[tex]\boxed{(x+6)^2+(y+2)^2=72}[/tex]
Step-by-step explanation:The center-radius form of the circle equation is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here we know that the y-intercepts are:
[tex]y=4 \ and \ y=-8[/tex]
So:
[tex]\bullet \ If \ y=4, \ x=0 \\ \\ \\ (0-h)^2+(4-k)^2=r^2 \\ \\ \therefore \mathbf{(I)} \ h^2+16-8k+k^2=r^2 \\ \\ \\ \bullet \ If \ y=-8, \ x=0 \\ \\ \\ (0-h)^2+(-8-k)^2=r^2 \\ \\ \therefore \mathbf{(II)} \ h^2+64+16k+k^2=r^2 \\ \\ \\ \bullet \ If \ x=-12, \ y=-8 \\ \\ \\ (-12-h)^2+(-8-k)^2=r^2 \\ \\ \therefore 144+24h+h^2+64+16k+k^2=r^2 \\ \\ \therefore \mathbf{(III)} \ h^2+208+16k+24h+k^2=r^2[/tex]
So we have the following system of equations:
[tex]\left\{ \begin{array}{c}(I)\:h^{2}+16-8k+k^{2}=r^{2}\\(II)\:h^{2}+64+16k+k^{2}=r^{2}\\(III)\:h^{2}+208+16k+24h+k^{2}=r^{2}\end{array}\right.[/tex]
[tex]Subtract \ II \ from \ I \\ \\ \\\left\{ \begin{array}{c}h^{2}+16-8k+k^{2}=r^{2}\\-(h^{2}+64+16k+k^{2}=r^{2})\\---------------------\\h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\end{array}\right.[/tex]
[tex]Simplifying: \\ \\ h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\\ \\ 16-8k-64-16k=0 \\ \\ -24k-48=0 \\ \\ k=-\frac{48}{24} \\ \\ \therefore \boxed{k=-2}[/tex]
From (I):
[tex]h^2+16-8k+k^2=r^2 \\ \\ \\ For \ k=-2 \\ \\ h^2+16-8(-2)+(-2)^2=r^2 \\ \\ \therefore r^2=h^2+36 \\ \\ \\ Substituting \ k \ and \ r^2 \ into \ (III): \\ \\ h^{2}+208+16(-2)+24h+(-2)^{2}=h^2+36 \\ \\ Simplifying: \\ \\ 180+24h=36 \\ \\ 24h=36-180 \\ \\ 24h=-144 \\ \\ h=-\frac{144}{24} \\ \\ \therefore \boxed{h=-6}[/tex]
Finding the radius:
[tex]r^2=(-6)^2+36 \\ \\ r^2=36+36 \\ \\ r^2=72 \\ \\ \therefore \boxed{r=6\sqrt{2}}[/tex]
Finally, the equation of the circle is:
[tex](x-(-6))^2+(y-(-2))^2=72 \\ \\ \boxed{(x+6)^2+(y+2)^2=72}[/tex]
Answer:
[tex](x+6)^2 + (y+2)^2 = 72[/tex]
Step-by-step explanation:
We are given the following information in the question:
y intercept = 4, -8
The circle passes through the point (-12, -8)
Equation of circle:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
where r is the radius of circle, (h,k) is the center of circle.
The circle passes through the points (0,4), (0,-8_ and (-12,-8)
Putting these points in the equation of circle we get:
[tex]1) (0-h)^2 + (4-k)^2 = r^2\\h^2 + (4-k)^2 = r^2\\2) (0-h)^2 + (-8-k)^2 = r^2\\h^2 + (-8-k)^2 = r^2\\3) (-12-h)^2 + (-8-k)^2 = r^2\\[/tex]
Now, we have three equations in three variables.
Solving the three equations, we obtain:
h = -6, k = -2, r = [tex]6\sqrt2[/tex]
Putting these values in the equation of circle:
[tex](x-(-6))^2 + (y-(-2)) = (6\sqrt{2})^2\\(x+6)^2 + (y+2)^2 = 72[/tex]
The above equation is the required equation of circle.
What is the solution to this equation
x +8=-3
Answer:
Step-by-step explanation:
x+8=3
X=-3-8= -11
X=-11
minus the 8 over and the answer will be -11
Answer:
{X:X=-11}
Step-by-step explanation:
It is done by making x the subject in that relation. Thus grouping of like terms.
the equation then becomes ;
x=-3-8
since moving a positive number to the = sign gives a negative number.
