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Molodets [167]
3 years ago
13

I desperately need this question answered. See attached image thanks so much

Mathematics
1 answer:
Dahasolnce [82]3 years ago
6 0

For this case we must follow the steps below:

step 1:

We place each of the given points on a coordinate axis

Step 2:

We join the AC points (represented by the orange line)

We join the BD points (represented by the blue line)

It is observed that the resulting figure after placing the 4 points on a coordinate axis, turns out to be a rhombus.

In addition, the blue and orange lines turn out to be perpendicular, that is, they have an angle of 90 degrees between them. This can be verified by finding the slopes of each of the two straight lines (blue and orange), which must be opposite reciprocal, that is, they comply: m1 * m2 = -1

In this case, the slope of the orange line is m1 = 1 and that of the blue line is m2 = -1

Then m1 * m2 = 1 * -1 = -1, it is verified that they are perpendicular.

Thus, the conclusion is that ABCD is a rhombus and AC is perpendicular to BD.

Answer:

See attached image

Option D

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Step-by-step explanation:

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Four times the square of a certain number increased by 6 times the number equals 108.find the number
slamgirl [31]
To effectively determine the correct answer, it would be helpful to write this into an algebraic expression. We let x as the number. We do as follows:

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Advocard [28]
1)

An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.

For the first answer choice, clearly \frac{1}{3} does not pass the first criterion so we look at the second choice.

Let's come back to \sqrt{2} and \pi.

\frac{2}{9} doesn't meet our first criterion, and let's skip \sqrt{3} for now.

It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are \sqrt{2},  \pi, e,  \sqrt{3}. For now, it's just helpful to know these and recognize them.

So we can check off \sqrt{2},  \pi and \sqrt{3}.

2) 

For this next question, we know that \sqrt{64} = 8. Clearly this isn't irrational. Likewise, \frac{1}{2} isn't irrational. \frac{16}{4} =  \frac{4}{4} = 1, which is rational, leaving only \frac{ \sqrt{20}}{5} =  \frac{2 \sqrt{5} }{5}. By process of elimination, this is the correct answer. Indeed, \sqrt{5} is an irrational number.

3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.

But it can be written as a fraction because its pattern repeats, unlike for an irrational number.

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