Answer:
C
Step-by-step explanation:
Since they are pythagorian triplets, ABC is a right angled triangle at the angle between the arc 3 and arc 4. Theta is the angle opposite to 3 and hence tan(theta)=3/4
(x-2)(x-2)+6(x-2)+9
so first we distribute
x^2-2x-2x+4+6x-12+9
group like terms
x^2+2x+1
factor
find what 2 numbers add to get 2 and multiply to get 1
the numbers are 1 and 1
(x+1)(x+1)
Answer:
(-1 , 1)
Step-by-step explanation:
Absicca of midpoint = 4-2 / 2 = -1
Ordinate of midpoint = -4+6 / 2 = 1
The given number arranged in order are:
9, 9, 10, 10, 12, 12, 14, 15, 15, 15, 17
1. To find the mean, add all the number together and divide the summation by 11[ which is the total number of the figures given]
Mean = [9 + 9 + 10 + 10 + 12 + 12 + 14+ 15 + 15 + 15 + 17] / 11 = 138 / 11
Mean = 12.5
Therefore, the mean is approximately equal to 13.
2. The median of a number refers to the number in the middle of a sorted set of number.
To find the median of a set of numbers, the numbers have to be arranged first in the correct increasing order and the number that falls in the middle will be the median. If two numbers fall in the middle, add the two together and find the average. For the set of number given above, the number that falls in the middle is 12.
Therefore, the median = 12.
3. The mode of a set of number refers to the number in the set, which has the highest frequency of occurrence, that is, it is the number that occur most. Looking at the set of number given above, 15 occurred three different times. Therefore, the mode of the set of number given above is 15.
Mode = 15.
4. The range of a set of number refers to the difference between the highest and the lowest numbers in the set of a given number. It represents the spread of the data. In the set of numbers given above the range is determined thus:
Range = 17 - 9 = 8.
Therefore, Range = 8.
Answer:
Let's define:
A = # of students in group A
B = # of students in group B
C = # of students in group C.
"The total number of students who could attend a field trip is represented by the variable t."
This can be written as:
A + B + C = t.
"The number of students in Group A is less than the number in Group B."
Here we have a strictly "less than", then this is written as:
A < B.
"Group A has 6 students more than 1/4 the total number of students"
A = t/4 + 6
"Group B has 3 less than the total number of students"
B = t - 3.
Then we have the equations:
A + B + C = t.
A = t/4 + 6
B = t - 3.
A < B.
We could replace the second and third equatio in the fourth one, to get:
t/4 + 6 < t - 3.
t/4 + 9 < t
9 < t - t/4
9 < t*(4/4 - 1/4)
9 < t*(3/4)
(4/3)*9 < t
12 < t.
Then we found an inequality that defines the minimum possible value of t,