The radius of the circle whose equation is x² + y² + 8x - 6y + 21 = 0 is 2 units
Radius of a circleSince the equation of the circle is x² + y² + 8x - 6y + 21 = 0, to find the radius, we complete the square in the terms x and y and convert it to the form (x - a)² + (y - b)² = r² (1) which is the standard equation of a circle.
So, x² + y² + 8x - 6y + 21 = 0
x² + 8x + y² - 6y + 21 = 0
x² + 8x + (8/2)² - (8/2)² + y² - 6y + (-6/2)² + (-6/2)² + 21 = 0
x² + 8x + 4² - 4² + y² - 6y + (-3)² - (-3)² + 21 = 0
(x + 4)² - 4² + (y - 3)² - (-3)² + 21 = 0
(x + 4)² - 16 + (y - 3)² - 9 + 21 = 0
(x + 4)² + (y - 3)² - 16 - 9 + 21 = 0
(x + 4)² + (y - 3)² - 4 = 0
(x + 4)² + (y - 3)² = 4 (2)
Comapring (1) and (2), r² = 4
So, r = √4
r = 2
So, the radius of the circle whose equation is x² + y² + 8x - 6y + 21 = 0 is 2 units
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The radius of the circle given by the equation is 2.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Given equation is,
x² + y² + 8x - 6y + 21 = 0
(x² + 8x + 16) + (y² - 6y + 9) - 4 = 0
(x + 4)² + (y - 3)² = 4
(x + 4)² + (y - 3)² = 2²
Hence the radius of the circle is 2.
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The distribution of student scores on the quantitative section of the SATs have an approximately normal distribution with a mean score of 501 points, and a standard deviation of 85 points. If you randomly select one student who has taken the SAT, what is the probability that the student will have scored greater than 600 points on the quantitative section of the SATs
Answer:
0.122 = 12.2% probability that the student will have scored greater than 600 points on the quantitative section of the SATs.
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.
Mean score of 501 points, and a standard deviation of 85 points.
This means that [tex]\mu = 501, \sigma = 85[/tex]
What is the probability that the student will have scored greater than 600 points on the quantitative section of the SATs?
This is 1 subtracted by the p-value of Z when X = 600. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{600 - 501}{85}[/tex]
[tex]Z = 1.165[/tex]
[tex]Z = 1.165[/tex] has a p-value of 0.878.
1 - 0.878 = 0.122
0.122 = 12.2% probability that the student will have scored greater than 600 points on the quantitative section of the SATs.
What is the distance between points W
and X to the nearest hundredth?
AY
8
W
4
х
-8
-4
o
4
00
-4
-8
*
0 24
O 16.97
8.49
O 12
Answer:
Step-by-step explanation:
W=(-6,4)
X=(6,-8)
here, x1=-6 , y1=4 , x2=6 , y2=-8
use formula
[tex]\sqrt{)x2-x1)^2+(y2-y1)^2}[/tex]
[tex]\sqrt{(6+6)^2+(-8-4)^2}[/tex]
[tex]\sqrt{12^2+(-12)^2[/tex]
[tex]\sqrt{144+144[/tex]
[tex]\sqrt{288[/tex]
16.97
If there are 1,800 members in the gym, how many are men?
Answer:
1050
Step-by-step explanation:
Find the area of the shape
Help quick plss
Answer:
7.14 in²
Step-by-step explanation:
A = LW
A = 2 x 2 = 4
-----------------------------------------------------------------------------------------------------------------
A = 3.14r²
A = 3.14 (1²)
A = 3.14 (1)
A = 3.14
-----------------------------------------------------------------------------------------------------------------
3.14 + 4 = 7.14
What is the missing side length in the triangle below?
Answer:
Step-by-step explanation:
pythagoras theorem
a^2+b^2=c^2
21^2+b^2=29^2
441+b^2=841
b^2=841-441
b^2=400
b=[tex]\sqrt{400[/tex]
b=20
therefore the length of a missing side is 20.
Answer:
20
Step-by-step explanation:
Use Pythagorean theorem. A^2+B^2=C^2
29 is the hypotenuse.
21^2+x^2=29^2
x=20
Please someone help me with this
Answer: Soup B
Step-by-step explanation: You can find the common denominator for each ratio, and then compare.
Soup A : 3 grams of sodium for 13 cups of soup,
therefore: 30 grams of sodium for 130 cups of soup
Soup B: 9 grams of sodium for 10 cups of soup,
therefore: 117 grams of sodium for 130 cups of soup
So, Soup B has more sodium per cup.
If you want to figure out the amount of sodium for 1 cup, divide the amount of sodium by the amount of soup. Hope this helped!
