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4 years ago

Justify each step used to simplify the expression 3x+2y-2x+2=3x-2x+2y+2

1 answer:

5 0

$3x+2y-2x+2=3x-2x+2y+2\ \ \ \ \ | combine\ like\ terms\\\\
x+2y+2=x+2y+2\\\\
0=0\\\\
 There\ are\ infinitely\ many\ solutions.$

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5 + 2x = 2x + 6 Step by step please

Fiesta28 [93]

Answer:

5 + 2x=2x + 6

Subtract 5 from both sides.

2x =2x + 6 - 5

Combine like terms (numbers).

2x = 2x + 1

Subtract 2x from both sides.

0 = 1

Since 0 doesn’t equal 1, there is no real solution to the problem.

8 0

3 years ago

Read 2 more answers

Find the best linear equation for the ordered pairs below.

kolbaska11 [484]

Answer:

y = -.075x +4.89

Step-by-step explanation:

The data set has almost no net slope, so the first equation is the most appropriate. (An absolute value function would be a much better fit.)

y = -.075x +4.89

4 0

3 years ago

Select the graph for the solution of the open sentence. Click until the correct graph appears. 2|x| + 1 < 5

Paul [167]

Answer:

The correct answer is x < 2 or x > -2. The graph would be a line between -2 and 2 with an open circle on both.

Step-by-step explanation:

To solve, first solve the equation for the absolute value portion of the equation.

2|x| + 1 < 5

2|x| < 4

|x| < 2

Now since there is an absolute value around it, we have to complete it for the positive and negative versions.

x < 2 OR x > -2

3 0

4 years ago

a wind up robot can travel 20m on a single wind. how many times will it need to wind to cover a distance of half a mile?

zepelin [54]

40 winds. To be exact 40.2336 winds. But that’s not really possible so I would say 41 winds.

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3 years ago

Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

2.21 and 2.23 are proved by contrapositive
2.22 is proved by induction

2.21: If $n^3$ is even, then n is even (By contrapositive)

The contrapositive of the above statement is that:

If n is odd, then $n^3$ is odd

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

i.e. If n is odd, then $n^3$ is odd

2.22 $3n + 4$ is even, if and only if n is even

We have: $3n + 4$

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

Hence, $3n + 4$ is even, if and only if n is even

2.22: $s \ne -1$ and $t \ne -1$ , then $s + t + st \ne -1$

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$