If arc AC = 44 and arc BD = 68, what is the angle measure of <P?*
1 answer:
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Answer:
x = -3, 0, or 7
Step-by-step explanation:
After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.
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<h3>Step 1</h3>Write the equation in standard form.
4x³ -16x² -84x = 0
<h3>Step 2</h3>Factor out the common factor from all terms.
= 4x(x² -4x -21) = 0
<h3>Step 3</h3>Compare to the factored form of a quadratic:
(x +a)(x +b) = x² +(a+b)x +ab
This tells you the constants 'a' and 'b' in the factors can be found by considering ...
(a+b) = -4 . . . . the coefficient of the x term of the quadratic
ab = -21 . . . . . the constant term of the quadratic
It is often helpful to list factor pairs of the constant:
-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum
The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...
a = -7, b = 3
<h3>Step 4</h3>Put it all together.
4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation
<h3>Step 5</h3>Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:
4x = 0 ⇒ x = 0
x -7 = 0 ⇒ x = 7
x +3 = 0 ⇒ x = -3
Solutions to the equation are x ∈ {-3, 0, 7}.
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<em>Additional comment</em>
What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.
A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.
Answer:
Option b. should not be rejected
Step-by-step explanation:
We are given that the contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces.
We have to test whether the variance of the population is significantly more than 0.003, i.e.;
Null Hypothesis, :
=
Alternate Hypothesis, :
The test statistics used here for testing variance is;
T.S. = ~
where, s = sample standard deviation = 0.06
n = sample size = 26 cans
So, Test statistics = ~
= 30
So, at 5% level of significance chi square table gives critical value of 37.65 at 25 degree of freedom. Since our test statistics is less than the critical so we have insufficient evidence to reject null hypothesis.
Therefore, we conclude that null hypothesis should not be rejected and variance of population is 0.003.