The <em>correct answer</em> is:
C) The set of all points in a plane that are equidistant from two points.
Explanation:
The set of all points in a plane that are equidistant from a given point and a given line is a parabola.
The set of all points in a plane at a given distance from a given point is a circle.
The set of all points in a plane that are equidistant from two points is a line.
The set of all points in a plane that are equidistant from three points is a plane.
1 gallon has 4 quarts
20 times 4 is 80 quarts.
Answer: Choice B
Open circle at 3. Shading to the right
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Work Shown:
3(8 - 4x) < 6(x - 5)
24 - 12x < 6x - 30
24 + 30 < 6x + 12x
54 < 18x
18x > 54
x > 54/18
x > 3
We use an open circle at 3 to indicate we don't include this endpoint as part of the solution. The solution set is everything larger than 3, so we shade to the right of this open circle.
The number of red marbles in the bag is 19 and the number of blue marbles is 8.
<u>Explanation:</u>
Let R be the number of red marbles
Let B be the number of blue marbles
According to the question,
R + B = 27 (Total number of marbles is 27
) -1
R = 3B - 5 (Number of red marbles is 5 less than 3 times the number of blue marbles
)
Substitute the right half of the second equation for R in the first equation
3B - 5 + B = 27
Add 5 to each side and combine the Bs
4B = 32
Divide both sides by 4
B = 8
Use this value of B in the first equation
R + 8 = 27
R = 19
Therefore, number of red marbles in the bag is 19 and the number of blue marbles is 8.
Answer:
![\displaystyle\frac{\sqrt[4]{3x^2}}{2y}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B%5Csqrt%5B4%5D%7B3x%5E2%7D%7D%7B2y%7D)
Step-by-step explanation:
It can work well to identify 4th powers under the radical, then remove them.
![\displaystyle\sqrt[4]{\frac{24x^6y}{128x^4y^5}}=\sqrt[4]{\frac{3x^2}{16y^4}}=\sqrt[4]{\frac{3x^2}{(2y)^4}}\\\\=\frac{\sqrt[4]{3x^2}}{2y}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csqrt%5B4%5D%7B%5Cfrac%7B24x%5E6y%7D%7B128x%5E4y%5E5%7D%7D%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B3x%5E2%7D%7B16y%5E4%7D%7D%3D%5Csqrt%5B4%5D%7B%5Cfrac%7B3x%5E2%7D%7B%282y%29%5E4%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5Csqrt%5B4%5D%7B3x%5E2%7D%7D%7B2y%7D)
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The applicable rules of exponents are ...
1/a^b = a^-b
(a^b)(a^c) = a^(b+c)
The x-factors simplify as ...
x^6/x^4 = x^(6-4) = x^2
The y-factors simplify as ...
y/y^5 = 1/y^(5-1) = 1/y^4
The constant factors simplify in the usual way:
24/128 = (8·3)/(8·16) = 3/16