Find the area of a regular heptagon with a side length of 14 units. Use 2 decimal places
in your calculations.
Answer:
Area of heptagon = 712.26 square units
Step-by-step explanation:
Given the following data;
Side length = 14 units
A heptagon is a polygon with seven sides.
Mathematically, the area of a heptagon is given by the formula;
Area of heptagon = 3.634a²
Where;
a represents the side length.
Area of heptagon = 3.634 * 14²
Area of heptagon = 3.634 * 196
Area of heptagon = 712.26 square units
Which equation represents the line that passes through the points (-4, 0) and (0, 6)
Answer:
y = 1.5x + 6
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (-4, 0)
Points on the y-axis (y1, y2) = (0, 6)
To find the equation of line;
First of all, we would determine the slope of the line.
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {6 - 0}{0 - (-4)} [/tex]
[tex] Slope, m = \frac {6}{4} [/tex]
Slope, m = 1.5
To find the equation of line, we would use the following formula;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - 0 = 1.5(x - (-4))
y = 1.5x + 6
y - 4.6 = 12
Pls help
Answer:
y = 16.6
Step-by-step explanation:
y - 4.6 = 12
Add 4.6 to each side
y - 4.6+4.6 = 12+4.6
y = 16.6
How do you write 6.00 × 10–5 in standard form?
Answer:
[tex]60x-5[/tex]
Step-by-step explanation:
Multiply 10 by 6
60x - 5
The width of a rectangle is 5 times its length. The perimeter is
53.
Find the width and length of the rectangle.
HELP. MATH FINAL DUE SOON....
Answer:
L = x
W = 5x
P = 2 (L + W)
53 = 2(x + 5x)
53 = 2(6x)
53 = 12x
x = 4/5/12
L = 4/5/12
W = 22/1/12
Cindy buys a boat for $15,000. This will be a simple interest
loan at 5.5% for 10 years. What is the interest on the loan?
Answer:
$8,250
Step-by-step explanation:
I = prt
I = ($15,000)(0.055)(10)
I = $8,250
The interest on the loan is $8250.00
The formula for determining simple interest is : loan amount x time x interest rate
Loan is the amount of money that Cindy borrowed. It is $15,000
interest rate = 5.5%
Time is the length of period of the loan. This is 10 years
$15,000 X 0.055x 10 = $8250
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Help plz ! find the measure of the central angle of an arc with length 5pi units and radius of 4.5 units
Answer:
Angle of Arc θ = 200°
Step-by-step explanation:
Given:
Length of arc = 5π
Radius of circle = 4.5 unit
Find:
Angle of Arc θ
Computation:
Using length of arc formula
Length of arc = [θ/360][2πr]
Putting value or length of arc and radius in given formula;
5π = [θ/360][(2)π(4.5)]
5π = [θ/360][9π]
5 = [θ/360][9]
5 = [θ/40]
θ = 40 x 5
θ = 200
Angle of Arc θ = 200°
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5
Madeline says that the two expressions 4(5 + x) and 20+ x equivalent.
(a)
Is Madeline correct?
A
Yes
B
No
Answer:
B No
Step-by-step explanation:
4(5 + x)
To simplify the expression, we must use the distributive property. We need to multiply 4 by the each of the two terms inside the parentheses.
4(5 + x) = 4 × 5 + 4 × x = 20 + 4x
20 + 4x is equivalent to 4(5 + x).
20 + x is not equivalent to 20 + 4x, so 20 + x is incorrect.
Answer: B No
PLWASE HELP WILL MARK BRAINLIST
Answer:
16 in
Step-by-step explanation:
Because you multiply 4in by 3in and you get 12 in. and you subtract 3in by 1in to get the height for the smaller box and you get 2in so multiply 2in by 2in to get 4in and add your products to 12in and 4 in to get 16 in!
Hope this helps!
When the daughter was born, the parents planted tree A. When the son was born, they planted the tree B. tree A and tree B combined have been growing for 18 years. What age will the daughter and the son be after 1 year?
Answer:
I’m pretty sure 19 years old.
Step-by-step explanation:
Hope I could help
PLEASE HELP!
A news story needs to be shared 1,500,000 times in 5 days to get featured on a talk show. The exponential model y=5⋅7x represents the number of shares, y, a news story receives in x days.
About how many days will it take for a news story to reach 1,500,000 shares?
Answer:
It will take 8.17 days for a news story to reach 1,500,000 shares.
Step-by-step explanation:
Note: The correct exponential model is as follows:
y = 5⋅7^x ......................................... (1)
Where:
y = 1,500,000
x = ?
