I will explain you and pair two of the equations as an example to you. Then, you must pair the others.
1) Two circles are concentric if they have the same center and different radii.
2) The equation of a circle with center xc, yc, and radius r is:
(x - xc)^2 + (y - yc)^2 = r^2.
So, if you have that equation you can inmediately tell the coordinates of the center and the radius of the circle.
3) You can transform the equations given in your picture to the form (x -xc)^2 + (y -yc)^2 = r2 by completing squares.
Example:
Equation: 3x^2 + 3y^2 + 12x - 6y - 21 = 0
rearrange: 3x^2 + 12x + 3y^2 - 6y = 21
extract common factor 3: 3 (x^2 + 4x) + 3(y^2 -2y) = 3*7
=> (x^2 + 4x) + (y^2 - 2y) = 7
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 7
=> (x + 2)^2 + (y - 1)^2 = 12 => center = (-2,1), r = √12.
equation: 4x^2 + 4y^2 + 16x - 8y - 308 = 0
rearrange: 4x^2 + 16x + 4y^2 - 8y = 308
common factor 4: 4 (x^2 + 4x) + 4(y^2 -8y) = 4*77
=> (x^2 + 4x) + (y^2 - 2y) = 77
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 77
=> (x + 2)^2 + (y - 1)^2 = 82 => center = (-2,1), r = √82
Therefore, you conclude that these two circumferences have the same center and differet r, so they are concentric.
Factor
in form
ax²+bx+c form
use the ac method
1. mulitply a and c
2. factor the result such that the 2 factors add to b
3. split b into those 2 factors
4. group the terms
5. undistribute common factors
6. undistribute again
first multiply ac
4 times 5=20
now
what 2 numbers multiply to 20 and add to 12
2 and 10
4x²+2x+10x+5
group
(4x²+2x)+(10x+5)
undistribute
2x(2x+1)+5(2x+1)
undistribute the (2x+1)
(2x+1)(2x+5) is factored form whih you have there, nice
Answer:
3/7
Step-by-step explanation:
The probability of at least is 1 - the probability of at most
P(at least x) = 1 - P(at most x)
The given is:
1. A bus arrives at a bus stop every 35 minutes
2. You arrive at the bus stop at a random time
3. You will have to wait at least 20 minutes for the bus
∵ The bus arrives at a bus stop every 35 minutes
∵ You arrive at the bus stop at a random time
∵ You will wait at most for 20 minutes for the bus
∴ P(at most 20 minutes) =
∵ P(at least 20 minutes) = 1 - P(at most 20 minutes)
∴ P(at least 20 minutes) = 1 -
∴ P(at least 20 minutes) =
- Simplify the fraction by divide up and down by 5 and you will get your answer!
please mark me brainliest!
Answer:
<em>F test</em>
Step-by-step explanation:
<em>For any test using the F-distribution, a "F Test" is a capture-all word. In certain circumstances, as individuals speak about the F-Test, it is the F-Test to compare two variances that they actually talk about. </em>
Moreover, in a multitude of tests, the f-statistics is used such as regression analysis, the Chow test and the Scheffe test (a post-hoc ANOVA test).
One should be using Excel, SPSS, Minitab or some other form of software to run the experiment if you are running a F test.
<em><u>Steps include.</u></em>
- State the hypothesis of nullity and the counter hypothesis.
- Determine the value of F. The F value is determined using equation F = (SSE1 – SSE2/m)/SSE2/n-k, where SSE = square residual, m = number of constraints, and k = number of independent variables.
- Find the statistics for F (the critical value for the test). The F statistical formula is: F Statistics = group mean / mean variance of variances within the group.
- The F Statistics can be found in the F-Table.
- The Null Hypothesis is accepted or denied.
