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4 years ago

1) Find the length of point A(-3,1) and B(2,6). Leave your answer in RADICAL FORM ONLY.

Mathematics

1 answer:

elena-14-01-66 [18.8K]4 years ago

7 0

Answer: The length of point A(-3,1) and B(2,6) is $5\sqrt{2}\text{ units}$ .

Step-by-step explanation:

We know that the distance between the two points (a,b) and (c,d) is given by :-

$d=\sqrt{(a-c)^2+(b-d)^2}$

Given points = A(-3,1) and B(2,6)

Therefore the distance between the points A(-3,1) and B(2,6) is given by :-

$d=\sqrt{(-3-2)^2+(1-6)^2}\\\\\Rightarrow\ d=\sqrt{(-5)^2+(-5)^2}\\\\\Rightarrow\ d=\sqrt{25+25}\\\\\Rightarrow\ d=\sqrt{50}\\\\\Rightarrow\ d=\sqrt{25\times2}\\\\\Rightarrow\ d=\sqrt{5^2\times2}\\\\\Rightarrow\ d=5\sqrt{2}\text{ units}$

Hence, the length of point A(-3,1) and B(2,6) is $5\sqrt{2}\text{ units}$ .

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anyanavicka [17]

ANSWER

$x = 2 \: \: or \: \: x = 15$

$x = - 2 \: \: or \: \: x = - 15$

EXPLANATION

The given polynomial is

$f(x) = {x}^{2} + kx + 30$

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

$m + n = - \frac{b}{a} = -k$

and the product of roots is

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The square difference of the zeroes is given by the expression.

$( {m - n})^{2} = {(m + n)}^{2} - 4mn$

From the question, this difference is 169.

This implies that:

$( { - k)}^{2} - 4(30) = 169$

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$k= \pm \sqrt{289}$

$k= \pm17$

We substitute the values of k into the equation and solve for x.

$f(x) = {x}^{2} \pm17x + 30$

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The zeroes are given by;

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Answer:

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Step-by-step explanation:

The given function are

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