Answers
The equation of a circle in center-radius form, is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]-Where the coordinates of the center of the circle are (h,k) and the radius of the circle is r.
From the given graph, we can see that the coordinates of the center are (-2,4) and the radius of the circle is 2.
a)
To determine the equation of the circle in center-radius form, replace h=-2, k=4 and r=2
[tex]\begin{gathered} \Rightarrow(x-(-2))^2+(y-(4))^2=2^2 \\ \Rightarrow(x+2)^2+(y-4)^2=4 \end{gathered}[/tex]Therefore, the equation of the circle in center-radius form is:
[tex](x+2)^2+(y-4)^2=4[/tex]b)
To find the equation of the circle in general form, expand the parentheses and take all the terms to the left member:
[tex]\begin{gathered} (x+2)^2+(y-4)^2=4 \\ \Rightarrow x^2+2(2)(x)+(2)^2+y^2-2(4)(y)+4^2=4 \\ \Rightarrow x^2+4x+4+y^2-8y+16=4 \\ \Rightarrow x^2+4x+y^2-8y+20=4 \\ \Rightarrow x^2+4x+y^2-8y+20-4=0 \\ \Rightarrow x^2+4x+y^2-8y+16=0 \end{gathered}[/tex]Write the quadratic terms first:
[tex]\Rightarrow x^2+y^2+4x-8y+16=0[/tex]Therefore, the equation of the circle in general form, is:
[tex]x^2+y^2+4x-8y+16=0[/tex]Related Questions
Can someone help me with this geometry question I don’t know if I’m right or wrong?
Answers
Given:-
A circle has a central angle 135 degrees.
The radius of the circle is 24.
To find the arc length.
So now we use the formula,
[tex]s=r\theta[/tex]Now we convert 135 degrees to radians. so we get,
[tex]135=\frac{135}{180}\times\pi[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} s=24\times\frac{135}{180}\times\pi \\ s=18\pi \end{gathered}[/tex]So the required value is,
[tex]18\pi[/tex]So the correct option is OPTION D.
Find the oth term of the geometric sequence 5,--25, 125,
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Given the geometric progression below
[tex]5,-25,125,\ldots[/tex]The nth term of a geometric progression is given below
[tex]T_n=ar^{n-1},\begin{cases}a=\text{first term} \\ r=\text{common ratio}\end{cases}[/tex]From the geometric progression, we can deduce the following
[tex]\begin{gathered} T_1=a=5 \\ T_2=ar=-25 \\ T_3=ar^2=125 \end{gathered}[/tex]To find the value of r, we will take ratios of two consecutive terms
[tex]\begin{gathered} \frac{T_2}{T_1}=\frac{ar}{a}=\frac{-25}{5} \\ \Rightarrow r=-5 \end{gathered}[/tex]To find the 9th term of the geometric, we will have that;
[tex]\begin{gathered} T_9=ar^8=5\times(-5)^8=5\times390625 \\ =1953125 \end{gathered}[/tex]Hence, the 9th term of the geometric progression is 1953125
4. You are making guacamole for a familygathering. Your first trip to the store, youpurchased 5 avocados and 3 pounds of tomatoesfor $13.30. The head count changed, and youwent back for an additional 3 avocados and 8pounds of tomatoes, spending another $22.55.What is the price per avocado and pound oftomatoes?
Answers
hello
to solve this question, we need to write an equation expressing the word problem and solve for the price of each item.
