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SIZIF [17.4K]
2 years ago
7

Write the general equation for the circle that passes through the points (-5,0), (0.4), and (2,4).

Mathematics
1 answer:
Advocard [28]2 years ago
7 0

Answer:

(x-1)^2+(y+19/8)^2=2665/64

Step-by-step explanation:

The general equation of a circle is

(x - h)^2 + (y - k)^2 = r^2

Substituting the values of the 3 given points:

(-5 - h)^2 + (0 - k)^2 = r^2

(0 - h)^2 + (4 - k)^2 = r^2

(2 - h)^2 + (4 -k)^2 = r^2

Subtracting the second equation from the first:

(-5-h)^2 - h^2 + k^2 - (4 - k)^2 = 0

25 + 10h + h^2 - h^2 + k^2 - 16 + 8k - k^2 = 0

10h + 8k = -9  ------------ (A).

Subtract the third equation for the second:

h^2 - (2 - h)^2 + 0 = 0

h^2 - 4 + 4h - h^2 = 0

4h = 4

h = 1.

Substituting for h in equation A:

10 + 8k = -9

8k = -19

k = -19/8

So r^2 = (-5-1)^2 + (0 + 19/8)^2 =

36  + 361/ 64

= 2665/64

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The olive trees in an orchard produce 3,000 pounds of olives a year. It takes 20 pounds of olives to make 3 liters of olive oil.
AleksAgata [21]

Answer:

450L

Step-by-step explanation:

This is a ratio and proportion problem. First you need to determine the known ratio and the unknown ratio. In this case we have the known ratio:

\dfrac{20 lbs}{3L}

The unknown ratio in this case is:

\dfrac{3,000lbs}{xL}

So to do this, we just set up the proportion and solve for it:

\dfrac{20lbs}{3L}=\dfrac{3,000lbs}{xL}\\\\{20lbs}=\dfrac{3L\times3,000lbs}{xL}\\\\{xL}=\dfrac{3L\times3,000lbs}{20lbs}\\\\{xL}=\dfrac{9,000L}{20}\\\\xL = 450L

7 0
3 years ago
Monica goes to a stationery shop to buy pens and pencils. She has $35 in pocket change, and she's looking to buy pens for $7 eac
Nana76 [90]

Answer:

7 pencils

Step-by-step explanation:

Let x equal the number of pencils Monica buys and y equal the number of pens.

The expression would then be 2x + 7y ≤ 35. Plugging in 3 for y:

2x + 7(3) ≤35

2x +21 ≤ 35

2x ≤ 14

x≤ 7

7 0
2 years ago
PRETTY PLEASE PLEASE PLEASE PLEASE HELP ME! I NEED IT! 50 PONTS
irinina [24]
It would be 30 dollars intrest maybe 
5 0
3 years ago
Read 2 more answers
Please help? Will make you the Brainliest!
Allushta [10]

Answer:

D. 19/2   D.-4/\sqrt{15}   D.cos^2x  look at explanation for last one

Step-by-step explanation:

1. Find the value of sec if cos delta  = 2/19

because sec is basically 1/cos, and since it's Quad I there's nothing weird, you can just flip the fraction

therefore it's  D. 19/2

2. Find the value of csc given cos delta = -1/4 and triangle is in third Quad

so cosine is adj over hypo: since the hypo can't ever be negative, the triangle must have a = -1 and c =4. to find bc use the c^2 = a^2 + b^2 to solve for b^2, and since it's third quad, b is negative, so b = -\sqrt{15}2. NOw that you know all three sides, finding csc is ez. So csc is hypo over opposite bc its opposite of sine, so therefore csc delta = -4/\sqrt{15}

3. simplify sin^2qcot^2

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4. determine the quad if sine delta = -1/4

sine is opposite over hypo, and as mentioned before, hypo can't equal to negative, so the opposite side must be negative. therefore, the triangle must lie in quad III or quad IV

ahem, these are your answers, idk why is it all D lol, I hope this helped. sorry this was so long!

8 0
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What is the area of the figure?
Ksivusya [100]

Answer:

The correct answer is C 252

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2 years ago
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