Use the graph below to determine the equation of the circle in a center radius form and a general form
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Related Questions
х- а
x-b
If f(x) = b.x-a÷b-a + a.x-b÷a - b
Prove that: f (a) + f(b) = f (a + b)
Answers
Given:
Consider the given function:
[tex]f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}[/tex]
To prove:
[tex]f(a)+f(b)=f(a+b)[/tex]
Solution:
We have,
[tex]f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}[/tex]
Substituting [tex]x=a[/tex], we get
[tex]f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}[/tex]
[tex]f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}[/tex]
[tex]f(a)=0+a[/tex]
[tex]f(a)=a[/tex]
Substituting [tex]x=b[/tex], we get
[tex]f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}[/tex]
[tex]f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}[/tex]
[tex]f(b)=b+0[/tex]
[tex]f(b)=b[/tex]
Substituting [tex]x=a+b[/tex], we get
[tex]f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}[/tex]
[tex]f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}[/tex]
[tex]f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}[/tex]
[tex]f(a+b)=\dfrac{b^2-a^2}{b-a}[/tex]
Using the algebraic formula, we get
[tex]f(a+b)=\dfrac{(b-a)(b+a)}{b-a}[/tex] [tex][\because b^2-a^2=(b-a)(b+a)][/tex]
[tex]f(a+b)=b+a[/tex]
[tex]f(a+b)=a+b[/tex] [Commutative property of addition]
Now,
[tex]LHS=f(a)+f(b)[/tex]
[tex]LHS=a+b[/tex]
[tex]LHS=f(a+b)[/tex]
[tex]LHS=RHS[/tex]
Hence proved.
4-2x=22 relationship can be written as
Answers
Answer:X=-9
Step-by-sep explanation:
4-2X=22
Move towards
⇒-2X=22-4
Multiply -1
⇒2X=-18
Divide by two
⇒X=-9
HELP ASAP. Find the set.
Answers
Given:
The given sets are:
[tex]U=\{x|x\in N\text{ and }x<10\}[/tex]
[tex]A=\{x|x\text{ is an odd natural number and }x<10\}[/tex]
[tex]B=\{x|x\text{ is an even natural number and }x<10\}[/tex]
[tex]C=\{x|x\in N\text{ and }3<x<5\}[/tex]
To find
The set [tex]B\cap U[/tex].
Solution:
We have,
[tex]U=\{x|x\in N\text{ and }x<10\}[/tex]
[tex]U=\{1,2,3,4,5,6,7,8,9\}[/tex]
[tex]B=\{x|x\text{ is an even natural number and }x<10\}[/tex]
[tex]B=\{2,4,6,8\}[/tex]
Now, [tex]B\cap U[/tex] is the set that contains all the common elements of both sets B and U.
[tex]B\cap U=\{2,4,6,8\}[/tex]
[tex]B\cap U=B[/tex]
Therefore, the correct option is A.
Có bao nhiêu hoán vị {1.2….9} mà 4,5,6 không đứng cạnh nhau theo thứ tự tăng dần
Answers
Answer: razon de ser
Step-by-step explanation:
Tu eres como agua Clara que lluvi del suelo
which expression is equivalent to 9 +y+y+3
Answers
Answer is : 2(y + 6)
Pls help, i just need Jonah's
Answers
Answer:
they are just diffrent varibless of numbers
Step-by-step explanation:
According to Money magazine, Maryland had the highest median annual household income of any state in at (Time website). Assume that annual household income in Maryland follows a normal distribution with a median of and standard deviation of . a. What is the probability that a household in Maryland has an annual income of or more (to 4 decimals)
Answers
Answer:
The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean income and [tex]\sigma[/tex] is the standard deviation of incomes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
What is the probability that a household in Maryland has an annual income of X or more?
The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean income and [tex]\sigma[/tex] is the standard deviation of incomes.
PLEASE HELP: The exact value of cos 13π/8 is: A. 0.99. B. √2- √2/4 c. √2+√2/4 D. 0.38.
Answers
The exact value of cos(13π/8) is 1/2 [tex]\sqrt{2-\sqrt{2} }[/tex].
What is trigonometric ratio?Trigonometriic ratios are the ratios of the sides of a right angled triangle. sin , cos, tan, sec, cosec, cot are some of the trigonometric ratios. Sin is the ratio of perpendicular and hypotenuse, cos is the ratio if base and hypotenuse, tan is the ratio of perpendicular and base, secant is the ratio of hypotenuse and base, cosecant is the ratio of hypotenuse and perpendicular, cot is the ratio of base and perpendicular.
How to find value?We have to find the value of cos (13π/8).
