<h3>Answer: Choice C</h3>
RootIndex 12 StartRoot 8 EndRoot Superscript x
12th root of 8^x = (12th root of 8)^x
![\sqrt[12]{8^{x}} = \left(\sqrt[12]{8}\right)^{x}](https://tex.z-dn.net/?f=%5Csqrt%5B12%5D%7B8%5E%7Bx%7D%7D%20%3D%20%5Cleft%28%5Csqrt%5B12%5D%7B8%7D%5Cright%29%5E%7Bx%7D)
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Explanation:
The general rule is
![\sqrt[n]{x} = x^{1/n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B1%2Fn%7D)
so any nth root is the same as having a fractional exponent 1/n.
Using that rule we can say the cube root of 8 is equivalent to 8^(1/3)
![\sqrt[3]{8} = 8^{1/3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%208%5E%7B1%2F3%7D)
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Raising this to the power of (1/4)x will have us multiply the exponents of 1/3 and (1/4)x like so
(1/3)*(1/4)x = (1/12)x
In other words,
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From here, we rewrite the fractional exponent 1/12 as a 12th root. which leads us to this
![8^{(1/12)x} = \sqrt[12]{8^{x}}](https://tex.z-dn.net/?f=8%5E%7B%281%2F12%29x%7D%20%3D%20%5Csqrt%5B12%5D%7B8%5E%7Bx%7D%7D%20)
![8^{(1/12)x} = \left(\sqrt[12]{8}\right)^{x}](https://tex.z-dn.net/?f=8%5E%7B%281%2F12%29x%7D%20%3D%20%5Cleft%28%5Csqrt%5B12%5D%7B8%7D%5Cright%29%5E%7Bx%7D%20)
Answer: 7 crayons
Step-by-step explanation:
To solve we first must find the total number of crayons available by adding up how many crayons are in each container.
56+12+96 = 160 crayons total
Next we take this number and divide it by 22 (the number of students in the class) to determine how many crayon each student gets
160 crayons/22 students = 7.272727 crayons per student
However, it's important to note that this number is not a whole number. We must then round down to the nearest whole number because students aren't given fractions of crayons.
7.272727 ==> 7 crayons per student
Answer:
- (x-4.5)^2 +(y +5)^2 = 30.25
- x = (1/8)y^2 +(1/2)y +(1/2)
- y^2/36 -x^2/64 = 1
- x^2/16 +y^2/25 = 1
Step-by-step explanation:
1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.
(x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15
(x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form
Important features: center = (4.5, -5); radius = 5.5.
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2. To put this in the form x=f(y), we need to add 8x, then divide by 8.
x = (1/8)y^2 +(1/2)y +(1/2)
Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.
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3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:
y^2/36 -x^2/64 = 1
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4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.
x^2/16 +b^2/25 = 1
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The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.
Answer:
y= -3/4x-2
Step-by-step explanation:
- perpendicular: opposite signs and reciprocal
m= -3/4
point-slope form: y-y1=m(x-x1)
y-(-1)= -3/4(x-(-4))
y+1= -3/4(x+4)
y+1= -3/4x -3
y= -3/4x-2
Answer:
Step-by-step explanation:
can you translate that into English please?