let x represent the cost of avocados
let y represent the cost of tomatoes
[tex]\begin{gathered} 5x+3y=13.30\ldots\text{.equation 1} \\ 3x+8y=22.55\ldots\text{.equation 2} \end{gathered}[/tex]from equation 1, let's make xthe subject of formula
[tex]\begin{gathered} 5x+3y=13.30 \\ 5x=13.30-3y \\ \text{divide both sides by 5 to solve for x} \\ x=\frac{13.30-3y}{5} \\ \text{this is equation 3} \end{gathered}[/tex]put equation 3 into equation 2
[tex]\begin{gathered} 3x+8y=22.55 \\ 3(\frac{13.30-3y}{5})+8y=22.55 \\ \frac{39.9-9y}{5}+8y=22.55 \\ \text{solve for y} \\ \frac{39.9-9y+40y}{5}=22.55 \\ \frac{39.9+31y}{5}=22.55 \\ 39.9+31y=22.55\times5 \\ 39.9+31y=112.75 \\ 31y=112.75-39.9 \\ 31y=72.85 \\ y=\frac{72.85}{31} \\ y=2.35 \end{gathered}[/tex]since y = 2.35, let's put that in either equation 1 or 2
from equation 2
3x + 8y = 22.55
put y = 2.35 and solve for x
[tex]\begin{gathered} 3x+8y=22.55 \\ y=2.35 \\ 3x+8(2.35)=22.55 \\ 3x+18.8=22.55 \\ 3x=22.55-18.8 \\ 3x=3.75 \\ x=\frac{3.75}{3} \\ x=1.25 \end{gathered}[/tex]from the calculations above, the price per avocado and pound of tomatoes are $1.25 and $2.35 respectively
Solve the following quadratic equation by factoring. If needed, write your answer as a fraction reduced to lowest terms
Answers
The given equation is
[tex]y^2-5y-36=0[/tex]For solving it we will factorize the number 36 as 9 x 4 which on subtraction gives 5 and on multiplication gives 36.
Then, we have
[tex]\begin{gathered} y^2-(9-4)y-36=0 \\ y^2-9y+4y-36=0 \\ y(y-9)+4(y-9)=0 \\ (y-9)(y+4)=0 \\ y-9=0\text{ and y+4=0} \\ y=p\text{ and y=-4} \end{gathered}[/tex]Hence, the values of y are 9 and -4.
Explain why (-1)^n = 1 for any even number n.How is this possible? I thought it would equal -1. Does that mean the answer is "not possible"?
Answers
The expression (-1)^n means the number -1 multiplies itself n times.
So for example if n = 2, we have that:
[tex](-1)^2=(-1)\cdot(-1)=1[/tex]For n = 3, we have:
[tex](-1)^3=(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1[/tex]For n = 4:
[tex](-1)^4=(-1)^2\cdot(-1)^2=1\cdot1=1[/tex]We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.
So for any even number n, the result will be 1.
what is the least common denominator for the two fractions 2 / 5 3 / 2
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The multiples of the denominator of 2/5 is,
5,10,15,20,25....
The multiples of the denominator of 3/2 is,
2,4,6,8,10.....
Thus, the required least common denominator is 10.
Which ordered pair represent points on the graph of this exponential function?f(x) = 2^x+1A(1, 3)B(-4, -7)C(-2, -3)D(4, 9)
Answers
Answer:
[tex]A(1,3)[/tex]Step-by-step explanation:
To determine which of the given ordered pairs belongs to the given function, substitute each x-value and see if the y-value is correct.
[tex]\begin{gathered} f(1)=2^1+1 \\ f(1)=3 \\ \\ f(-4)=2^{-4}+1 \\ f(-4)=\frac{17}{16} \end{gathered}[/tex][tex]\begin{gathered} f(-2)=2^{-2}+1 \\ f(-2)=\frac{5}{4} \\ \\ f(4)=2^4+1 \\ f(4)=17 \end{gathered}[/tex]Therefore, the only point that represents points on the given function is A(1,3)
Complete the sentence. The amount of time it takes to complete a puzzle is most likely to be a function of the .
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"The ammount of time it takes to complete a puzzle is most likely to be a function of the number of pieces in the puzzle."
X 즈 - + 3 = 15 -4someone help me confused
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First we have to transfer the number 3 the other side of equal sign as follows,
[tex]\begin{gathered} \frac{x}{-4}=15-3 \\ \frac{x}{-4}=12 \end{gathered}[/tex]Now, we need to transfer (-4) to the other side of the equal side by multiplying with the number 12.
[tex]\begin{gathered} \frac{x}{-4}=12 \\ x=12\ast(-4) \\ x=-48 \end{gathered}[/tex]Thus, the answer of the x is (-48).
