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dangina [55]
3 years ago
7

Show that if the point with coordinates (x,y) is equidistant from the point (2,0) and the line y=−4, then y=1/8(x-2)²-2.

Mathematics
1 answer:
harkovskaia [24]3 years ago
6 0

Answer:

The demonstration is showed below

Step-by-step explanation:

The distance betwenn two points is given by:

d = \sqrt{(x2-x1)^2+(y2-y1)^2}

If the point is equidistant from a point and a line, the distance must be equal. For the line let's select the point (x,-4), because the distance will be ortogonal, and is the small distance between a point and a line. So:

\sqrt{(x-2)^2+(y-0)^2}  = \sqrt{(x-x)^2+(y+4)^2}

Removing the squares:

(x-2)² + y² = (y+4)²

(x-2)² + y² = y² + 8y + 16

y² - y² - 8y = 16 - (x-2)²

8y = (x-2)² - 16

y = (1/8)*(x-2)² - 16/8

y = (1/8)*(x-2)² - 2

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Scorpion4ik [409]

if we take 4100 to be the 100%, what is 870 off of it in percentage?


\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 4100&100\\ 870&x \end{array}\implies \cfrac{4100}{870}=\cfrac{100}{x} \\\\\\ 4100x=87000\implies x=\cfrac{87000}{4100}\implies x=\cfrac{870}{41}\implies x\approx 21.22

8 0
3 years ago
What is -7(x-2)=1=15-7x
Soloha48 [4]

Answer:

0

Step-by-step explanation:

Simplifying

-7(x + -2) + 1 = 15 + -7x

Reorder the terms:

-7(-2 + x) + 1 = 15 + -7x

(-2 * -7 + x * -7) + 1 = 15 + -7x

(14 + -7x) + 1 = 15 + -7x

Reorder the terms:

14 + 1 + -7x = 15 + -7x

Combine like terms: 14 + 1 = 15

15 + -7x = 15 + -7x

Add '-15' to each side of the equation.

15 + -15 + -7x = 15 + -15 + -7x

Combine like terms: 15 + -15 = 0

0 + -7x = 15 + -15 + -7x

-7x = 15 + -15 + -7x

Combine like terms: 15 + -15 = 0

-7x = 0 + -7x

-7x = -7x

Add '7x' to each side of the equation.

-7x + 7x = -7x + 7x

Combine like terms: -7x + 7x = 0

0 = -7x + 7x

Combine like terms: -7x + 7x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

3 0
2 years ago
4. Find the value of x.
oksano4ka [1.4K]

Answer:

x = 50°

Step-by-step explanation:

The sum of the measures of the angles of a quadrilateral is 360°

360 - 40 - 80 - 110 = 130

130 is the measure of the quad that is adjacent to the angle of x° and is supplementary to that angle also.

Therefore, x = 180 - 130 = 50

7 0
3 years ago
The question is above in the picture​
anzhelika [568]
Yea his answer is right ^^
6 0
3 years ago
Does 10p/2q = 5p/q<br> I don't think so but it doesn't seem right.
Vladimir [108]
Yes it does equal since they are equivalent!
4 0
3 years ago
Read 2 more answers
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