-3-8= -11
Therefore ,{x:x=-11} is the solution
Write a subtraction expression using integers, whose difference equals -5.
-3+ -2= -5
same sign add
-7 + 2 = -5
different signs subtract and keep the sign of the BIGGER number
Please help me idk this
Answer:
it would be 2.8150
Step-by-step explanation:
since there is a one in the tenths place it rounds down to 0 with makes it 50
State a true conclusion.
1) If B is between A and C then AB + BC = AC.
2) Q is between R and S.
Conclusion
Answer: QR + RS = QS
Step-by-step explanation:
Answer:
Step-by-step explanation:
a. 2.95 + 18.3 +11
b.9.2 - 0.375
c. 0.275 + 27.5
d. 90 - 0.903
Answer:
a. 32.25
b. 8.825
c. 27.775
d. 89.097
If y= -7 when x= -3, find y when x=9
if i am right you would multiply x= -3 by -3 and you get 9 so you would do the same thing to the y as well so y= -7 and you multiply it by -3 and then y= 21
how do you solve the following equation:
6(3x-5)=21
Answer:
17/6
2 5/6
Step-by-step explanation:
18x-30=21
18x=51
x=51/18
x=17/6
A company packs boxes at a constant rate of 3/4 of a box every of a box every
1/2 minute. What is the number of boxes per
A company packs boxes at a constant rate of
minute the company packs?
Answer:
1 1/2 boxes per minute
Step-by-step explanation:
The company packs boxes at a rate of 3/4 of a box every 1/2 minute. By multiplying this rate by the reciprocal of the time (2/1), we find that the company packs 1.5 boxes per minute.
The student's question involves finding out the rate at which a company packs boxes. The company packs boxes at a constant rate of 3/4 of a box every 1/2 minute.
To find how many boxes are packed per minute, we need to adjust the given rate to reflect the number of boxes packed in one full minute. We can do this by dividing the number of boxes (3/4) by the fraction of the minute (1/2) during which they are packed.
Here's a step-by-step explanation:
Multiply the number of boxes by the reciprocal of the time fraction: (3/4) × 2/1.Simplify the result: 3/4 × 2 = 6/4, which reduces to 3/2 or 1.5.Therefore, the company packs 1.5 boxes per minute.
A man caught a fish. It weighed 5/7kg + 5/7 its own weight what did it weigh
which property is shown? 4/5+(-4/5)=0
Answer:
Inverse Property
Step-by-step explanation:
Any number X plus the negative of itself = 0
what is the volume of the sphere shown below with a radius of 3
Answer:
The answer to your question is: letter A
Step-by-step explanation:
Data
radius = 3
Formula
V = (4/3)πr³
V = (4/3) π (3)³ = Substitution
V = (4/3) π (27) Simplify
V = 108π / 3
V = 36 π u³
A. The volume of the sphere is 36[tex]\pi[/tex] cubic units.
What is formula of volume of sphere ?Let, r be the radius of the sphere.
Then the volume of the sphere = [tex]\frac{4}{3}\pi r^{3}[/tex] cubic units
What is the required volume ?Given radius of sphere (r) = 3 units
So, the volume of sphere = [tex]\frac{4}{3}\pi r^{3}[/tex] cubic units
= [tex]\frac{4}{3}\pi *3^{3}[/tex] cubic units
= [tex]\frac{4}{3}*27\pi[/tex] cubic units
= [tex]36\pi[/tex] cubic units
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What is my number?
Clue 1 My number is a multiple of 2 and 7.
Clue 2 My number is less than 100 but greater than 50.
Clue 3 My number is the product of three different prime numbers.
Answer:
56 is the correct answer
Step-by-step explanation:
50<X<100 it could be 56,70,84,98
56=2*7*5 V
70=2*7*6 X
84=2*7*7 X
98=2*7*8 X
The number that satisfies all the given clues is 84.
Explanation:The number that satisfies all the given clues is 84.
Clue 1: The number is a multiple of 2 and 7. The least common multiple of 2 and 7 is 14. So, any multiple of 14 will be a valid answer.Clue 2: The number is less than 100 but greater than 50. 84 satisfies this condition.Clue 3: The number is the product of three different prime numbers. Prime factorizing 84 gives 2 × 2 × 3 × 7, which are different prime numbers.Therefore, the number that meets all the given clues is 84.
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hi i need help please
BRAINLIEST!!!!!!!!!!!!!!!
