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KonstantinChe [14]
3 years ago
11

Find the midpoint of the line segment with the endpoints (1, 0) and (2, -10).

Mathematics
1 answer:
Mariulka [41]3 years ago
7 0

Answer:

\bigl(\frac{3}{2},-5\bigr)

or in decimal form

(1.5,-5)

Step-by-step explanation:

The midpoint of the line with endpoints (x_1,y_1) and (x_2,y_2) is \bigl(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigr). just take the average between the points

so given the points (1,0) and (2,-10)

x_1=1

y_1=0

x_2=2

y_2=-10

the midpoint is found as follows:

\bigl(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigr)

\bigl(\frac{1+2}{2},\frac{0-10}{2}\bigr)

\bigl(\frac{3}{2},\frac{-10}{2}\bigr)

\bigl(\frac{3}{2},-5\bigr)

or in decimal form

(1.5,-5)

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This is number 14 answer

7 0
2 years ago
Two perpendicular lines intersect at the origin. If the slope of the first line is -1/2, what is the equation of the second line
Dovator [93]

bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.

now, they both intersect at 0,0, namely they both pass through it, we know the slope of the first one, so

\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{1}\implies 2}}

so, we're really looking for the equation of a line whose slope is 2, and runs through (0,0).

\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=2(x-0)\implies y=2x

5 0
3 years ago
Anyone know the answer?
lilavasa [31]
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6 0
3 years ago
Suppose for some value of x the solution to the equation 2.5(y−x)=0 is y = 6. What must be true about x?
Varvara68 [4.7K]

Step-by-step explanation:

In this case, you input the value of y (y = 6) into the equation ( 2.5(y-x)= 0)

2.5(6-x) = 0

Open the bracket,

(2.5×6)-2.5x= 0

Collect like terms.

2.5x= 2.5×6

Divide both sides by the coefficient of x (2.5)

x = 6

So,

x= 6 is true.

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Substituting 6 for x in the equation,

2.5(6-6)= 0

2.5•0 = 0

0= 0

Which is also true.

7 0
2 years ago
Can you help me i don’t know the answers
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.

Let's say x=0.36363636.... Would you agree that 100x=36.36363636...? (We choose to multiply by 100 because there are two decimals that repeat. For 1, choose 10, for 3 choose 1,000, and so on.)

Now, let's subtract x from 100x and solve.

100x=36.36363636\\-x \ \ \ \ \ \ \ -0.36363636\\99x=36\\\\x= \dfrac{36}{99}= \dfrac{4}{11}

Voila!
4 0
3 years ago
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