Find the equation of the circle: y-intercepts 4 and –8, contain (–12, –8)
1 answer:
Answer:
(x +6)^2 +(y +2)^2 = 72
Step-by-step explanation:
The given points are vertices of a right triangle. The circle circumscribing that triangle (through all 3 vertices) will have its center at the midpoint of the hypotenuse:
((0, 4) +(-12, -8))/2 = (-6, -2)
The equation of a circle with center (h, k) through point (a, b) is ...
(x -h)^2 +(y -k)^2 = (a -h)^2 +(b -k)^2
For center (-6, -2) and point (0, 4), the equation is ...
(x +6)^2 +(y +2)^2 = (0+6)^2 +(4 +2)^2
(x +6)^2 +(y +2)^2 = 72
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<em><u>Simplified </u></em><em><u>Recap:</u></em>
PQR and XYR are similar.
PQ: 4 inches (shortest side)
PR: 9 inches
QR: 12 inches (longest side)
<em><u>Solving:</u></em>
Because they are similar triangles, we know that the sides of one triangle are proportional to the ones on the other. Therefore, the smallest side of PQR is proportional to the smallest side of XYZ. Now, we just need to figure out the constant of proportionality , and we can do that by dividing the smallest side of XYZ triangle by the smallest side of PQR.
Now we know that the constant of proportionality is 4. All we have to do now is solve the problem. The question is asking what the longest side of XYZ is, and to find that we just need to multiply the longest side of PQR by our constant of proportionality.
Therefore, our answer is 48.
ANSWER
The resulting parabola in vertex form is:
EXPLANATION
The original equation of the parabola is given as
This parabola has its vertex at the origin.
If the graph of this parabola is shifted four units right and three units down, then the new equation is:
This the equation of the transformed parabola.
Its vertex is now at (4,-3).
Answer:
(i) 30
(ii) 8
Step-by-step explanation:
Start by drawing 3 rings for the Venn diagram. Each ring represents either Audi, BMW, or Citroën.
Next, add the information provided in the problem statement. We know that 20 choose BMW only. Another 20 choose Citroën only.
We know the number who choose all 3 is the same as the number that choose BMW and Citroën, but not Audi. We'll call this number x.
Similarly, we know that the number who choose all 3 is half of those choose Audi and BMW, but not Citroën. So we'll say that number is 2x.
We know the total number of Audi votes is 48, the total number of BMW votes is 36, and the total number of Citroën votes is 34.
Finally, we know the total number of voters is 100, including those who voted for no favorites (we'll call that number n).
We know that BMW got 36 votes, so:
20 + x + x + 2x = 36
20 + 4x = 36
4x = 16
x = 4
We know that Citroën got 34 votes, so:
20 + x + x + z = 34
20 + 4 + 4 + z = 34
28 + z = 34
z = 6
We know that Audi got 48 votes:
y + 2x + x + z = 48
y + 2(4) + 4 + 6 = 48
y + 18 = 48
y = 30
Finally, we know that the total number of voters is 100.
20 + 20 + x + x + 2x + y + z + n = 100
20 + 20 + 4 + 4 + 2(4) + 30 + 6 + n = 100
92 + n = 100
n = 8
