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Lelu [443]
3 years ago
15

Find the distance between points P(2, 2) and Q(7, 4) to the nearest tenth.

Mathematics
1 answer:
kirill115 [55]3 years ago
8 0

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

We have the points P(2, 2) ans Q(7, 4). Substitute:

|PQ|=\sqrt{(7-2)^2+(4-2)^2}=\sqrt{5^2+2^2}=\sqrt{25+4}=\sqrt{29}\approx5.4

<h3>Answer: PQ = 5.4</h3>
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What is the sum of all values of m that satisfy 2m (squared) -16m+8=0?
vodomira [7]
<h2>Steps:</h2>

So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:

2m^2-16m=-8

Next, divide both sides by 2:

m^2-8m=-4

Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:

-8 ÷ 2 = -4, (-4)² = 16

Add 16 to both sides of the equation:

m^2-8m+16=12

Next, factor the left side:

(m-4)^2=12

Next, square root both sides of the equation:

m-4=\pm \sqrt{12}

Next, add 4 to both sides of the equation:

m=4\pm \sqrt{12}

Now, while this is your answer, you can further simplify the radical using the product rule of radicals:

  • Product rule of radicals: √ab = √a × √b

√12 = √4 × √3 = 2√3.

m=4\pm 2\sqrt{3}

<h2>Answer:</h2>

In exact form, your answer is m=4\pm \sqrt{12}\ \textsf{OR}\ m=4\pm 2\sqrt{3}

In approximate form, your answers are (rounded to the hundreths) m=7.46, 0.54

6 0
3 years ago
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