Answer:
all the ekements of set A lies in set B
Answer: were is the question and how do you put down brainliest
Step-by-step explanation:
The left and right page numbers of an open book are two consecutive integers whose sum is 519. Find these page numbers.
Answer:
The answer is 259 and 260
Step-by-step explanation:
519/2= 259.5
259+260=519
is the function even, odd, or neither?
Rewrite the radical expression with a rational exponent
3✔️ x7.
A. X21
B. X4
C. X 7/3
D. 3/7
Answer:
[tex]x^{\frac{7}{3} }[/tex]
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{x^{7} }[/tex]
There's a exponent which relates fractional exponents and roots, that is
[tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
So, if we apply this property, the results would be
[tex]\sqrt[3]{x^{7} }=x^{\frac{7}{3} }[/tex]
Therefore, the right answer is the third choice [tex]x^{\frac{7}{3} }[/tex]
Answer:
c
Step-by-step explanation:
i took the test
Write an exponential growth function and explain the growth pattern it models. Use complete sentences?
The function which grows or decreases at a constant % growth rate is known as an exponential function, and further discussion can be defined as follows:
This equation can be written as [tex]\bold{ f(x) = a(1 + r)^x\ or\ f(x) = ab^x}[/tex], where [tex]\bold{b = 1 + r}[/tex].These functions were frequently used to represent real-world applications.These bacterial growth & decay, demographic growth or decline, and compound interest.Growth curve modeling is a statistical technique for examining change over time using observational studies.Learn more:
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9 divided by 4/9 in simplest form
Answer:
The answer is [tex]\frac{81}{4}[/tex]
Step-by-step explanation:
The formula is: [tex]\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}[/tex]
In this case we have: [tex]\frac{9}{1} \div \frac{4}{9} = \frac{9\times 9}{1\times 4} = \frac{81}{4}[/tex]
Since 81 y 4 do not have common divisors. The fraction [tex]\frac{81}{4}[/tex]
is in its simplest form.
Final answer:
9 divided by 4/9 equals 81/4 or 20.25. This is done by multiplying 9 by the reciprocal of 4/9, resulting in 81/4, which is already in simplest form.
Explanation:
To calculate 9 divided by 4/9, we can rewrite the division as a multiplication by the reciprocal of 4/9. Here's the step-by-step explanation:
First, identify the reciprocal of 4/9, which is 9/4.Next, multiply 9 by the reciprocal of 4/9: 9 × (9/4).Perform the multiplication: 9 × 9 = 81 and keep the denominator 4.Now you have the fraction 81/4.Therefore, 9 divided by 4/9 equals 81/4 or 20.25 in decimal form. Since the problem asks for the simplest form, 81/4 is the final answer and cannot be simplified further because 81 and 4 have no common factors other than 1.
how many times does 26 go into 80
Answer:
80/26 = 3.07
Step-by-step explanation:
Answer: 3 times!
Step-by-step explanation:
80 divided by 26 is 3.07 but you can round it to 3
what is the smallest number that rounds to 40
Answer: 2
Step-by-step explanation:
Answer:35
Step-by-step explanation: the reason this is true is because 5is the smallest number that can round up to ten
find the quotient of 144 and 12
Answer:
The answer is 12
Step-by-step explanation:
12 can go into 14 one time and 12 goes into 24 twice
Answer: 144 divided by 12 = 12
Step-by-step explanation:
2x+y=4________(1) and x²+xy=-2_______(2) solve this simultaneously find X and Y
Answer:
[tex][2 - \sqrt{6}, 2\sqrt{6}] \\ [2 + \sqrt{6}, -2\sqrt{6}][/tex]
The work is shown above.
I am joyous to assist you anytime.
As of the 2010 census, there were 3,669 people living in Marlboro, New York. Brooklyn, New York, has 681 times as many people. How many more people live in Brooklyn than in Marlboro?
Answer:
2,494,920
Step-by-step explanation:
We have been given that in 2010 census, there were 3,669 people living in Marlboro, New York. Brooklyn, New York, has 681 times as many people.
[tex]\text{People live in Brooklyn}=681\times 3,669[/tex]
[tex]\text{People live in Brooklyn}=2,498,589[/tex]
Now, we will subtract 3,669 from 2,498,589 to find the number of people more in Brooklyn than Marlboro.
[tex]\text{People more in Brooklyn than Marlboro}=2,498,589-3,669[/tex]
[tex]\text{People more in Brooklyn than Marlboro}=2,494,920[/tex]
Therefore, there are 2,494,920 more people live in Brooklyn than in Marlboro that is 680 times the people in Marlboro.