University DataReceiving Not ReceivingFinancial Aid Financial AidTotalUndergraduates422238988120Graduates18797312610Total6101462910730If a student is selected at random, what is theprobability that the student receives aid and is agraduate (rounded to the nearest percent)? [? ]%
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1) Circle the tables that represent y as a function of x.хХ-31X-10у-5515-3y3608-2-4- 1-2-2-5- 1290у-1-1- 1-11-2-52-5
Answers
The answer is the last table
The answer is the last table
Find all the zeros of the following function.
f(x)=x^4+8x²-9
The zeros of the function are
(Use a comma to separate answers as needed. Express complex numbers in terms of i.)
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All the zeros of following function f(x)=x4−8x2−9 are 3, -3, i, -i
What do you mean by the roots of function?A number x that reduces the value of a function f to 0 is known as its root in mathematics: f(x) = 0.
Roots are actual objects since polynomials are functions as well.
Every polynomial with complex coefficients has at least one (complex) root, according to the fundamental theorem of algebra.
f(x)=x4−8x2−9
You should set (x4 - 8x2 - 9) to 0.
x4−8x2−9=0
Learn what x's value is.
Put u=x2 in the equation's place.
As a result, applying the quadratic formula will be straightforward.
u2−8u−9=0
Consider the equation x2+bx+c.
Write out the factored form (u-9)(u+1) = 0.
The answer is the set of all numbers that add up to (u9)(u+1)=0.
u=9,−1
If u=x2 has a genuine value, change it to x2=9, x2= -1
In the case of these equations, x = +3, -3, and -i, +i .
The whole solution is made of of the solution's positive and negative components.
x4- 8x2- 9 = 0 has a solution.
is x=3,−3, i,−i
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Isabella earns interest at an annual rate of 10% compounded annually on her savings account. She deposits $2,000 into her account. What is the total amount of money Isabella will have in her account after 2 years? (Use the formula to calculate compound interest: A = P(1 + r)')
Answers
As it indicates on the text, compound interest is represented by the following expression:
[tex]\begin{gathered} A=P(1+r)^t \\ \text{where,} \\ A=\text{ Amount} \\ P=\text{ Principal} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Then, substituing the information given:
[tex]\begin{gathered} A=2,000(1+0.1)^2 \\ A=2,420 \end{gathered}[/tex]Isabella will have $2,420 after 2 years.
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula,and solve the two equations for x and y.)midpoint (1,17), endpoint (-5,13)
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The coordinates of a midpoint of a line delimited by two endpoints is:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m=\frac{y_1+y_2}{2} \end{gathered}[/tex]Where (xm,ym) are the coordinates of the midpoint, (x1,y1) are the coordinates of the first endpoint and (x2,y2) are the coordinates of the second endpoint. We want to find (x2,y2), therefore:
[tex]\begin{gathered} 1=\frac{-5+x_2}{2} \\ 2=-5+x_2 \\ x_2=2+5=7 \end{gathered}[/tex][tex]\begin{gathered} 17=\frac{13+y_2}{2} \\ 34=13+y_2 \\ y_2=34-13 \\ y_2=21 \end{gathered}[/tex]The coordinates of the endpoint two are (7,21).
Debra the trainer has two solo workout plans that she offers her clients: plan A and plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did plan A and 3 who did plan B. On Thursday there were 7 clients who did plan A and 9 who did plan B. Debra trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?
Answers
The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .
According to the question the plan only ran on wednesday and thursday.
Wednesday = plan A has 5 client and plan B has 3 clients.
Thursday = plan A has 7 client and plan B has 9 clients.
On wednesday she trained her client for 6 hours.
