Answer:
x = 9cm
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2 + x^2 = ( sqrt(117) ^2)
36 + x^2 = 117
Subtract 36 from each side
x^2 = 117 -36
x^2 = 81
Take the square root of each side
sqrt(x^2) = sqrt(81)
x = 9
Answer:
The 80% confidence interval for difference between two means is (0.85, 1.55).
Step-by-step explanation:
The (1 - <em>α</em>) % confidence interval for difference between two means is:
Given:
Confidence level = 80%
*Use a <em>t</em>-table for the critical value.
Compute the 80% confidence interval for difference between two means as follows:
Thus, the 80% confidence interval for difference between two means is (0.85, 1.55).
Answer:
x^4 - 14x^2 - 40x - 75.
Step-by-step explanation:
As complex roots exist in conjugate pairs the other zero is -1 - 2i.
So in factor form we have the polynomial function:
(x - 5)(x + 3)(x - (-1 + 2i))(x - (-1 - 2i)
= (x - 5)(x + 3)( x + 1 - 2i)(x +1 + 2i)
The first 2 factors = x^2 - 2x - 15 and
( x + 1 - 2i)(x +1 + 2i) = x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i - 4 i^2
= x^2 + 2x + 1 + 4
= x^2 + 2x + 5.
So in standard form we have:
(x^2 - 2x - 15 )(x^2 + 2x + 5)
= x^4 + 2x^3 + 5x^2 - 2x^3 - 4x^2 - 10x - 15x^2 - 30x - 75
= x^4 - 14x^2 - 40x - 75.
Answer:
30° = m∠GFH
Step-by-step explanation:
Since ∠EFH and ∠GFH are complementary, the sum of their measures i 90.
Let x = m∠GFH
2x = m∠EFH
m∠GFH + m∠EFH = 90
x + 2x = 90
3x = 90
x = 30° = m∠GFH