Randy's football team had the ball on the zero yard line.On their first play they gained 6 yards.On the second play they lost 4 yards.On what yard line is the ball now?
Answer:
2 yard line
Step-by-step explanation:
It starts at the 0 yard line then goes up to the 6 yard line
0 + 6 = 6
After, from the 6 yard line they go back 4 yards
6 - 4 = 2
Now they're at the 2 yard line.
The amount of money,
A
(
t
)
A(t)
in a savings account that pays 3% interest, compounded quarterly for
t
t
yesrs, when an initial investment of $2000 is made, is given by
A
(
t
)
=
2000
(
1.0075
)
4
t
A(t)=2000(1.0075)4t
.
good luck man i hate having to do this kind of thing in class
The formula [tex]\(A(t) = 2000(1.0075)^{4t}\)[/tex] represents the amount of money in a savings account with quarterly compounding interest over time.
The formula [tex]\(A(t) = 2000(1.0075)^{4t}\)[/tex] describes the amount of money, [tex]\(A(t)\),[/tex] in a savings account over time, where [tex]\(t\)[/tex] represents the number of years. The initial investment is $2000, and the account earns interest at a rate of 3%, compounded quarterly.
The term [tex]\((1.0075)^{4t}\)[/tex] represents the growth factor of the investment over time.
The base, [tex]\(1.0075\),[/tex] represents the factor by which the investment grows each quarter, considering the 3% annual interest rate.
Since the interest is compounded quarterly, it is raised to the power of [tex]\(4t\)[/tex] to account for the total number of quarters over [tex]\(t\)[/tex] years.
Multiplying the initial investment by this growth factor yields the total amount of money in the account after[tex]\(t\)[/tex]years.
As time increases, the exponential term increases, leading to exponential growth in the account balance.
This formula provides a mathematical model for calculating compound interest and understanding how investments grow over time.
BRAINLIEST FIRST TO ANSWER! Which property is shown in this example? (8.1+7.9)+5.4=8.1+(7.9+5.4)
Identity/ Commutative/ Associative/ Distributive/
Answer: Associative
Associative says it doesn't matter what is added or multiplied first, and this question shows this
Hope this helps!
Answer: Associative
Step-by-step explanation:
My first number is -2 my fifth number is 26 what’s my third number
Answer:
Answer:
12
Step-by-step explanation:
28 / 4 = 7
1) -2
2) -2+7=5
3) 5+7=12
4) 12+7=19
5)19+7=26
My first number is -2 my fifth number is 26
My third number is 12
Given :
My first number is -2 my fifth number is 26
Lets assume the given numbers are in arithmetic sequence
First term is -2 and fifth term is 26
[tex]a_1=-2\\a_5=26[/tex]
Formula for nth term is
[tex]a_n=a_1+(n-1)d[/tex]
where d is the difference and n is the number of terms
[tex]a_5=a_1+(5-1)d\\a_5=-2+4d\\26=-2+4d\\26+2=4d\\28=4d\\divide \; by \;4 \\d=7[/tex]
Common difference is 7
First term is -2
second term is [tex]-2+7=5[/tex]
Third term is [tex]5+7=12[/tex]
So , the third number is 12
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Last month haos dog ate 40 cans of dog food in 30 days how many cans hao buy to feed his dog for the next 6 days?
Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. he currently has a 40% solution and a 70% solution. how many liters of each does he need to make the needed 30 liters of 60% acid solution?
To make 30 liters of a 60% solution from 40% and 70% solutions, set up two simultaneous linear equations representing volume and concentration; solve them to find the required volumes.
Explanation:To solve the question posed by Gabe, a nuclear physicist, we will need to use the concept of mixtures in Mathematics. The total volume he needs is 30 liters of a 60% acid solution, and he has available 40% and a 70% acid solutions.
The solution to this problem involves setting up two equations, one for the total volume and second for the amount of acid.
Let's denote the volume of the 40% solution by x and the volume of the 70% solution by y. Our first equation based on volume is: x + y = 30 (because total volume needed is 30 liters).
Our second equation represents the fact that the volume times the percentage of acid present (converted to a decimal) for each solution should match up to the total volume times the overall percentage of acid (also converted to a decimal) in the final 60% solution. This gives us: 0.4x + 0.7y = 30*0.6.
Solving these two linear equations simultaneously using methods such as substitution or elimination will give us the value of x and y, which are the required liters of 40% solution and 70% solution respectively.
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