - - - -- - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - -- - -- -
Nancy buys 15 m of ribbon. Her sister buys 6 m less ribbon but pays twice as much per metre. Together they pay R66. What is the price per metre of each type of ribbon?
Answers
Answer: 44/9 ----> 22/9
I hope this helps you
If f(x) = 3x+ 2 and g(x) = 2x-2, what is (f-8)(x)?
Answers
Answer: x + 4
Step-by-step explanation:
If it is asking us for (f - g)x, then we will subtract the function g from function f. Why? The x distributes creating f(x) - g(x), so we use this to solve.
Given:
g(x) = 2x - 2
f(x) = 3x + 2
Set up:
f(x) - g(x)
(3x + 2) - (2x - 2)
Distribute the negatie:
3x + 2 - 2x + 2
Reorder to combine like terms:
3x - 2x + 2 + 2
Combine like terms:
x + 4
(f - g)(x) = x + 4
how many inches are in 1 1/2 ?
Answers
Answer:
18 inches
Step-by-step explanation:
Assuming that 1 1/2 is measured in feet:
1.5ft × 12
= 18"
