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3 years ago

The table shows the solution to the equation |2x − 5| − 2 = 3:

Mathematics

2 answers:

andrew-mc [135]3 years ago

8 0

Answer:

All steps are correct

Step-by-step explanation:

|2x − 5| − 2 = 3

Step 1

|2x − 5| = 3 + 2 (adding 2 on both sides)

Step 2

|2x − 5| = 5

Step 3

2x − 5 = 5 or 2x − 5 = −5 (on opening the modulus, we get 2 cases)

Step 4

2x = 10 or 2x = 0 (adding 5 on both sides)

Step 5

x = 5 or x = 0 (dividing by 2 on both sides)

Hence, each step was correct

deff fn [24]3 years ago

5 0

|2x - 5| - 2 = 3 |add 2 to both sides

|2x - 5| = 5

2x - 5 = 5 or 2x - 5 = -5 |add 5 to both sides

2x = 10 or 2x = 0 |divide both sides by 2

x = 5 or x = 0

All steps are correct.

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Charles has 24 marbles. He has 6 more marbles than blue marbles. Which equation represents this situation.

statuscvo [17]

Answer:

n + (n + 6) = 24.

Step-by-step explanation:

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He has a total of 24 marbles, so:

n + (n + 6) = 24.

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Find the rule, and type the missing number in the sequence.<br><br> 96, 192, ____, 384

Wittaler [7]

Answer:

Missing number is 288, and the rule is +96

Step-by-step explanation:

First subtract 96 from 192, which is 96

then add that to 192 and the missing value is 288

you should also add 96 to 288 just to make sure it gets you to the last number which is 384.

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2 years ago

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit of 750.a. Calculate the mean a

DENIUS [597]

You can compute both the mean and second moment directly using the density function; in this case, it's

$f_X(x)=\begin{cases}\frac1{750-670}=\frac1{80}&\text{for }670\le x\le750\\0&\text{otherwise}\end{cases}$

Then the mean (first moment) is

$E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x\,\mathrm dx=710$

and the second moment is

$E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x^2\,\mathrm dx=\frac{1,513,900}3$

The second moment is useful in finding the variance, which is given by

$V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2=\dfrac{1,513,900}3-710^2=\dfrac{1600}3$

You get the standard deviation by taking the square root of the variance, and so

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3 years ago

Which equation is a solution to (x-3)(x+9)=27?

Shtirlitz [24]

Answer:

x = ± $3\sqrt{7}$ - 3

Explanation:

I'm assuming you want the solutions to that equation, so here goes! (If not, please comment.)

(x-3)(x+9)=27

Let's FOIL this all out and expand. (Remember: First, Outer, Inner, Last.)

x^2 + 9x - 3x - 27

(first+ inner + outer + last)

x^2 + 9x - 3x - 27 = 27

Combine like terms, and add 27 to both sides.

x^2 + 6x - 27 + 27 = 27 + 27

x^2 + 6x = 54

Let's complete the square, because factoring doesn't work, and because it's good practice.

x^2 + 6x + ___ = 54 + ____

In the blank we will put b/2 ^2 = 6/2 ^2 = 3^2 = 9 to complete the square.

x^2 + 6x + 9 = 54 + 9

Now we've got a perfect square factor:

(x + 3)^2 = 63

sqrt(x+3)^2 = $\sqrt{63}$

x + 3 = ± $3\sqrt{7}$

x = ± $3\sqrt{7}$ - 3

7 0

3 years ago