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3 years ago

Solving an Absolute Value Equation

Mathematics

1 answer:

Andre45 [30]3 years ago

8 0

Answer:

Solution set = {-12, 12}

Step-by-step explanation:

Start by dividing both sides of the given equation by negative one, to get rid of the negative signs on both sides:

$-\,|-x|=-\,12\\|-x|=12$

Now we consider the two possible cases:

1) The expression inside the absolute value symbol is a positive number, then :

$|-x|=-x\\$

and replacing it in the equation, this becomes:

$|-x|=12\\-x=12\\x=-12$

which is our first answer.

2) The expression inside the absolute value symbol is a negative number, then :

$|-x|=x\\$

and replacing it in the equation, this becomes:

$|-x|=12\\x=12$

which is our second possible answer.

Then the set of solutions is: {-12, 12}

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Move two choices to the blanks to correctly complete the sentences.

Pavel [41]

Answer:

(A) There should have been 5 outcomes of HT

(B) The experimental probability is greater than the theoretical probability of HT.

Step-by-step explanation:

Given

$S = \{HH,HT,TH,TT\}$ -- Sample Space

$n(S) = 4$ --- Sample Size

Solving (a); theoretical outcome of HT in 20 tosses

First, calculate the theoretical probability of HT

$P(HT) = \frac{n(HT)}{n(S)}$

$P(HT) = \frac{1}{4}$

Multiply this by the number of tosses

$P(HT) * n= \frac{1}{4} * 20$

$P(HT) * n= 5$

Solving (b); experimental probability of HT

Here, we make use of the table

$P(HT) = \frac{n(HT)}{n(S)}$

$P(HT) = \frac{6}{20}$

$P(HT) = 0.30$ ---- Experimental Probability

In (a), the theoretical probability is:

$P(HT) = \frac{1}{4}$

$P(HT) = 0.25$ ---- Experimental Probability

By comparison;

$0.30 > 0.25$

6 0

3 years ago

At every company meeting, the president speaks for 20 minutes and then takes questions from her employees. Let q represent the n

ololo11 [35]

Answer:

t = 20 + q (minutes)

Step-by-step explanation:

The meeting consists of speaking and Question & Answer (Q&A) sessions.

Speaking session = 20 minutes

Q&A session = q minutes

Total number of minutes spent for the two sessions = 20 + q (minutes)

But total number of minutes meeting lasted = t minutes.

Therefore, t = 20 + q (because they both represent the total number of minutes the meeting lasted)

4 0

3 years ago

Gwar [14]

Answer:

It is A and I am positive its A

Step-by-step explanation:

6 0

3 years ago

Help ASAP I don’t get it

GarryVolchara [31]

9514 1404 393

Answer:

positive
negative

Step-by-step explanation:

The thrust of the question is to make sure you understand that increasing the y-coordinate of a point will move the point upward, and decreasing it will move the point downward.

That is adding a positive value "k" to x^2 will move the point (x, x^2) to the point (x, x^2+k), which will be above the previous point by k units.

If k is subtracted, instead of added, then the point will be moved downward.

The blanks are supposed to be filled with positive , and negative .

_____

Comment on the question

The wording of the statement you're completing is a bit odd. If k is negative (-2, for example), this statement is saying the graph is translated down -2 units. It is not. It is translated down |-2| = 2 units. The direction of translation depends on the sign of k. The amount of translation depends on the magnitude of k.

If you thoroughly understand (x, y) coordinates and how they are plotted on a graph, it should be no mystery that changing the y-coordinate will change the vertical position of the graph.

3 0

3 years ago

The area of a right triangle with one leg measuring 5 ft. and hypotenuse measuring 13 ft. is_______ a0. Type a numerical answer

Snowcat [4.5K]

Area of the triangle = (1/2)*base*height

For right triangle base and height can be legs.

We have one leg = 5 ft. (Lets think it is a base.)

We need to find the other leg.

We are going to use Pythagorean theorem.

5² + b²=13²

b²=144

b=12 (It is going to be our height.)

Area of the triangle = (1/2)*5*12= 30 ft²

Area of the triangle = 30 ft²

5 0

3 years ago