The radius of a circle having the equation x² + y² + 8x - 6y + 21 = 0 is 2 units .
In the question ,
it is given that ,
the circle is having the equation ⇒ x² + y² + 8x - 6y + 21 = 0 ,
we know that ,
general equation of circle is written as x² + y² + 2fx + 2gy + c = 0 ;
so , radius of circle is calculated using the below formula ,
radius = √(f² + g² - c)
On comparing, given equation of circle with general equation of circle ,
we get , the values of f = 4 and g = -3 .
So after substituting the values of f , g and c in the radius formula ,
we get ,
radius = √(16 [tex]+[/tex] 9 - 21)
= √(16 [tex]+[/tex] 9 - 21)
= √(25 - 21) = √4 = 2 .
Therefore , the given circle has radius = 2 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 ?
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Evaluate the expression for the given value of the variables.
0.7g - 2.7h
g= 17, h =2
The value of the expression 0.7g - 2.7h at g = 17 and h = 2 is 6.5.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A numerical expression 0.7g - 2.7h.
Now, The values of the expression at g = 17 and h = 2 can be obtained if we replace these numerical values of g and h.
∴ 0.7g - 2.7h.
= 0.7(17) - 2.7(2).
= 11.9 - 5.4.
= 6.5
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PLEASE HELP
Graph g(x) = −4x + 8 and identify its x-intercept.
(0, 2)
(0, 8)
(2, 0)
(8, 0)
The x-intercept is (2,0). And the correct option is C: (2,0).
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
We have the standard form of the slope-intercept form:
y = mx + b,
where m is the slope and b is the intercept.
In order to find the x-intercept,
substitute y=0 to the equation.
And solve for x.
Given equation is;
g(x); y = -4x+8
y = -4x+8
The slope of the equation is -4.
To find the x-intercept,
Now, -4x + 8 = 0
-4x = -8
x = 2
And the graph is given in the image.
Where (2,0) is the x-intercept.
The point (2,0), where a line crosses x-axis, is known as the x-intercept.
Therefore, the x-intercept is (2,0).
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Answer: (2, 0)
Step-by-step explanation: I took the test and got it right.
I promise it is right!
Just make sure it is the same problem!!
Good luck!!!!! ;)
a-9y
1
a=−5 and y=5.
-5
X
Answer:
What do you need here Any help?
A urvey found that 27% of high chool tudent and 94% of teacher and chool employee drive to chool. The ratio of tudent to employee i about 10 to 1 Roger tate that the number of employee who drive to chool explain how Roger tatement could be correct
The information provided indicates that 188 teachers and staff members own vehicles.
What does number mean?An arithmetic value used to compute and describe a quantity is, in fact, a number. In writing, numerical symbols like "3" are used to represent numbers. Using numerals or symbols to symbolize numbers, a numbering system seems to be a logical approach to convey numbers.
Briefing:27% of students (s) 94 percent are teachers and workers (t).
The ratio between these two variables is 10:1, which suggests that there is only one employee for every 10 pupils, meaning that students outnumber teachers and other workers by a factor of 10.
Thus, 27% of 10 pupils is equal to 2.7 students, and 94% of 1 employee is equal to 0.94 employees and teachers. Therefore, if there are 2000 pupils, there must be 200 teachers. The number of students who own automobiles is 0.27(2000)=540, whereas 0.94(200)=188 is the number of teachers and staff who own cars.
You can see from this ratio and percentages that more pupils drive themselves to school than do teachers and other staff members. Roger's assertion is accurate for this reason.
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we roll two six-sided fair dice. list all the outcomes that the sum of the numbers showing face up is at least 9. what is the probability of the event that the sum of the numbers showing face up is at least 9?
the probability of the event that the sum of the numbers showing face up is at least 9 is 1/9.
What is probability?
The chance of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes.
Rolling two dice produces a total of 36 possible results.
One of the following will be necessary to reach the amount of 9: (3,6),(6,3),(4,5), or (5,4). 4 final results out of 36 overall.
Rolling two dice results in a 4/36 or 1/9 chance of having a sum of nine.
Hence the probability of the event that the sum of the numbers showing face up is at least 9 is 1/9.
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What is square example?
A square is any 2-dimensional shape that has all 4 sides equal and opposite sides parallel.
A square is typically identified when we see any shape which has 4 sides. These sides are equal to one another. The opposite sides are parallel. Another very important feature to be noted is that a square makes an angle of 90° with its adjacent sides.
If the angles are not 90°, then the shape is a rhombus and not a square.
A perfect example of a square is the game board of ludo. That is a perfect square. Another example is a handkerchief.
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I need help!!! I need to know what the graphed linear equation is???
The graphed linear equation will be [tex]y= 6+ (\frac{-3}{2}x )[/tex].
What is Graphed linear equation?
