Pat bought running shoes for $60. This was four

Write the standard form of the equation for the circle that passes through the points (2,31),(-15,14),(33,0)

stepladder [879]

Answer:

Step-by-step explanation:

Begin with the standard form of a circle as a conic:

$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$

For a circle, A and C will be the exact same, and B will equal 0. If B is non-zero, the equation represents a rotation of a conic, which is reserved for college-level courses. Shortening this, then:

$x^2+y^2+Dx+Ey+F=0$ is good enough for us for this. Start with the first point on the circle, (2, 31) and fill in the equation above with x and y:

$2^2+31^2+2D+31E+F=0$ which simplifies down to:

$(1):2D+31E+F=-965$

Do the same with the next point on the circle, (-15, 14):

$-15^2+14^2-15D+14E+F=0$ which simplifies down to:

$(2):-15D+14E+F=0$

Do the same with the last point, (33, 0):

$33^2+0^2+33D+0E+F=0$ which simplifies down to:

$(3):33D+F=-1089$

Now we will add (1) and (2) to get (4):

2D + 31E + F = -965

-15D + 14E + F = -421

Multiply the top equatio by -1 to get rid of the F terms:

-2D - 31E - F = 965

-15D + 14E + F = -421

which simplifies to

(4): -17D - 17E = 544

Now add (2) and (3) to get (5):

-15D + 14E + F = -421

33D + F = -1089

Multiply the bottom equation by -1 to get rid of the F terms:

-15D + 14E + F = -421

-33D - F = 1089

which simplifies to

(5): -48D + 14E = 668

Now add (4) and (5) together and eliminate the E terms:

-17D - 17E = 544

-48D + 14E = 668

In order to eliminate the E terms, multiply the top equation by 14 and the bottom equation by 17 to solve for D:

-238D - 238E = 7616

-816D + 238E = 11356

Which gives you that

D = -18

Now plug the value for D into (4) to find E:

-17(-18) - 17E = 544 and

306 - 17E = 544 and

-17E = 238 so

E = -14

Now plug the values for both D and E into (1) to find F:

2(-18) + 31(-14) + F = -965 and

-36 - 434 + F = -965 and

-470 + F = -965 so

F = -495

Now we can fill in the standard form of the conic:

$x^2+y^2-18x-14y=495$

but we're not done til we complete the square on both the x terms and the y terms (and I am assuming you know how to complete the square):

$(x^2-18x+81)+(y^2-14y+49)=495+81+49$ which simplifies to

$(x-9)^2+(y-7)^2=625$

The second choice down matches that equation, but the center they have there is not correct. The center of that circle is (9, 7) and they have it as being (7, 10) with a radius of 5. The radius is 25. The center is wrong in the equation that represents the circle as is the radius. Maybe let someone know that...

4 0

3 years ago

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Determine how (if possible) the triangles can be proved similar.

HACTEHA [7]

Answer:

opposite sides are congruent and parrallel

Step-by-step explanation:

im pretty sure im correct because i learned this in 10th grade for Algebra

7 0

2 years ago

70% of kids who visit a doctor have a fever, and 40% of kids who visit a doctor have a sore throat. If the probability that a ki

krek1111 [17]

Answer:

52.5%

Step-by-step explanation:

Let A be kids who have a fever, and B be kids who have a sore throat, so

Based on the given information we have

P(A) = 70%, P(B) = 40%, and P(B|A) = 30% (B|A is read as "B given A", which means probability of B happening given that A has already happened)

We are asked to find P(A|B), the probability of a kid having a fever given that we already know he has a sore throat.

Step 1: First find P(A and B), this is the probability of a kid having both a fever and a sore throat. We use the formula

P(B|A) = P(A and B)/P(A)

We have 2 of these values listed above, so we plug them in...

30% = P(A and B)/70%

This give us a value for P(A and B) which equals 21% [multiply both sides by 70% to isolate P(A and B), (30%)(70%) = 21%]

Now we flip the equation to P(A|B), which is

P(A|B) = P(A and B)/P(B)

We have 2 of the values, so we plug them in...

P(A|B) = 21%/40%

This gives us a value of 52.5% (divide 21% by 40%)

6 0

3 years ago

A rectangular storage box is 12 inches wide, 15 inches long, and 9 inches high. How many square inches of colored paper are need

wolverine [178]

Answer is 846 square inches.

5 0

3 years ago

I need help What is the surface area of the following figure? A 168 B 192 PLEASE HELP

Juliette [100K]

Answer:

Step-by-step explanation:

First step is always to break up the problem into parts and write out our formulas- in this case, let's solve the easier part first, the bottom rectangular box type shape.

Area of a square or rectangle: A= length * height

Area of a triangle: A = 1/2 * length * height

Each side is 6x2, making each side 12 in^2, times four sides equals 48 in^2

The box also has a bottom, with dimensions of 6x6, equaling 36 in^2. <em>be careful not to include the top, it may be included in this part of the problem that we're splitting up, but it's not in the actual figure</em>.

Next up is the top portion- let's calculate the two triangular sides first. again, A=(1/2)l*h . so, these triangles are (1/2) * 5 * 4 , or 10 in^2 . With two triangular sides that's 20 in^2 total.

And now we only have two sides left, the rectangular parts of the triangular prism. They have a dimension of 5*6, equalling 30, and with two sides its a total of 60 in^2.

All of these sides can be added together:

48 + 36 + 20 + 60 = 305 in^2

3 0

3 years ago

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