On thursday she trained her client for 12 hours.
let
x = hour of plan A workout for each client
y = hour of plan B workout for each client
[tex]\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }\frac{6}{3}\text{ - }\frac{5}{3}x \\ y\text{ = 2 - }\frac{5}{3}x \\ 7x\text{ + 9(2 - }\frac{5}{3}x\text{) = 12} \\ 7x\text{ + 18 - }\frac{45}{3}x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }\frac{6}{8} \\ x\text{ = }\frac{3}{4} \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5(\frac{3}{4})\text{ + 3y = 6} \\ \frac{15}{4}\text{ + 3y = 6} \\ 3y\text{ = 6 - }\frac{15}{4} \\ 3y\text{ = }\frac{24-15}{4} \\ 3y\text{ = }\frac{9}{4} \\ y\text{ = }\frac{9}{4}\text{ }\times\text{ }\frac{1}{3} \\ y\text{ = }\frac{9}{12} \\ y\text{ = }\frac{3}{4} \end{gathered}[/tex]on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs
On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs
Each of the work out lasted for 3/4 hrs = 0.75 hrs
In the expression 27 = 9x3-4x2, explain why 27 = 9 is the first operation you would do.
Answers
You follow the rule
PEMDAS
When doing order of operation questions.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Note: You can interchange M and D. Also A and S.
Thus, in the expression shown, we can do the division first.
27 and 9
f(t) = 2t-3g(t) = t^3 + tFind (f •g)(0)
Answers
1) Given those functions, f(t) and g(t) let's find the composite function, for (f(g(0)) or (f •g)(0)
2) Let's pick the function f(t)
f(t) = 2t-3
And plug into that g(t), like this
f(g(t))= 2(t³ +t) -3
3) Finally, let's plug the value 0 into that composite function:
f(g(t))= 2(t³ +t) -3
f(g(0))= 2(0³ +0) -3 ⇒f(g(0))= 2(0) +3
f(g(0))= 3
(f •g)(0)=3
A sample of 25 measurements at breaking strength of cotton thread gave a mean of 7.4 and a standard deviation of 1.2 gms. Find 95% confidence limits for the mean breaking strength of cotton thread.
Answers
Answer:
(6.9296, 7.8704)
Explanation:
Given:
• Sample Mean = 7.4
,• Sample Standard Deviation = 1.2
,• n = 25
First, determine the standard error.
[tex]S.E.=\frac{\sigma}{\sqrt{n}}=\frac{1.2}{\sqrt{25}}=\frac{1.2}{5}=0.24[/tex]At 95% confidence limits, Z=1.96.
Using the formula below:
[tex]\bar{x}-Z_{\frac{\alpha}{2}}(S.E)<\mu<\bar{x}+Z_{\frac{\alpha}{2}}(S.E)[/tex]The limits is calculated below:
[tex]\begin{gathered} 7.4-(1.96\times0.24)<\mu<7.4+(1.96\times0.24) \\ 7.4-0.4704<\mu<7.4+0.4704 \\ 6.9296<\mu<7.8704 \end{gathered}[/tex]At 95%, the confidence limits for the mean breaking strength of cotton thread is (6.9296, 7.8704).
A group of friends' dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill,
including tax and tip, rounded to the nearest cent?
O $150.57
O $154.29
o $154.67
O $156.43
Answers
Their total dinner bill including sales tax rate is 8% and 18% tip will be $156.43 by using the concept of percentages and addition.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
What is sales tax?A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.
Here,
$122.75 dollars to be paid without tax and tip,
=8% of $122.75
=$9.82.
=122.75+9.82
=$132.57
=18% of 132.57
=$23.86
=132.57+23.86
=$156.43
Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.
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the perimeter of the rectangle belowis 112 units. Find the value of y
Answers
Question:
Solution:
The perimeter of a rectangle is the sum of the lengths of its sides. According to this, we get the following equation:
[tex]P\text{ = 2(4y+2)+2(5y)}[/tex]since P = 112, we obtain:
[tex]112\text{ = 2(4y+2)+2(5y)}[/tex]Applying the distributive property, we obtain:
[tex]112\text{ = 8y+4+10y}[/tex]this is equivalent to:
[tex]18y\text{ = 112-4}[/tex]that is:
[tex]18\text{ y = 108}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{108}{18}=6[/tex]that is:
[tex]y\text{ = 6}[/tex]so that, we can conclude that the correct answer is:
[tex]6[/tex]46) The hundreds digit of the smallest six-digit number divisible by 12, 13,
14, 15 and 16 is
Answers
Answer: 2
Step-by-step explanation:
[tex]12=2^2 \times 3\\\\13=13\\\\14=2 \times 7\\\\15=3 \times 5\\\\16 =2^4\\\\\therefore \lcm(12, 13, 14, 15, 16)=2^4 \times 3 \times 5 \times 7 \times 13=21840[/tex]
Multiplying this by 5 to make it the smallest possible six-digit number, we get 109200, meaning the hundreds digit is 2.
