Answer: 4) The center is located at (1, 3), and the radius is 6
Step-by-step explanation:
Solve the general equation of the circle.
x^2 -2x +1+ y^2-6y+9= 26+1+9 (x-1)^2+(y-3)^2=36=6^2
Hence, the coordinates of the center (1,3) And the radius will be 6
The center is located at (1,3) and the radius is 6.
What is center of the circle?"The center is the point from which all of the points on the circle are the same distance."
What is radius of the circle?"The radius is the exact distance from the center to any point on the circle."
We have
[tex]x^{2} -2x+y^{2}-6y = 26\\[/tex]
Add 1 and 9 on both sides of equation
⇒[tex]x^{2} -2x+1+y^{2}-6y+9 = 26+1+9[/tex]
⇒[tex](x-1)^{2} +(y-3)^{2}= 36[/tex]
⇒[tex](x-1)^{2}+(y-3)^{2}=6^{2}[/tex].......(1)
We know the Standard form of equation of the circle
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
By comparing the standard form and equation (1)
Center (h, k) = (1, 3) and radius is 6
Hence, The center is located at (1,3) and the radius is 6.
Learn more about circle here
https://brainly.com/question/13658927
#SPJ2
Write the log equation as an exponential equation. You do not need to solve for x:
log(x^2+5x-18)=x+2
Answer: 10ˣ⁺² = x² + 5x - 18
Step-by-step explanation: The base of the log becomes the base of the power, the right side of the equation becomes the exponent, and the result in the original equation moves to the other side.
Notice that we aren't given a base, so we know that we are
dealing with a common log which has a base of 10.
what number does the 9 have least vaule
Answer:
The least value is 7.079 because it is in the thousandths place.
John finances his daughter's college education by making deposits into a fund earning interest at an annual effective rate of 8%. For 18 years he deposits X at the beginning of each month. In the 16th through the 19th years, he makes a withdrawal of 25,000 at the beginning of each year. The final withdrawal reduces the fund balance to zero. Calculate X.
Answer:
Monthly payment = 241.925
Step-by-step explanation:
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
Solving, we have i = 0.6434% monthly approximately
To balance the deposits and withdrawals, we note that the last withdrawal is the beginning of year 19, and the last deposit is the last month of year 18. We therefore conclude that the "future values" fall on the same day, and that they are equal.
We consider the annual deposits D (accumulated at the end of the year, and annual withdrawals W are in separate accounts. By the end of the operations, one will balance the other (they are equal).
We will need the following formula to calculate future value F given the periodic amount, A, interest rate per period, i, and the number of periods.
F(A,i,n) = A*((1+i)^n-1)/i
Step 1:
calculate the future value of the withdrawals
A = W = 25000 (annual withdrawal)
i = 8% (effective annual interest)
n = 4 years (beginning of 16,17,18,and 19th years)
F(A,i,n) = A*((1+i)^n-1)/i
= 25000( (1+0.08)^4 - 1)/(0.08)
= 112652.80
This is also the total deposit after eighteen years.
Step 2:
calculate the future value of the annual deposits D
A = D (total of annual deposits)
i = 8% (effective annual interest)
n = 18 years
Future value of deposits
F(A,i,n) = A*((1+i)^n-1)/i
= D( (1+0.08)^18 -1 ) / 0.08
= 37.45024373981167D
Since this must equal the total withdrawal, we equate the two to calculate D.
37.45024373981167D=112652.80
and solve for D
D = 112652.80 / 37.45024373981167
= $3008.0659
Step 3
Calculate monthly deposit, X
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
The actual monthly interest rate is therefore
i = 1.08^(1/12)-1
Over a 12 month period, (one year), the monthly amount X to accumulate an annual amount D (=$3008.0659) is therefore given by
D = X*((1+i)^n-1)/i
3008.0659 = X*(1.08-1)/(1.08^(1/12)-1)
or the monthly amount
X = $3008.0659 / ( 1.08^(1/12)-1)
= 241.925 per month.
=
One year, the population of a city was 99,000. Several years later it was 82,170. Find the percent decrease.
Select the correct answer.
Evaluate the following expression when x = -4 and y = 4.
x6-x/4y
Answer:
[tex]{ \tt{ {x}^{6} - \frac{x}{4y} }} \\ = { \tt{ {( - 4)}^{6} - \frac{ - 4}{4(4)} }} \\ \\ { \tt{ = 4096 + 4}} \\ \\ = 4100[/tex]
The value of the equation ( x⁶ - x ) / 4y = 1025/4 when x = -4 and y = 4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( x⁶ - x ) / 4y be equation (1)
The value of x = -4
The value of y = 4
Substituting the values of x and y in equation (1) , we get
A = ( ( -4 )⁶ - ( -4 ) ) / ( 4 x 4 )
On simplifying the equation , we get
A = ( 4096 + 4 ) / 16
A = 4100 / 16
A = 1025 / 4
Therefore , the value of A is 1025/4
Hence , the value of the equation is 1025/4
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
Please help me.
The table below represents the closing prices of stock ABC for the last five
days. Using your calculator, what is the equation of linear regression that fits
these data?
Answer:
Step-by-step explanation:
I can tell you how to do this on your calculator, but I have no idea what kind of calculator you have and the methods are different for the various TI graphing calculators, so I'll just tell you that your answer is the last choice given. It's a terrible fit, but if the instructions say linear, the last choice is the equation that the calculator gives.
The regression equation for Y is: ŷ = -0.223X + 20.523
What is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Sum of X = 15
Sum of Y = 99.27
Mean X = 3
Mean Y = 19.854
The sum of squares (SSX) = 10
The sum of products (SP) = -2.23
Regression Equation = ŷ = bX + a
b = SP/SSₓ = -2.23/10 = -0.223
a = My - bMₓ = 19.85 - (-0.22*3) = 20.523
ŷ = -0.223X + 20.523
Learn more about Linear equations here:
https://brainly.com/question/11897796
#SPJ5
"Darcie wants to crochet a minimum of 333 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal." pls help lol
Answer:
Ive seen this question before, its supposed to be 3 blancckets and 15 days can be skipped
Step-by-step explanation:
60-45= 15
15 times 3 is 45
Evaluate: 4+8 / 2 x (6 - 3)
Answer:
16
Step-by-step explanation:
4+8/2*(6-3) = 4+8/2*3 = 4+4*3 = 4+12 =16
Answer:
18
Step-by-step explanation:
4+8 /2 *(6-3)
=4+8/2 * 3
=(4+8)*3/2
=12*3/2
=36/2
=18
Evaluate the expression 4q(q + 3w)^2 when q = 2 and w = 3
Answer:
512
Step-by-step explanation:
when q = 2, w = 3
4q(q + 3w)^2
= 4(2) ((2)+3(3))^2
= 512
Find the measure of angle c
Solve simultaneous equation x-y=4 and x²+y²=10
Step-by-step explanation:
hear is your answer please check attachment
The equation (x-7)^2 + (y - 6)^2 = 36 represents a Ferris wheel plan displayed on a grid, where each unit represents 1 meter. What is the diameter of the Ferris Wheel?
Answer:
[tex]12m[/tex]
Step-by-step explanation:
we are given a circle equation
[tex] \displaystyle (x - 7 {)}^{2} + (y - 6 {)}^{2} = 36[/tex]
since it's a circle equation where 36 is the square of the redious we can figure out redious by solving the following equation
[tex] \displaystyle {r}^{2} = 36[/tex]
square root both sides:
[tex] \displaystyle {r}^{} = 6[/tex]
remember that,
[tex]\displaystyle d = 2r[/tex]
thus substitute the value of r:
[tex]\displaystyle d = 2.6[/tex]
simplify multiplication:
[tex]\displaystyle d = 12[/tex]
hence,
the diameter of the Ferris Wheel is 12m
Find an equation for the graph shown.
Answer:
y=-sin(x)
Step-by-step explanation:
y=-sin(x)
The base salary of 500$ per week plus a commission of 10.5% of sales
Answer:
salary = $ 500 + 0.105 sales
Step-by-step explanation:
Weekly Income = 500 + 0.105S where S= weekly sales
in x, y math format that's
y=500+0.105x
Economics often uses Q for quantity and Y for income
so,
Y=500+0.105Q
Hope this answer helps you :)
Have a great day
Mark brainliest
what is the smallest perimeter of area 12 cm can have?
edit: at cm there should have been a small 2 at the top but I forgot just pretend it's there pls.
Answer:
14
Step-by-step explanation:
area = lb
4*3 or 6*2 or 1*12
perimeter= 14,16,26
Plz find the surface area
Answer:
What are the answers?
If sin θ = square root of three over two, which could not be the value of θ?
(-32) +(-8) -(+40)+(40)+(78)-(46)
Answer:
or -32-8-40+40+78-46=-8
Step-by-step explanation:
Answer:
-8 is the answer!!!!
Step-by-step explanation:
you can use calculaTor
A group of 42 monkeys meet in the forest for a swinging competition. The monkeys divide into teams with 8 monkeys on each team. They make as many teams as they can, but not every monkey is in a team. How many teams of monkeys will there be? Answer must be a whole number. How many monkeys remain without a team? Answer must be a whole number.
Answer:
the a answer is five
Step-by-step explanation:
divide 42 by 8 and round it it up to the closest whole number
the cone and cylinder above have the same radius and height the volume of the cone is 222 cubic cm what is the volume of the cylinder
Answer:
Step-by-step explanation:
volume of cone v=1/3πr²h
volume of cylinder V=πr²h
V=3v
volume of cylinder=3×222=666 cubic cm.
Xavier shoots a basketball in which the height, in feet, is modeled by the equation, h(t) = -4t^2+10t +18, where t is time, in
seconds. What is the maximum height of the basketball?
Answer:
h = 24.25 feet
Step-by-step explanation:
Xavier shoots a basketball in which the height, in feet, is modeled by the equation.
[tex]h(t) = -4t^2+10t +18[/tex] ....(1)
For maximum height,
Put dh/dt=0
So,
[tex]\dfrac{dh}{dt}=\dfrac{d}{dt}(-4t^2+10t +18)\\\\=-8t+10[/tex]
So,
-8t = -10
t =1.25s
Put t = 1.25 s in equation (1)
[tex]h(t) = -4(1.25)^2+10(1.25) +18\\\\=24.25\ feet[/tex]
So, the maximum height of the basketball is equal to 24.25 feet.
Please help ASAP with number 8 please
Answer:c
Step-by-step explanation:
subtract 5x-7y+6 from 3x-4y-2
Answer:
[tex]2x−3y+8[/tex]
Step-by-step explanation:
[tex](5x−7y+6)−(3x−4y−2)[/tex]
[tex]5x−7y+6−(3x)−(−4y)−−2[/tex]
[tex]5x−7y+6−3x+4y+2[/tex]
[tex]2x−7y+6+4y+2[/tex]
[tex]2x−3y+6+2[/tex]
[tex]2x−3y+8[/tex]
Hope it is helpful...Tyrone's bowling scores for the first four games of the season were 120,123,105, and 109. He wants to increase his mean score to 125.
• What score does Tyrone need in the fifth game so that his mean score is 125?
• Explain your reasoning or show all of your work.
Answer:
He should measure the length of the bowling alley using meters
Step-by-step explanation:
The score does Tyrone need in the fifth game so that his mean score is 125 is 168.
What is an arithmetic mean?
It is defined as the sum of all observations divided by the number of observations.
Given
Tyrone's bowling scores for the first four games of the season were 120,123,105, and 109. He wants to increase his mean score to 125.
[tex]\frac{120+123+105+109+x}{4+1} =125[/tex]
⇒ [tex]\frac{457+x}{4+1} =125[/tex]
⇒ [tex]\frac{457+x}{5} =125[/tex]
⇒ [tex]{457+x} =125[/tex] × [tex]5[/tex]
⇒ [tex]{457+x} =625[/tex]
⇒ [tex]x =625-457[/tex]
⇒ [tex]x =168[/tex]
Hence, the score does Tyrone need in the fifth game so that his mean score is 125 is 168.
Learn more about mean here
https://brainly.com/question/23706022
#SPJ2
What is the factorization of 81a6 - 100? (9a2 − 10)(9a3 + 10) (9a2 − 10)(9a3 − 10) (9a3 − 10)(9a3 + 10) (9a3 − 10)(9a3 − 10)
Answer:
(9a³ − 10)(9a³ + 10)
Step-by-step explanation:
Difference of squares
(9a³ − 10)(9a³ + 10)
Answer:
What is the factorization of 81a6 - 100?
(9a2 − 10)(9a3 + 10) (9a2 − 10)(9a3 − 10) (9a3 − 10)(9a3 + 10) <<< CORRECT (9a3 − 10)(9a3 − 10)
Step-by-step explanation:
Oct 2021 Edge
Work out the perimeter of this semicircle.
Take a to be 3.142
10 cm
Answer:
perimeter=1/2*2πr
Step-by-step explanation:
1/2*2*3.142*10
=31.42
Select all the equations
represented by this tape diagram.
A. 6 + 6 + 6 + 6 + 6 = ?
B. 5 + 6 = ?
C. ? = 6.5
D. ? = 6.6.6.6.6
E. ? = 5 = 6
F.5 = ?= 6
Answer:
D.
is the correct answer
Is anyone good at Spanish ? I need help with Spanish homework. I’ll mark you brainliest
Answer:
...
Step-by-step explanation:
what help do you need ??
Farah spent $13 on 4 items from the
snack stand at the airport. The
snack stand charges $7 per
sandwiches and $2 per bags of
snack mix. It she purchased a
combination of sandwiches and
snack mix bags, how many of each
food item did Farah purchase?
Answer:
Farah bought 1 sandwich which cost $7 and three snack mix bags which also cost (2 + 2 + 2)$
2+2+2+7=$13
On my other question I posted I forgot to add the attachment, but uh please help down below 3
Answer:
6 crayons more
Step-by-step explanation:
At Dante's party, each child gets 192/16 = 12 crayons each
At Maria's party, each child gets 234/13 = 18 crayons each.
Therefore, each child at Maria's party gets 18-12 = 6 crayons more each than at Dante's party.
Answer:
answer is 6
Step-by-step explanation:
each child at Dante's party receive 192÷ 16 crayons, which is 12
each child at Maria's party receive 234÷ 13 crayons, which is 18