Answer:
50° & 90°
Step-by-step explanation:
it's a right angle triangles, so one must be 90°
Interior angles in a triangle add up to 180.
180 - 90 - 40 = 50°
Answer:
1
x = 0, x = 3
2
x = -3, x = 3
3
x = -2/3, x = 1
4
x = -1, x = 1, x = -3/2
Step-by-step explanation:
1
3x^2 - 9x = 0
3x(x - 3) = 0
when 3x = 0, x = 0
when x - 3 = 0, x = 3
2
x^2 - 9 = 0
(x - 3)(x + 3)
when x + 3 = 0, x = -3
when x - 3 = 0, x = 3
3
3x^2 - x = 2
3x^2 - x - 2 = 0
(3x + 2)(x - 1 ) = 0
when 3x + 2 = 0, 3x = -2, x = -2/3
when x - 1 = 0, x = 1
4
2x(x^2 - 1) + 3(x^2 - 1) = 0
2x^3 - 2x + 3x^2 - 3 = 0
2x^3 + 3x^2 - 2x - 3 = 0
(x + 1)(x - 1)(2x + 3) = 0
when x + 1 = 0, x = -1
when x - 1 = 0, x = 1
when 2x + 2 = 0, 2x = -3, x = -3/2
Answer:
(8.213 ; 8.247)
Step-by-step explanation:
Given the data :
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24
Sanple size, n = 15
Sample mean, xbar = Σx / n = 123.45 / 15 = 8.23
The sample standard deviation, s = √(x -xbar)²/n-1
Using calculator :
Sample standard deviation, s = 0.03116
s = 0.031 (3 decimal places)
The 95% confidence interval :
C.I = xbar ± (Tcritical * s/√n)
Tcritical at 95%, df = 15 - 1 = 14
Tcritical = 2.145
C.I = 8.23 ± (2.145 * 0.031/√15)
C.I = 8.23 ± 0.0171689
C.I = (8.213 ; 8.247)