All categories

3 years ago

What is the answer for |x|=9

Mathematics

1 answer:

Maru [420]3 years ago

8 0

The absolute value $|x|$ returns the "positive version" of a number.

In other words, if the number is positive, it remains positive; if the number is negative, it changes sign.

So, if we want $|x|=9$ , we want the "positive version" of x to be 9.

This can happen in two ways: if x is already 9, then its absolute value is still nine. If instead x=-9, its positive value will be 9 again.

In formula, we have

$|x|=9 \iff x=\pm 9$

because

$|9|=9,\quad |-9|=9$

You might be interested in

HELPPPPPPP PLEASEEE

spin [16.1K]

Answer:

y = - $\frac{5}{4}$ x - $\frac{13}{4}$

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y + 6 = $\frac{4}{5}$ (x - 5) ← is in point- slope form

with slope m = $\frac{4}{5}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{4}{5} }$ = - $\frac{5}{4}$

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - $\frac{5}{4}$ , thus

y = - $\frac{5}{4}$ x + c ← is the partial equation

To find c substitute (- 1, - 2) into the partial equation

- 2 = $\frac{5}{4}$ + c ⇒ c = - 2 - $\frac{5}{4}$ = - $\frac{13}{4}$

y = - $\frac{5}{4}$ x - $\frac{13}{4}$ ← equation of perpendicular line

3 0

3 years ago

Read 2 more answers

— 8х + 3y = 17<br> 8x — 9y = — 19

bija089 [108]

Answer:

x= 83y−17 and y= 83x+17

hope it helps

8 0

3 years ago

Factor the following equations to find the zeros of the equation.

olasank [31]

Answer:

1) 4, -5 and 3 are the ZEROES of the expression j = (p - 4)(p + 5)(p - 3)

Step-by-step explanation:

Here, the given phrase is:

j = (p - 4)(p + 5)(p - 3)

Now, here j is Expressed as the product of roots.

(p - 4),(p + 5) and (p - 3) are 3 given roots of the polynomial j.

Now, if (x-a) is the ROOT of the polynomial, then x = a is the ZERO of the POLYNOMIAL.

In this given expression:

(p-4) is the ROOT⇒ 4 is the ZERO of the polynomial j.

(p+5) is the ROOT⇒ (-5) is the ZERO of the polynomial j.

(p-3) is the ROOT⇒ 3 is the ZERO of the polynomial j.

Hence, here 4, -5 and 3 are the ZEROES of the expression

j = (p - 4)(p + 5)(p - 3)

8 0

3 years ago

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backu

JulsSmile [24]

Answer:

a) There is a 10.24% probability that both generators fail during a power outage.

b) There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

Step-by-step explanation:

For each emergency backup generator, there are only two possible outcomes. Either they work correctly, or they fail. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

Assume that emergency backup generators fail 32% of the times when they are needed. So they work correctly 100-32 = 68% of the time. So $p = 0.68$

There are two generators, so $n = 2$

a. Find the probability that both generators fail during a power outage

This is $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.68)^{0}.(0.32)^{2} = 0.1024$

There is a 10.24% probability that both generators fail during a power outage.

b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed.

Either there are no working generators, or there is at least one working generator. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$