When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
Answer:
-(1/3)x+1>y
2x-3≥y
If x<12/7 then 2x-3≥y
and if x≥12/7 then -(1/3)x+1>y
The answer here is 13. 20 divided by 4 is 5 /‘d 2 to tbe third power is 8. It is 5+8 which is 13
Answer:
Step-by-step explanation:
A. Two measurements(AandB)are taken on the same round.\oIs there a difference in the measurement of the muzzle velocity between device A and device B at the α=0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
B. Construct a 99% confidence interval about the population mean difference. Compute the difference as device A minus device B. Interpret your results. The confidence interval is (__,__)?
Answer:
Open chart in StatCrunch --- Stat --- T Stats --- Paired --- Enter values: Sample 1 = A, Sample 2 = B --- Click on Confidence Interval… and enter Level which is my #%. --- Compute
240/6=x
x=40
the number is 40