A linear equation with two variables has a line as its graph, which is why it is referred to as linear. Plotting the points (x1,y1) and (x2,y2) and the line that connects them.
Solution:
[tex]Slope \ of\ line= \frac{(y_{2-} y_{1} )}{(x_{2-} x_{1} )} \\\\Slope \ of\ line = \frac{-6} {4} \\\\Slope \ of\ line = \frac{-3}{2}[/tex]
One point on the line is (0,6)
The equation of the line is,
[tex]y-6= (\frac{-3}{2} )(x-0)\\\\y-6= (\frac{-3}{2} )(x)\\\\y= 6+ (\frac{-3}{2}x )[/tex]
The graphed linear equation will be [tex]y= 6+ (\frac{-3}{2}x )[/tex].
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A spinner is separated into nine equal sections, each with a different color. According to theoretical probability, how many times can we expect to land on each color, if we spin one hundred and eighty times?
We are expected to land on each color 20 times in 180 spins
What is probability?Probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%
probability of landing any color on any given attempt is 1/9 or 0.11, since all colors are different, the probability for each is the same.
if you multiply the probability by 180 you will find the amount of time you will expect to land on each color
Hence, 1/9 x 180 = 20times
Hence are expected to land on each color 20 times in 180 spins
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Given the following formula, solve for v.
8 = 1/2 a^2v + c
Answer:
[tex]v = \frac{16-2c}{a^{2} }[/tex]
Step-by-step explanation:
Original equation
[tex]8 = \frac{1}{2}a^{2} v + c[/tex]
Multiply both sides by 2 to get rid of fraction
[tex]16 = a^{2}v + 2c[/tex]
Get constant on right, [tex]a^{2} v[/tex] on left
[tex]-a^{2}v = 2c - 16[/tex]
Divide both sides by [tex]a^{2}[/tex]
[tex]v = \frac{16 - 2c}{a^{2} }[/tex]
this is a partially decoupled system. solve for v(t) first by separation of variables. then substitute into the second equation and solve for y(t). if c1 is the constant that is in the general solution for v(t), and c2 is the constant that appears when solving for y(t), what is the value of c2?
For the given partially decoupled system, dv/dt = -v , v(0) = -1 and dy/dt = v , y(0) = 100
The value of the constant that appears when solving for y(t) i.e, c₂ is 99..
We have given that
dv/dt = -v ; v(0) = -1
By separtion of variables ,
dv/v = - dt
=> ₋₁∫ᵛ dv/v = ₀∫ᵗ -1 dt
=> ₋₁[ ln(v) ]ᵛ = ₀[ -t]ᵗ
=> ln(v) - (-ln(-1)) = -t - 0
=> ln(v/-1) = - t
=> -v = e⁻ᵗ
=> v = - e⁻ᵗ
Now, dy/dt = v = - e⁻ᵗ
Integrating both sides y = 0 to 100 and t =0 to t
₀∫ʸ 1dy = ₀∫ᵗ - e⁻ᵗ dt
=> ₀[ y ]ʸ = - ₀[- e⁻ᵗ ]ᵗ
=> y - 100 = e⁻ᵗ - 1/e⁰ (since y(0)= 100) => y - 100 = e⁻ᵗ - 1
=> y = e⁻ᵗ - 1 + 100
=> y = e⁻ᵗ + 99
Which is general solution of dy/dt .
So, the constant that appears when solving for y(t), c₂ is 99.
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Complete question:
dy/dt =v, y(0) = 100 ; dv/dt = -v , v(0) = - 1 ..This is a partially decoupled system. Solve for v(t) first by separation of variables. Then substitute into the second equation and solve for y(t). If C1 is the constant that is in the general solution for v(t), and C2 is the constant that appears when solving for y(t), what is the value of C2?
Which expression is equivalent to 8j+8j?
Answer:
16j
Step-by-step explanation:
Since 8j is equal to 8j, you can just add 8j+8j=16j
At a sale, the price of a washing machine
was reduced by 12% to $440. What was the original price of the washing machine?
Answer:
$500
Step-by-step explanation:
100-12=88
88/100=440/x
88x=100(440)
88x=44000
/88. /88
x=500
hopes this helps
2100 dollars is placed in an account with an annual interest rate of 6%. To the nearest tenth of a year, how long will it take for the account value to reach 9400 dollars.
It will take 57.9 years for the account value to reach 9400 dollars.
What does the term "simple interest" mean?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
The fact that
The equation for simple interest is:
A = P(1+rt)
where
The final investment value is A.
P is the initial investment's principal.
The interest rate is r.
There are t time periods.
We have a problem with this.
t = ?
P = $2100
A = $9400
r = 6% = 6/100 = 0.06
In the formula above, substitute
9400 = 2100 (1+t[0.06])
1 + 0.06t = 94/21
t = 94 - 21 / 21 * 0.06
t = 73/1.26
t = 57.9 years
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What is the slope of 1/3 and 3 5?