We have to use formula which is following:
cos[tex]Θ[/tex]=[tex]\sqrt{1/2(1+cos 2Θ}[/tex]
=[tex]\sqrt{1/2(1+cos(2*13 π/8)}[/tex] (π=[tex]π[/tex])
=[tex]\sqrt{1/2(1+cos(3 π+π/4)}[/tex]
=[tex]\sqrt{1/2(1-cos(π/4)}[/tex]
=[tex]\sqrt{1/2(1-1/\sqrt{2} }[/tex]
=[tex]\sqrt{\sqrt{2}-1/2\sqrt{2} }[/tex]
=1/2[tex]\sqrt{2-\sqrt{2} }[/tex]
Hence the value of cos (13π/8) is [tex]1/2\sqrt{2-\sqrt{2} }[/tex].
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the sum of 10 and the product of 12 and s in agebraic expression
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Answer and Step-by-step explanation:
10 + 12s would be the algebraic expression.
Because 10 is being added to the product of 12 and s, meaning 12 and s multiply each other.
#teamtrees #PAW (Plant And Water)
What angle is supplementary to 123.9
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A perpendicular bisector crosses a line segment. Which type of angle does it
form with the segment?
A. Acute
B. Straight
C. Right
D. Obtuse
Answers
Answer:
C. Right
Step-by-step explanation:
Hi there!
Perpendicular lines always create right angles when they intersect each other. This is what makes them perpendicular. Therefore, the perpendicular bisector forms a right angle with the line segment.
I hope this helps!
MA + q ² A =g
Someone help me to do this Aquarian
Answers
Answer:
a=g/q2+m
Step-by-step explanation:Let's solve for a.
ma+q2a=g
Step 1: Factor out variable a.
a(q2+m)=g
Step 2: Divide both sides by q^2+m.
a(q2+m)
q2+m
=
g
q2+m
a=
g
q2+m
ASAP show work pleaseee for all of them. 20pst
Answers
Answer:
Answer is in picture
Step-by-step explanation:
Hope it is helpful...
In Centerville, 45% of the population is female, and 60% of the population commutes to work daily. Of the total Centerville population, 21% are females who commute to work daily. What percentage of the total Centerville population are males who do NOT commute to work daily?
Answers
Answer:
16%
Step-by-step explanation:
100%-45%=55%
60%-21%=39%
55%-39%=16%
the total Centerville population are males who do NOT commute to work daily is 16%.
The percentage of Centerville population of males do not commute to work is 16%.
Given that, in Centerville, 45% of the population is female, and 60% of the population commutes to work daily.
What is the 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 "%".
The total Centerville population, 21% are females who commute to work daily.
Now, the percentage of Centerville population of males commute to work = 60 - 21
= 39%
Total percentage of male = 100 - 45 =55
The percentage of Centerville population of males do not commute to work
= 55 - 39 = 16%
Therefore, the percentage of Centerville population of males do not commute to work is 16%.
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draw a poster that symbolizes-the importance of grammatical signals in developing patterns of idea in communiting to your readers.You will be graded according to the rubrics provided. .an example is provided as your guide.
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_________
#LetsStudy
Using grammatical signals in developing patterns of ideas can be like a zipper because it zips our ideas or combined some information.
What are Grammatical signals?Grammatical signals are writing devices that serve to maintain text coherence. The short story is one of the written mediums where we can find these signals.
Important's of Grammatical signals
Grammatical signals are important because they signal relationships between sentences using backreference through the use of pronominal forms, determiners, repetition of keywords, synonyms, and superordination.
In short, they signal the relationship between new sentences and the one before them and they are also important writing devices in text construction.
Learn more about Grammatical signals;
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the perimeter of rectangle math is 297 cm. the ratio of the length to width is 3:8. what is the width of the rectangle?
Answers
Answer:
Width = 108 cm
Step-by-step explanation:
Perimeter = 2 x (length + width)
297 = 2 x (length + width)
148.5 = Length + width
Ratio of Length to Width = 3 : 8
Sum of ratio = 11
[tex]Length = \frac{3}{11} \times 148.5 = 40.5 \ cm\\\\Width = \frac{8}{11} \times 148.5 = 108 \ cm[/tex]
Karim had a packet of 200 chocolates. He gave 35% of them to his sister. How many chocolates were left with him?
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Answer:
Karim had 130 chocolates left.
Step-by-step explanation:
The quick way to do this is to notice that if he gave away 35% of his chocolates, he must have 65% left. That comes about by doing
100% (which is what he started with) - 35% = 65%
65% of 200 Change 65% into a fraction
65/100 * 200 Multiply 200 * 65
13000 / 100 Divide by 100
130
Answer:
130 left
Step-by-step explanation:
35% of 200 chocolates is equal to 70 chocolates.
200-70=130 chocolates
If PO and RS intersect to form four right angles, which statement is true?
