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Anna007 [38]
2 years ago
7

I need help with this question. Melissa is baking a birthday cake for her best friend and the preparation time is 12 minutes, wh

ich is one third of the baking time. Write and solve an equation to find the baking time
Mathematics
1 answer:
Otrada [13]2 years ago
5 0

Answer:

I put all the steps down. I don't know which one you want. I hope you understand it now.

Step-by-step explanation:

b = baking time

p = preperation time

p = 1/3b

12 = 1/3b

b = 12*3

b = 36 minutes

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<span>
On the other hand, the general form is given as follows:

</span>x^{2}+y^{2}+Dx+Ey+F=0 \\ \\ where: \\ D=-2h, \ E=-2k, \ F=h^{2}+k^{2}-r^{2}<span>

In this way, we can order the mentioned equations as follows:

Equations in Standard Form:

</span>\bold{a)} \ (x-6)^{2}+(y-4)^{2}=56 \\ \bold{b)} \ (x-2)^{2} + (y+6)^{2}=60 \\ \bold{c)} \ (x+2)^{2}+(y+3)^{2}=18 \\ \bold{d)} \ (x+1)^{2}+(y-6)^{2}=46

Equations in General Form:

\bold{1)} \ x^{2}+y^{2}-4x+12y-20=0 \\ \bold{2)} \ x^{2}+y^{2}+6x-8y-10=0 \\ \bold{3)} \ 3x^{2}+3y^{2}+12x+18y-15=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 3, \ the \ equation \ becomes: \\ x^{2}+y^{2}+4x+6y-5=0 \\ \\ \bold{4)} \ 5x^{2}+5y^{2}-10x+20y-30=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 5, \ the \ equation \ becomes: \\ x^{2}+y^{2}-2x+4y-6=0 \\ \\ \bold{5)} \ 2x^{2}+2y^{2}-24x-16y-8=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 2, \ the \ equation \ becomes: \\ x^{2}+y^{2}-12x-8y-4=0

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So let's match each equation:

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x^{2}+y^{2}-12x-8y-4=0

<em><u>First. a) matches 5) </u></em>

\bold{From \ b)} \\ \\ (h,k)=(2,-6),\ r=2\sqrt{15} \\ D=-4, \ E=12 \\ F=-20

Then, its general form is:

x^{2}+y^{2}-4x+12y-20=0

<em><u>Second. b) matches 1) </u></em>

\bold{From \ c)} \\ \\ (h,k)=(-2,-3),\ r=3\sqrt{2} \\ D=4, \ E=6 \\ F=-5

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x^{2}+y^{2}+4x+6y-5=0

<em><u>Third. c) matches 3)</u></em>

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