-4x - 2y = - 12
4x + 8y = - 24
_____________(+)
/ +6y = - 36
y = -36/6;
y = -6;
4x - 48 = -24;
4x = 24;
x = 24/4;
x = 6.
Completing the squares, the correct statements regarding the equation of the circle are given by:
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis.
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
<h3>What is the equation of a circle?</h3>
The equation of a circle of center and radius r is given by:
In this problem, the equation is given by:
x² + y² - 2x - 8 = 0.
Completing the squares:
(x - 1)² + y² = 8 + 1²
(x - 1)² + y² = 9.
Hence the center is (1,0), the radius is 3, and the correct statements are:
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis.
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
More can be learned about the equation of a circle at brainly.com/question/24307696
#SPJ1
Solution :
A permutation in the field of mathematics may be defined as the arrangement of its members into a linear order or a sequence. However, if a set is already being ordered, then it is the rearrangement of the elements of the set.
In the context, the next largest permutation set is :
a). (1,2,3,4,5,6,7)
b). The given permutation is the last one in the lexicographic order.
c). (1,7,6,4,2,5,3)
d). (4,1,2,3,5,6,7)
e). (5,6,7,4,3,2,1)
We first take the sum of the squares of the differences between the sample data and the limit 45 mph: 1^2 + 11^2 + 0^2 + (-1)^2 + 0^2 + 16^2 + 10^2 + 8^2 + (-6)^2 = 579. Dividing by 8 (# of cars less 1) gives 72.375, which is the variance. Taking the square root gives the SD of 8.5.
The measure of central tendency most affected by the 10th value of 1.5 mph is the mean. The median and mode are relatively unaffected since both involve the frequency of terms, and having a tenth term that is far below (like 1.5) will not affect it much as compared to if it was near the rest of the values (like anything below 39).
The new SD including the tenth car involves adding the deviation of (-43.5)^2 to the sum of 579, which gives 2471.25. Dividing by 9 (there are now 10 data points) and taking the square root gives the new SD of 16.6.