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3 years ago

Solve for x: |x -2| + 10 = 12

Mathematics

2 answers:

Arturiano [62]3 years ago

8 0

|x -2| + 10 = 12

subtract 10 from both sides

|x -2| = 2

set it equal to positive and negative

x-2 = 2 and x-2=-2

add 2 to each side

x=4 and x=0

Answer: x=0,4

zavuch27 [327]3 years ago

5 0

Answer:

Let's solve your equation step-by-step.

|x−2|+10=12

Step 1: Add -10 to both sides.

|x−2|+10+−10=12+−10

|x−2|=2

Step 2: Solve Absolute Value.

|x−2|=2

We know eitherx−2=2orx−2=−2

x−2=2(Possibility 1)

x−2+2=2+2(Add 2 to both sides)

x=4

x−2=−2(Possibility 2)

x−2+2=−2+2(Add 2 to both sides)

x=0

Answer:

x=4 or x=0

Step-by-step explanation:

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The equation y=9. 5x 0. 4 represents the line of best fit for the distance (in feet) that Marcella traveled over time (in second

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The average speed of Marcella in feet per seconds is 9.5 feet per second.

<h3>How are time taken for travel, distance traveled, and the average speed are related?</h3>

We have this below shown relation between them

$\text{Average speed} = \dfrac{\text{Distance traveled}}{\text{Total time taken to travel that distance}}\\\\or\\\\\text{Total time taken to travel that distance}= \dfrac{\text{Distance traveled}}{\text{Average speed} }$

For the given case, we have:

The equation $y=9.5x + 0.4$ represents the line of best fit for the distance (in feet) that Marcella traveled over time (in seconds)

The line of best fit can be taken as approximately telling about the data points ( y = distance traveled in feet, and x = time spent )

Let the initial time be 'x' with initial distance traveled 'y', then the time after one second will be (x+1), and the distance traveled be $y_1$

The value of y and $y_1$ are calculated as:

$y = 9.5x + 0.4\\y_1 = 9.5(x+1) + 0.4 = 9.5x + 9.9$

Thus, the average speed is calculated at time 'x' as:

$\text{Average speed} = \dfrac{\text{Distance traveled}}{\text{Total time taken to travel that distance}}\\\\or\\\\\text{Average speed} = \dfrac{y_1 - y}{x + 1 - x} = \dfrac{9.5x + 9.9 - 9.5x - 0.4}{1} = 9.5 \: \rm feet/sec$

We could've also used the fact that in the relation of y to x as $y = mx + c$ , 'm' denotes the rate of y as x changes.

Thus, the average speed of Marcella in feet per seconds is 9.5 feet per second.

Learn more about average rate here:

brainly.com/question/12322912

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