MATH SOLVE

4 months ago

Q:
# 30 points I really need your help pronto!so for the first one, I need help with how to solve the equation. detailed please or notthe second one I understand a bit more I think I have to increase the size or radius by 3 move it 8 units to the right and 2 units up. however, I'm not sure if I should increase the radius by 3 or 4. the third one I'm just plain lost I don't even know where to start.

Accepted Solution

A:

Answer:Part 1) the center is [tex](2,-1)[/tex], the radius is [tex]4\ units[/tex]Part 2) see the procedurePart 3) [tex]m<B=33.2\°[/tex]Step-by-step explanation:Part 1) we know thatThe equation of a circle in center radius form is equal to[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]where(h,k) is the center of the circler is the radiusIn this problem we have[tex](x-2)^{2}+(y+1)^{2} =16[/tex]sothe center is the point [tex](2,-1)[/tex]the radius is [tex]r=\sqrt{16}=4\ units[/tex]Part 2) we know thatThe center of circle F' is[tex](-2,-8)[/tex] and the radius is [tex]r=2\ units[/tex]The center of circle F is[tex](6,-6)[/tex] and the radius is [tex]r=4\ units[/tex]step 1
Move the center of the circle F' onto the center of the circle Fthe transformation has the following rule
[tex](x,y)--------> (x+8,y+2)[/tex]8 units right and 2 units upso[tex](-2,-8)--------> (-2+8,-8+2)-----> (6,-6)[/tex]center circle F' is now equal to center circle F The circles are now concentric (they have the same center)
step 2
A dilation is needed to increase the size of circle F' to coincide with circle F
scale factor=radius circle F/radius circle F'=4/2=2
radius circle F' will be=2*scale factor=2*2=4 unitsradius circle F' is now equal to radius circle F
A translation, followed by a dilation will map one circle onto the other
Part 3) we know thatThe sum of the interior angles in a quadrilateral is equal to 360 degreesso[tex]<A+<B+<C+<D=360\°[/tex]substitute the values[tex](x+16)+(x)+(6x-4)+(2x+16)=360\°[/tex]solve for x[tex](10x+28)=360\°[/tex][tex]10x=360\°-28\°[/tex][tex]x=332\°/10=33.2\°[/tex]The measure of angle B is[tex]m<B=x\°[/tex]so[tex]m<B=33.2\°[/tex]