Answer:
x = 29, C
Explanation: We are given that total angle is 90°, or a right angle. This means that the two complementary angles must equal 90° together.
Create the equation:
2x - 4 + x + 7 = 90
Solve algebraically:
3x + 3 = 90
3x + 3 - 3 = 90 - 3
3x = 87
3x / 3 = 87 / 3
x = 29 or C
We can solve this with the following system
a(2)^2 + b(2) + c = 23
a(4)^2 + b(4) + c = 55
a(10)^2 + b(10) + c = 247 simplifying, we have
4a + 2b + c = 23 (1)
16a + 4b + c = 55 (2)
100a + 10b + c = 247 (3)
Subtract (1) from (2) and (2) from (3) ...and we get the following system
12a + 2b = 32
84a + 6b = 192 these simplify to
6a + b = 16 → b = 16 - 6a (4)
28a + 2b = 64 (5)
Substitute (4) into (5)
28a + 2[16 - 6a] = 64 simplify
28a + 32 - 12a = 64
16a + 32 = 64 subtract 32 from both sides
16a = 32 divide both sides by 16
a = 2
And using (4) .....
b = 16 - 6(2) = 16 - 12 = 4
And using (1) ......
4(2) + 2(4) + c = 23
8 + 8 + c = 23
16 + c = 23
So c = 7
And our cost function is :
c(x) = 2x^2 + 4x + 7 and the cost to produce 8 widgets is
c(8) = 2(8)^2 + 4(8) + 7 = 2*64 + 32 + 7 = 128 + 39 = $ 167
Determine the mean ,median,modes ,IQR,and rage for the data 3,8,6,6,4,6,9,9,12
Verdich [7]
Mean:
Add all the numbers:
3 + 8 + 6 + 6 +4 + 6 + 9 + 9 + 12 = 63
There are 9 numbers.
63 / 9 = 7
Mean = 7
Median:
Order all the numbers:
3, 4, 6, 6, 6, 8, 9, 9, 12
The median is 6.
Mode:
The number that appears the most is 6.
The mode is 6.
Inter-Quartile Range :
Median of 2nd part = 9
Median of 1st part = 5
Subtract:
9 - 5 = 4
The IQR is 4.
Range:
The highest number is 12. The lowest is 3
Subtract:
12 - 3 = 9
The range is 9.
Hope this helped☺☺
Answer:
x = 0
Step-by-step explanation: