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2 years ago

NEED HELP PLEASE ANSWER ASAP! (41)

Mathematics

2 answers:

Cerrena [4.2K]2 years ago

7 0

Answer:

(2) $x^2-3x-4=0$

Step-by-step explanation:

Standard form of a quadratic equation: $ax^2+bx+c=0$

When factoring a quadratic (finding the roots) we find two numbers that multiply to $ac$ and sum to $b$ , then rewrite $b$ as the sum of these two numbers.

So if the roots sum to 3 and multiply to -4, then the two numbers would be 4 and -1.

$\implies b=1+-4=-3$

$\implies ac=1 \cdot -4$

As there the leading coefficient is 1, $c=-4$ .

Therefore, the equation would be: $x^2-3x-4=0$

Proof

Factor $x^2-3x-4=0$

Find two numbers that multiply to $ac$ and sum to $b$ .

The two numbers that multiply to -4 and sum to -3 are: -4 and 1.

Rewrite $b$ as the sum of these two numbers:

$\implies x^2-4x+x-4=0$

Factorize the first two terms and the last two terms separately:

$\implies x(x-4)+1(x-4)=0$

Factor out the common term $(x-4)$ :

$\implies (x+1)(x-4)=0$

Therefore, the roots are:

$(x+1)=0 \implies x=-1$

$(x-4)=0 \implies x=4$

So the sum of the roots is: -1 + 4 = 3

And the product of the roots is: -1 × 4 = -4

Thereby proving that $x^2-3x-4=0$ has roots whose sum is 3 and whose product is -4.

ExtremeBDS [4]2 years ago

3 0

Answer:

41. (2) x² - 3x - 4 =0

Step-by-step explanation:

Question 41

Standard form of polynomial

x² - (sum of roots) + product of roots = 0
(2) x² - 3x - 4 =0

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almond37 [142]

Answer:

$=14a^5+14a^4-10a^3-16a$

Step-by-step explanation:

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2 years ago

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Nimfa-mama [501]

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Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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 p-value, we get the probability that the value of the measure is greater than X.

When two normal distributions are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

In this question:

We have to find the distribution for the difference in times between when you arrive and when the bus arrives.

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