Which has quotient of 0.5
Answers
An example of a fraction that has a quotient of 0.5 is 2/4.
What is a quotient?A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio.
In mathematics, the quotient is the number that is produced when two integers are divided. It is essentially the outcome of the division procedure. In arithmetic division, four primary terms are used: divisor, dividend, quotient, and remainder.
In this case, 2/4 = 0.5. This is the quotient.
Note that the information is incomplete and.an overview was given.
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U.S. Customary unit conversion with mixed number values: One...Charlie bought 5 feet of fabric. How much is this in yards?Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.0OlaDOinftyd목x 5?Please help
Answers
Converting feet into yards.
Recall that one yard =3 feet
[tex]1\text{ yard=3 f}eet[/tex]Multiply by 5/3 on both sides, we get
[tex]1\times\frac{5}{3}\text{ yard=3 }\times\frac{5}{3}\text{f}eet[/tex][tex]\frac{5}{3}\text{ yard=}5\text{f}eet[/tex][tex]\text{Use }\frac{5}{3}=1\frac{2}{3}[/tex][tex]1\frac{2}{3}\text{ yard=}5\text{f}eet[/tex]The answer is
[tex]1\frac{2}{3}\text{ yards}[/tex]Place the numbers in the table to show them in order from least to greatest
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Given the following question:
[tex]\begin{gathered} -\frac{3}{8},\frac{1}{8},-\frac{1}{4},-\frac{3}{5},\frac{1}{5} \\ \text{ Negatives go first} \\ -\frac{3}{8}>-\frac{3}{5}>-\frac{1}{4} \\ \frac{1}{5}>\frac{1}{8} \\ -\frac{3}{5}<\frac{-3}{8}<\frac{-1}{4}<\frac{1}{8}<\frac{1}{5} \end{gathered}[/tex]Write the standard form of the equation of the circle described below
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Given:
Center ( 8, -4)
Radius (r) = 3
Find-:
Standard equation of a circle
Explanation-:
The standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where,
[tex]\begin{gathered} (h,k)=\text{ Center} \\ \\ r=\text{ Radius} \end{gathered}[/tex]So equation of circle is:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (h,k)=(8,-4) \\ \\ r=3 \end{gathered}[/tex][tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (x-8)^2+(y-(-4))^2=3^2 \\ \\ (x-8)^2+(y+4)^2=9 \end{gathered}[/tex]Pls. Help me ;( thx ur the best
Answers
Answer:
**NEED USEFUL ANSWER ASAP, H.W QUESTION**
Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?
Step-by-step explanation:
What is eight plus four minus three equal?
Answers
Answer:
9
Step-by-step explanation:
8+4-3=9
im pretty sure 8+4-3=9
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle? N O svē units O 4/3 units 10,5 units O 165 units M
Answers
The all the sided of the equlatral triangle have the same lentgth. All the angles of the triangles are 60 degrees.
The expression for the hight of a equlatral triangle is,
[tex]\sin (60^0)=\frac{h}{l}_{}[/tex]Here, ''
i need help with this question
Answers
Answer:
8%.
Step-by-step explanation:
The perimeter = 2(20 + 30)
= 100 cm.
The new perimeter = 2(20 + 0.05*20 + 30 + 30*0.10)
= 2(21 + 33)
= 2*54
= 108 cm.
Percent increases = 8%.
Order the following from least to greatest: 0.232, 1.2, 1.09, 0, 3, 0.9
Answers
Answer:
0, 0.232 , 0.9 , 1.09, 1.2 , 3