The slope of the two points, (1,3) and (-3,5) is -1/2 and can be calculated by the point-slope formula.
We know that the slope is a change in y divided by a change in x or we can say "rise over run". The point-slope formula is given by-
(y2-y1) = m (x2-x1) ........where m is the slope.
Hence, we can manipulate it into m= (y2-y1) /(x2-x1) to find the slope of the given points.
let (1,3) = (x1,y1)
and (-3,5) = (x2,y2)
substituting these coordinates in the equation of the slope we get,
slope= (5-3) /(-3-1)
= 2/-4
= -1/2
Hence, the slope of the given two points (1,3) and (-3,5) is -1/2.
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The complete question is -
What is the slope of (1, 3) and (-3, 5)?
In any solution, the part in the greatest quantity or volume is called the ___________.
The solvent is the defined as a part of the solution that is in the greater quantity, and the solute is the smaller portion of the solution.
The part broken up in a liquid to frame an answer is known as a solute. The solute fixation is a game changer in deciding if the arrangement is strong, fluid, or vaporous.
A solvent is normally a fluid that is utilized to break up a solute. A fluid breaks down different parts to produce an answer. Presently, particle creation is leaned toward by polar solvents like water yet not by nonpolar solvents like hydrocarbons. Water is a genuine illustration of a dissolvable.
The contrast among solute and dissolvable can be resolved in light of their definition, actual appearance (fundamentally a condition of issue:- strong, fluid, or gas structure), dissolvability, and limit.
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(Complete question) is:
The __________ is defined as the part of the solution that is in the greater quantity, and the __________ is the smaller portion of the solution.
Scarlet must build a rectangular pen for her peacock, Paulie. Scarlet has P feet of fencing.
Scarlet decides that the width of Paulie's pen will be a third of the length of his pen.
(a) Write an equation describing the relationship between P and the width of the pen, w.
(b) Solve the equation for w
The equation describing the relationship between P and the width of the pen, w is P = 1/3L².
Tbe equation for w is; w = 1/3(√3P)What is the width of the rectangular pen?Area of the pen = P square feetLength of the rectangular pen = LWidth of the rectangular pen = 1/3LArea of a rectangular pen = Length × width
P = L × 1/3L
P = 1/3L²
L² = P ÷ 1/3
multiply by the reciprocal of 1/3
L² = P × 3/1
L² = 3P
Find the square root of both sides
L = √3P
To solve the equation for w
Width of the rectangular pen = 1/3L
w = 1/3(√3P)
In conclusion, the relationship between P and the width of the pen, w is P = 1/3L².
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Two triangles are shown on the coordinate grid.
Two diagonals of rectangle are 3x+2cm and 2x +3cm Find the measurement of each diagonal.
The measurement of each diagonal is 5 cm in the given rectangle.
The diagonals of a rectangle are the two line segments that connect opposite corners of the rectangle and divide the rectangle into four right triangles.
Two diagonals of the rectangle are 3x+2cm and 2x +3cm which is given in the question.
The diagonals of a rectangle are equal in length, so we can set the two given lengths equal to each other:
3x + 2 cm = 2x + 3 cm
Subtracting 2x and 3 from both sides gives us:
x = 1 cm
Substituting this value back into the original equations gives us:
3(1) + 2 cm = 2(1) + 3 cm
3 + 2 cm = 2 + 3 cm
5 cm = 5 cm
Therefore, each diagonal has a length of 5 cm.
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c. A circular puzzle is 20 inches in diameter. All of the pieces are about the same size. You want to know about how many pieces there are in the puzzle.
Answer:
There is no exact answer to this question as it depends on the complexity of the puzzle. Generally speaking, a puzzle with a diameter of 20 inches would contain between 1000 and 2000 pieces.
Step-by-step explanation:
Solve 65,254 ÷ 37 = _______
O1,763
O1,763 6/37
O1,763 23/37
O1,764
Answer:
01763
Step-by-step explanation:
Because i use calculator
A jar contains 350 marbles of two colors. of all the marbles, 4 out of every 7 marbles are white. enter a number in the box to show the number of marbles of the color white.
The number of marbles of the color white, if A jar contains 350 marbles of two colors of all the marbles, 4 out of every 7 marbles are white, is 200.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1.
Given:
A jar contains 350 marbles, n = 350,
4 out of every 7 marbles are white,
Calculate the number of whites balls as shown below,
Number of one white ball in 7 marbles = 4 / 7
Number of white balls in 350 marbles = 4 / 7 × 350
Number of white balls in 350 marbles = 200
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WILL GIVE 20 POINTS
Margaret identified the different transformations of graphs. She made at least one mistake. For each transformation, identify whether she made a mistake and, if so, correct her error.