O A. POIRS
O B. PO - RS
O C. PO and RS are parallel
O D. PO and RS are skew
PEASE HELP
Answers
Answer
its A
Step-by-step explanation:
The length of PQ is perpendicular to RS. The correct option is A.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.
Two geometric objects are perpendicular in elementary geometry if they intersect at a right angle. The perpendicular symbol can be used to represent the condition of perpendicularity graphically. It can be defined between two lines, a line and a plane, or two planes.
Given that the PO and RS intersect to form four right angles. If PO and RS intersect to form four right angles, the side PQ should be perpendicular to the side RS.
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SOMEONE SMART PLEASE HELP!! If the area of a triangle is 32 yd^2 and the base is 6.4 yds long, find the height
Answers
Answer:
Height = 10 yd
Step-by-step explanation:
GIVEN :-
Area of the triangle = 32 yd²Base of the triangle = 6.4 ydTO FIND :-
The height of the triangleGENERAL FORMULAE TO BE USED IN THIS QUESTION :-
For a triangle with base 'b' & height 'h' , its area = [tex]\frac{1}{2} \times b \times h[/tex]
SOLUTION :-
[tex]Area = \frac{1}{2} \times Base \times Height[/tex]
[tex]=> 32 = \frac{6.4h}{2}[/tex]
[tex]=> 6.4h = 32 \times 2 = 64[/tex]
[tex]=> h = \frac{64}{6.4} = 10\: yd[/tex]
in a fruit basket there were 24 oranges and the rest were lemos if 20% of fruits were lemons how many fruits were there altogether
Answers
Answer:
30
Step-by-step explanation:
.2(24 + L) = L
.48 + .2L = L
.48 = .8L
6 = L
24 + 6 = 30
this circle has a diameter of 5 inches which of these measurements is closest to the circumference of the circle 15.7 7.85 31.4 19.625
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Answer:
The closest measurement is 15.7
Step-by-step explanation:
The formula for circumference is [tex]2\pi r[/tex]
The diameter is double the radius, so to get the radius we divide by 2.
5 divided by 2 is 2.5
Knowing "r" is 2.5 we can plug that into our equation and solve.
2 · [tex]\pi[/tex] · 2.5 ≈ 15.71
The closest measurement is 15.7
Mention 3 places
where you can get
pre-approved for a
car loan
Answers
Answer:
Auto Credit Express, Carvana, Capital one auto loan
¿Cual es la fórmula del trapecio?
Ayuda plis
Answers
Answer:
Por lo tanto, el área de la fórmula de trapecio se da como: Área de un trapecio, A = h (a + b) / 2 unidades cuadradas. "h" es la altitud o altura. Sea a y b la longitud de los lados paralelos de un trapecio ABCD, como a es la longitud de la base y b es la longitud del lado paralelo a a.
Step-by-step explanation:
Which of the following systems of linear inequalities is represented by the
solution graphed below?
Answers
Answer:
please make the drawings cleared
If G = {(-1, 7),(-8, 2),(0, 0),(6, 6)), then the range of G is
(7, -1),(2, -8),(0, 0),(6, 6)}
(-8,-1, 0,6)
(0, 2, 6, 7)
Answers
9514 1404 393
Answer:
(0, 2, 6, 7)
Step-by-step explanation:
The range is the list of 2nd numbers in the ordered pairs:
(0, 2, 6, 7)
The product of a number n and 2 is 2. 50 POINTS
Answers
Answer: The equation is 2n = 2
If triangle ABC is reflected across the y-axis and then rotated 90 degrees clockwise about the origin, what would the coordinates of point A’ of the transformed triangle be?
Answers
Answer:
A' (2,-1) B' (4.-1) C' (1,-4)
Step-by-step explanation:
Answer:
(-2,-1)
Step-by-step explanation:
What is an equation that is true for all values of the variable
Answers
Answer:
x=x
Step-by-step explanation:
The height of the wall is 77 inches tall. What is its height in feet?
Answers
Answer:
6.41667
Step-by-step explanation:
Answer:
I think 6.4
Step-by-step explanation:
hope it's help
The height of a cylinder is 10 yards. The volume of the cylinder is 1,540 cubic yards. What is the radius of the cylinder? Use 22/7 or 3.14 for pie
Answers
Answer:
Radius ≈ 7 yd
Step-by-step explanation:
Height = 10
Volume = 1540
Missing radius
Use the formula and work backwards
Formula : πr²h
Plug in the given info:
1540 = 3.14 * r² * 10
Work backwards:
1540/10 = 3.14 * r²
154 = 3.14 * r²
154/3.14 = r²
49.044 = r²
√49.044 ≈ 7
Radius = 7
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-Chetan K