If the equation of the circle is x^2+ y^2 = 41, we must first understand the parts of the equation.
A general circle's equation is (x-h)^2+(y-k)^2= r^2
(h.k) is the radius of the circle
r is the radius of the circle
Another useful fact to know is that tangent lines touch the circle at one point (4,5)
Since in our original equation there are no h or k values, we can assume that the center of the circle is (0,0).
The formula for slope is <u>Y1-Y2</u>
X1-X2
We can break this down with our two points (center and tangent)
(0,0) and (-4,-5)
(X1,Y1) and (X2,Y2)
therefore, we will put the equation as such
<u>0-(-5)= 5</u> = <em> </em><u><em>5</em></u>
0-(-4)= 4 <em> 4</em>
<em>this is our slope from the center to the point of tangency.</em>
We know that tangent lines are perpendicular to the radius, which we've already found the slope of. Perpendicular lines are opposite reciprocals of the line they are perpendicular to.
Therefore, we take our slope from center to the tangent, and make it opposite and then take the reciprocal of that slope, which will give us the slope of the tangent line itself. (note: reciprocal means flip the numerator and denominator)
<u>5</u> = <u>-5</u> = <u>-4</u><u>
</u>4 4 5
Now, we have a point on the line, and the line's slope. We can use slope-intercept equation to find the equation of the line.
Slope-int y=mx+b
(x,y) is a point,
m is the slope
b is the y intercept ( the point where x=0, or where its on the y axis)
now we plug things in
(-4,-5) is our point,
<u>-4</u> is our slope
5
-5=<u>-4</u>(-4)+b After we plug things in, solve for b
5
-5= 3.2+b
-1.8= b or b= <u />1 <u>4</u>
5
Now we just need to rewrite our equation with all our components.
(-4.-5) = point
<u>-4</u> = slope<u>
</u>5
1 <u>4</u> = y-intercept<u>
</u> 5
<em>y=</em><u><em>-4</em></u><em> x+ 1 </em><u><em>4</em></u><em> This is the equation of the tangent line</em><u>
</u><em> 5 5</em>
Hope that helped
Answer:
I believe it's 240°
Step-by-step explanation:
It's been awhile since I've done this but I believe that's the answer, here's a picture of a pug. Smile and have a good day!
Answer:
13= -14x
Step-by-step explanation:
(4×2)-(4×1x)=(5×1)-(5×2x)
8-4x=5-10x
8+5=-4x-10x
13=-14x
Hopefully this will help
Answer:
The parallelograms PQRS and TUVW are not alike.
Step-by-step explanation:
In a parallelogram, if one angle is known, then all the other angles can also be determined.
Now, parallelograms PQRS and TUVW have one angle of 120° equal.
So, the other three angles will be the same for them.
The adjacent sides of the parallelogram PQRS are 8 ft and 12 ft. and the adjacent sides of the parallelogram TUVW are 2.4 ft and 5.2 ft.
So the ratios of sides of the two parallelograms are 
and 
which are not equal.
So, the parallelograms PQRS and TUVW are not alike. (Answer)
Answer:
13 cm, 84 cm, 85 cm
Step-by-step explanation:
Let the sides of triangle are be a, b, c
- a = x, b = 5x + 19, c = 5x + 20
<u>As per Pythagorean theorem:</u>
- c² = a² + b²
- (5x+20)² = (5x +19)² + x²
- 25x² + 200x + 400 = 25x² + 190x + 361 + x²
- x² - 10x - 39 = 0
<u>Solving the quadratic equation we get:</u>
<u>Then:</u>
- a= 13 cm
- b = 5*13 +19 = 84 cm
- c= 5*13 + 20 = 85 cm