Answer:
20
Step-by-step explanation:
Andy rapidly pedaled his bike to reach a certain speed, then continued at that speed. He rapidly pedaled again, then quickly pressed on his brakes to come to a stop.
Which graph best represents Andy’s bike ride?
The 1st graph best represents Andy’s bike ride
How to determine which graph best represents Andy’s bike ride?(Consider the image I attached)
Andy's speed and time were initially at point 1 (starting point). That is he is not moving
If he rapidly pedaled his bike to reach a certain speed. That is, he moved from point 1 to point 2. This implies the speed increase with an increase in time.
Then continued at that speed. That is, he moved from point 2 to point 3. This implies the speed remains the same with an increase in time
He rapidly pedaled again. That is, he moved from point 3 to point 4. The speed increase with an increase in time again.
Then quickly pressed on his brakes to come to a stop. That is, he moved from point 4 to point 5.
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Reduce to simplest form.
Divide the numerator and denominator by the
greatest common factor, 3.
[?]
15 27
=
Enter the number that belongs in the numerator.
Answer: 5/9
Step-by-step explanation: 15/27 divided by 3. 15 divided by 3 is 5 and 27 divided by 3 is 9.
HELP PLS Determine the type of correlation represented in the scatter plot below
Answer:
this is a positive correlation
Step-by-step explanation:
it is going up so its positive
What are the 3 types of investors?
The three types of investors in a business are, active investors, pre-investors and passive investors.
Pre-investors:
A person who is simply not involved in any kind of investments, are
called as pre-investors. A pre-investor's financial world is primarily
based upon consumption by giving a little preference to savings or
investments.
Passive investors:It is a starting point of an individual's entering into the investment
world for an individual. When an individual graduates, and learn and
gain knowledge about investments, he sub-divides his income into
investments to expand his income further.
Active investors:Active investors are basically built upon the foundation of the
passive investors. They take their investments into higher heights in
order to handle their wealth as their business.
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when adding fractions with like denominators it is important for students to focus on which key idea?
the only factor that someone has to focus that unit is the same.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.A fraction in mathematics is a number that is stated as a percentage, such as 1/2 or 2/3. The bottom number indicates all of the components that make up a single unit.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
when adding fractions with like denominators it is important for students to focus on which key idea that
Units are the same.
Hence the only factor that someone has to focus that unit is the same.
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what percentage of women in the united states work and have a child under 6 years of age?
77.2 percent of mothers with children under age 6 work in the United states.
Mothers are less likely to work when their children are young than when they are older: In 2019, women with children under the age of six had a labor force participation rate of 66.4%, while those with children aged six to seventeen had a rate of 76.8%.
Among mothers with children under the age of three, married mothers were less involved than mothers of other marital situations — 62% versus 66%.
Working women confront child care challenges: According to a Center for American Progress poll, half of American families reported trouble getting child care.
Based on the amount of time and resources based on the amount of time based on the amount of time based on the length of time based on the length of time based on the length of time based on the duration of time based on the amount of time.
More over two-thirds of homemakers indicated they would "search for employment" if they could find more affordable child care. One-third of part-time parents stated they would work more hours if child care was available.
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what needs to be known to determine the critical values for an independent-samples t test?
In order to determine the critical values for an independent-samples T-test, the following information needs to be known:
The size of the sample (n)The significance level (alpha)The degrees of freedom (df)The type of t-test being conducted (one-tailed or two-tailed)What needs to be known to determine the critical values for an independent-samples T test?The critical values for an independent-samples t test are used to determine if the differences between two samples are statistically significant. In order to calculate the critical values, the size of the sample (n), the significance level (alpha), the degrees of freedom (df), and the type of t-test (one-tailed or two-tailed) must be known. The degrees of freedom are equal to the number of observations in the sample minus
The size of the sample is the total number of observations in the two samples. The significance level is the probability of making a type-I error (rejecting the null hypothesis when it is true). Finally, the type of t-test is used to determine if the test is one-tailed (testing for a difference in one direction) or two-tailed (testing for a difference in both directions). Once all of this information is known, the critical values can be calculated to determine if the differences between the two samples are statistically significant.
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If one measurement of a golden rectangle is 6. 1 inches, what is the other measurement? a. 4. 482 b. 7. 718 c. 9. 87 d. 1. 618.
The other measurement of the golden rectangle is 9.87 inches. (Option C)
Golden rectangle refers to a rectangle whose sides are in the golden ratio. Golden ratio refers to the ratio between two quantities if their ratio is equal to the ratio of their sum to the larger of the two quantities. In other words, it exists when a line is divided into two parts and the longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a) which both approximately equal to 1.618.
Hence, if one measurement of the rectangle is 6.1 inches, the other measurement would be = 6.1*1.618 ≈ 9.87 inches
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