Substituting y = 1,500,000 into equation (1), we have:
1,500,000 = 5⋅7^x ........................ (2)
Taking the natural log of both sides of equation (2) and solve for x, we have:
ln1,500,000 = xln5.7
x = ln1,500,000 / ln5.7
x = 14.2209756660724 / 1.7404661748405
x = 8.17241379310345
Approximating to 2 decimall places, we have:
x = 8.17
Therefore, it will take 8.17 days for a news story to reach 1,500,000 shares.
Can somebody please help me. I am really stuck and the tutor option really isn’t working!!!!
Answer:
its fourth one in my opinoin
Find the value of x in the figure at the right. Please help!
9514 1404 393
Answer:
x° = 88°
Step-by-step explanation:
The sum of interior angles of a hexagon is 180°(6 -2) = 720°. The unknown angle is found by subtracting known angles from the total.
x° = 720° -172° -120° -95° -120° -125°
x° = 88°
Answer:
[tex]\large \sf {\underline{\underline{ \fcolorbox{j}{g}{x = 88 °}}}}[/tex]
Step-by-step explanation:
We know that
➟ The sum of interior angles of a hexagon is 180° × ( 6 - 2 ) = 720 °
Now add all the angles that are given in the question and subtract from the total angles and we get the unknown number .
let unknown number be x.
720 ° - 172 ° + 120 ° + 120 ° + 125 ° + 95 ° = x °720 ° - 632 ° = x°88 ° = x–––––––––☆––––––––––Solve the inequality: a - 4 <10
Α. α >14
B. a < 14
C. a <-14
D. a > 6
E. a<6
HELP!!
==================================================
Explanation:
Add 4 to both sides
a-4 < 10
a-4+4 < 10+4
a < 14
The reason why we add 4 to both sides is to undo the "minus 4" that's happening to the variable.
Which company would cost the most to serve
300 students?
Click on the correct answer.
Company B
Company C
Company A
Answer:
Company a
Step-by-step explanation:
I got it right on the test for plato <3
Solve equation using addition of equality x-2=25 simplify as a integer or fraction
Answer:
x=27
Step-by-step explanation:
1. x-2=25 so add 2 to both sides x=25+2
2. 25+2= 27 so, the answer is x=27 Can you make me Brainliest
Can someone help me please
3x^2 = 48
Divide both sides by 3
3x^2 ÷ 3 = 48 ÷ 3
x^2 = 16
Take a square root from both sides
√x^2 = + √16 " OR " √x^2 = - √16
x = 4 " OR " x = - 4
Thus the correct answer is option 3 .
What is the smallest number that can be divided by 3,9,12 without a remainder
Answer:
36
Step-by-step explanation:
Factor each into prime numbers
3 = 3
9 = 3 * 3
12 = 2 * 2 * 3
least common multiple
product of greatest number of different primes in any of the numbers
3 * 3 * 2 * 2
36
Answer:
LCM = 36
Step-by-step explanation:
Basically you want to find LCM which is the Least Common Multiple. This is the process of coming up with the smallest positive multiple that is common to two or more numbers.
Look up how to solve using cake ladder method. Basically you are going to list all numbers and use the same number to divide them in whole number without remainder. You do this until you encounter a point where you cannot further divide without remainder. Then you multiply the left most column and last row.
I have listed the process below and answer is 36 (multiply the left most column and last row. )
I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS
please help this is very important
this is a big part of my grade
Answer:
They are both wrong
Step-by-step explanation:
exponents are repeated multiplication. so it would be 2*2*2*2... that 28 times.
Please answer this question for me
Which lists all of the y-intercepts of the continuous
function in the table?
O (0,0)
O (-1,0), (2, 0)
O (-1,0), (0, 0)
O (-1,0), (0, 0), (2, 0)
Answer: (0,0)
Step-by-step explanation:
got it correct
The value of y-intercept of the given function is (0,0).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Since, We know that;
When a function intersects the y-axis then the point of intersection is called y-intercept of the function,
Also, for y-intercept x = 0.
That is, if f(x) is the function then its y-intercept is (0, f(0) )
By the given table for x = 0, f(x) = 0
Hence, tWhen a function intersects the y-axis then the point of intersection is called y-intercept of the function,
Also, for y-intercept x = 0.
That is, if f(x) is the function then its y-intercept is (0, f(0) )
By the given table for x = 0, f(x) = 0
Hence, the y-intercept of the given function is (0,0),
Thus, The value of y-intercept of the given function is (0,0).
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Solve
4x > 16
..............
Answer:
256. fffddddddssddddd
Solve the equation 8 - 12 = 20. S = ?
Answer:
This is the answer that I got.
s= - 1/5
Step-by-step explanation:
see the steps below:)
What is the first step in solving -40=12x+8
Answer:
it's in the picture
Step-by-step explanation: