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3 years ago

Find the missing values of x and y

Mathematics

1 answer:

Rasek [7]3 years ago

8 0

5x = 90° → x = 18°

9y = 90° → x = 10°

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2 years ago

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2 years ago

Find an equation for those points P such that the distance from P to A(0, 1, 2) is equal to the distance from P to B(6, 4, 2). W

suter [353]

Answer: The required equation for points P is $4x+2y=17.$

Step-by-step explanation: We are give two points A(0, 1, 2) and B(6, 4, 2).

To find the equation for points P such that the distance of P from both A and B are equal.

We know that the distance between two points R(a, b, c) and S(d, e, f) is given by

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

Let the point P be represented by (x, y, z).

According to the given information, we have

$PA=PB\\\\\Rightarrow \sqrt{(x-0)^2+(y-1)^2+(z-2)^2}=\sqrt{(x-6)^2+(y-4)^2+(z-2)^2}\\\\\Rightarrow x^2+y^2-2y+1+z^2-4z+4=x^2-12x+36+y^2-8y+16+z^2-4z+4~~~~~~~[\textup{Squaring both sides}]\\\\\Rightarrow -2y+1=-12x-8y+52\\\\\Rightarrow 12x+6y=51\\\\\Rightarrow 4x+2y=17.$

Thus, the required equation for points P is $4x+2y=17.$

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2 years ago

Is (1, 3) a solution to the system of inequalities below?

Oxana [17]

<h3>Substitute and Check:</h3>

$y > 2x + 1 \\ 3 > 2(1) + 1 \\ 3 > 3 \\ false$

<h3>We can stop here and conclude that ( 1 , 3 ) is not a solution to this system, since it does not even satisfy the first equation, but check for the other one just in case:</h3>

$y < - 3x \\ 3 < - 3(1) \\3 < - 3 \\ also \: false$

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2 years ago