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1 year ago

Which of the number(s) below are potential roots of the function? p(x) = x4 + 22x2 – 16x – 12

Mathematics

1 answer:

Neporo4naja [7]1 year ago

6 0

Complete question is;

Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² – 16x – 12

A) ±6

B) ±1

C) ±3

D) ±8

Answer:

Options A, B & C: ±6, ±1, ±3

Step-by-step explanation:

We are given the polynomial;

p(x) = x⁴ + 22x² – 16x – 12

Now, the potential roots will be all the rational numbers equivalent of p/q.

Where;

p are the factors of the constant term of the polynomial

q are the factors of the leading coefficient of the polynomial

Now, in the given polynomial, the constant term is seen as -12 while leading coefficient is 1 which is the coefficient of x⁴.

We know that factors of 12 are any of:

±1, ±2, ±3, ±4, ±6 and ±12

While possible factors of 1 is just ±1.

Thus, all the potential roots of the polynomial function are;

±1, ±2, ±3, ±4, ±6 and ±12

From the options given, option A, B & C could be the potential roots.

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The amount of time a passenger waits at an airport check-in counter is random variable with mean 10 minutes and standard deviati

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Answer:

(a) less than 10 minutes

= 0.5

(b) between 5 and 10 minutes

= 0.5

Step-by-step explanation:

We solve the above question using z score formula. We given a random number of samples, z score formula :

z-score is z = (x-μ)/ Standard error where

x is the raw score

μ is the population mean

Standard error : σ/√n

σ is the population standard deviation

n = number of samples

(a) less than 10 minutes

x = 10 μ = 10, σ = 2 n = 50

z = 10 - 10/2/√50

z = 0 / 0.2828427125

z = 0

Using the z table to find the probability

P(z ≤ 0) = P(z < 0) = P(x = 10)

= 0.5

Therefore, the probability that the average waiting time waiting in line for this sample is less than 10 minutes = 0.5

(b) between 5 and 10 minutes

i) For 5 minutes

x = 5 μ = 10, σ = 2 n = 50

z = 5 - 10/2/√50

z = -5 / 0.2828427125

= -17.67767

P-value from Z-Table:

P(x<5) = 0

Using the z table to find the probability

P(z ≤ 0) = P(z = -17.67767) = P(x = 5)

= 0

ii) For 10 minutes

x = 10 μ = 10, σ = 2 n = 50

z = 10 - 10/2/√50

z = 0 / 0.2828427125

z = 0

Using the z table to find the probability

P(z ≤ 0) = P(z < 0) = P(x = 10)

= 0.5

Hence, the probability that the average waiting time waiting in line for this sample is between 5 and 10 minutes is

P(x = 10) - P(x = 5)

= 0.5 - 0

= 0.5

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1 year ago

How to factorise 5h^2-12hg

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Answer:

$h(5h-12g)$

Step-by-step explanation:

$5h^2-12hg$

When we factor expressions, we look for factors within the terms that are alike, or in other words, we look for common factors. Here, $5h^2$ and $12hg$ only have one common factor: $h$ . Therefore, to factorize this expression, divide both terms by $h$ .

$= h(\frac{5h^2}{h}-\frac{12hg}{h} )\\= h(5h-12g)$

Now, we've "carried" $h$ out of the expression and have therefore factored it.

I hope this helps!

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1 year ago

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Answer:

Porter is $n-m$ inches taller than Henry.

Porter is $\frac{n}{m}$ times taller than henry.

Step-by-step explanation:

The difference in height can be found using subtraction.

Since Porter is taller than Henry, we'll subtract away Henry's height from Porter's height. This will leave us with only the difference between the heights.

n = Porter's height

m = Henry's height

Difference in height is thus:

$n-m$

Answer: Porter is $n-m$ inches taller than Henry.

To find out how many times taller Porter is than Henry, we can use division.

An example: if Porter was 200cm, and Henry was 100cm, Porter is obviously 2 times as tall.

If we divide Porter's height by Henry's height...

$\frac{200}{100}=2$

..we'll get 2. This is because Henry's height "fits in twice" in Porter's height. 100 fits twice in 200.

Using our values, n and m, we'll divide n by m.

$\frac{n}{m}$

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