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3 years ago

Solve for x: 12 (x – 4)| + 7 = 25.

Mathematics

1 answer:

Rasek [7]3 years ago

8 0

Question:

Solve for x: $12|x-4|+7=25$ . Fill in both values for x below. Write the greater value for x in the first column.

Answer:

$x=5.5$ and $x=2.5$ are the values for x.

Explanation:

The equation is $12|x-4|+7=25$

Subtracting both sides by 7,

$12|x-4|=18$

Dividing both sides by 12,

$|x-4|=1.5$

Now, we shall write the equation by removing modulus by adding plus and minus on the other side of the equation.

$x-4=1.5$ or $x-4=-1.5$

Solving the equation $x-4=1.5$ , we get,

$\begin{aligned} x-4 &=1.5 \\ x &=1.5+4 \\ x &=5.5 \end{aligned}$ or $\begin{aligned} x-4 &=-1.5 \\ x &=-1.5+4 \\ x &=2.5 \end{aligned}$

Thus, the solutions are $x=5.5$ and $x=2.5$

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3 years ago

What is the distance rounded to the nearest tenth between the points (2 -2) and (6 3)

kotegsom [21]

Answer:

The distance between the points is approximately 6.4

Step-by-step explanation:

The given coordinates of the points are;

(2, -2), and (6, 3)

The distance between two points, 'A', and 'B', on the coordinate plane given their coordinates, (x₁, y₁), and (x₂, y₂) can be found using following formula;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Substituting the known 'x', and 'y', values for the coordinates of the points, we have;

$l_{(2, \, -2), \ (6, \, 3) } = \sqrt{\left (3-(-2) \right )^{2}+\left (6-2 \right )^{2}} = \sqrt{5^2 + 4^2} = \sqrt{41}$

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3 years ago

The ages in years of 21 people in a swimming pool are displayed in the stem-and-leaf plot. Determine the median age of

LenaWriter [7]

Answer:

<h3>5 years</h3>

Step-by-step explanation:

To get the median of the ages given

2, 4, 5, 6, 7, 8, 8, 8, 0, 3, 5, 9, 1, 4, 7, 6, 1, 2, 4, 4, 8

First we will need to rearrange the median ages in ascending order (from lowest to highest)

0, 1, 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9

Next is to locate the middle value of the arranged data

(0, 1, 1, 2, 2, 3, 4, 4, 4, 4), 5, (5, 6, 6, 7, 7, 8, 8, 8, 8, 9)

The total values in both parenthesis are the same(10 in numbers) leaving 5 as the middle number.

Hence the median age of the people in the pool is 5years

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3 years ago

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olga_2 [115]

Answer:

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2. Dylan's answer is correct. He subtracted the exponents correctly, then moved the decimal place over one place towards the left.

3. Ethan is wrong. He added the exponents, instead of subtracting. However, you cannot do this, because when you are dividing exponents, you must subtract.

Step-by-step explanation:

I have this acronym I learned called MADSPM, which has helped me a lot. I never learned it in Algebra, but I wish that they had taught it. Each letter corresponds with an exponent rule. If this makes sense, here is what it stands for:

When you multiply, you add.

When you divide, you subtract.

When there are parentheses, you multiply.

In this case, it was solely division. So, you just need to remember division = subtraction, when it comes to exponents.

Hopefully this helped. If you need me to explain it better, please let me know, and I will try. Thanks much & have a wonderful day!

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3 years ago