Share £40 in the ratio 1:4 between Tim and Sam

Can you show us how to find the discriminant of the quadratic x^2 + 2x -2 =0

lorasvet [3.4K]

<em>Step #1: </em>
Make sure the equation is in the form of [ Ax² + Bx + C = 0 ].

Yours is already in that form.
A = 1
B = 2
C = -2

<em>Step #2:</em>
The 'discriminant' for that equation is [ B² - 4 A C ].
That's all there is to it, but it can tell you a lot about the roots of the equation.

-- If the discriminant is zero, then the left side of the equation is a perfect square,
and both roots are equal.

-- If the discriminant is greater than zero, the the roots are real and not equal.

-- If the discriminant is less than zero, then the roots are complex numbers.

The discriminant of your equation is [ B² - 4 A C ] = 2² - 4(1)(-2) = 4 + 8 = 12

Your equation has two real, unequal roots.

4 0

3 years ago

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4b - 5 + (-a-3) i = 7 * 8i

Rudik [331]

Answer:

Simplifying

4b + -5 + (-1a + -3) * i = 7 + -8i

Reorder the terms:

4b + -5 + (-3 + -1a) * i = 7 + -8i

Reorder the terms for easier multiplication:

4b + -5 + i(-3 + -1a) = 7 + -8i

4b + -5 + (-3 * i + -1a * i) = 7 + -8i

Reorder the terms:

4b + -5 + (-1ai + -3i) = 7 + -8i

Reorder the terms:

-5 + -1ai + 4b + -3i = 7 + -8i

Solving

-5 + -1ai + 4b + -3i = 7 + -8i

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + -1ai + 4b + 5 + -3i = 7 + 5 + -8i

Reorder the terms:

-5 + 5 + -1ai + 4b + -3i = 7 + 5 + -8i

Combine like terms: -5 + 5 = 0

0 + -1ai + 4b + -3i = 7 + 5 + -8i

-1ai + 4b + -3i = 7 + 5 + -8i

Combine like terms: 7 + 5 = 12

-1ai + 4b + -3i = 12 + -8i

Add '-4b' to each side of the equation.

-1ai + 4b + -4b + -3i = 12 + -4b + -8i

Combine like terms: 4b + -4b = 0

-1ai + 0 + -3i = 12 + -4b + -8i

-1ai + -3i = 12 + -4b + -8i

Add '3i' to each side of the equation.

-1ai + -3i + 3i = 12 + -4b + -8i + 3i

Combine like terms: -3i + 3i = 0

-1ai + 0 = 12 + -4b + -8i + 3i

-1ai = 12 + -4b + -8i + 3i

Combine like terms: -8i + 3i = -5i

-1ai = 12 + -4b + -5i

Divide each side by '-1i'.

a = -12i-1 + 4bi-1 + 5

Simplifying

a = -12i-1 + 4bi-1 + 5

Reorder the terms:

a = 5 + 4bi-1 + -12i-1

4 0

3 years ago

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The amount of soft drink in a bottle is a Normal random variable. Suppose that in 7% of the bottles containing this soft drink t

WITCHER [35]

Answer:

The mean is 15.93 ounces and the standard deviation is 0.29 ounces.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

7% of the bottles containing this soft drink there are less than 15.5 ounces

This means that when X = 15.5, Z has a pvalue of 0.07. So when X = 15.5, Z = -1.475.

$Z = \frac{X - \mu}{\sigma}$

$-1.475 = \frac{15.5 - \mu}{\sigma}$