Answer:
Step-by-step explanation:
The relevant rule of exponents is ...
(a^b·c^d)^e = a^(be)·c^(de)
Then ...
(m^(5/4)·n^(-4/5))^(7/3) = m^(5/4·7/3)·n^(-4/5·7/3)
= m^(35/12)·n^(-28/15)
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Since you want positive rational exponents, you can write this as ...
= m^(35/12)/n^(28/15)
There are 4 pairs of overlapping triangles that I can see that are congruent. Two pairs share vertically opposite angles.
One more pair have right angles at the bottom of the rectangle.
One other pair have right angles at the top of the rectangle.
The hint says that volume of a rectangular solid = l*w*h, where l = length, w = width, and h = height. Use this to solve for the height of the solid by plugging in the numbers you know.
You know that length, l = 2cm, width, w = 8cm, and, *EDITED* volume = 160 cm^3. Plug these values into the equation for volume (the hint) and solve for h, the height:
Volume = lwh
160 = (2)(8)(h)
160 = 16h
h = 10cm
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Answer: The height is 10 cm
It will take him 28 weeks. If he already has $60 of $200 saved, you would do 200 - 60. That would give you 140. To find out how long it would take him to make $140, you would have to do 140 divided by 5 to get the number of weeks.
Ok, so the function form is y = a * bx.
Substitute in the values:
750 = a * b5
and
48 = a * b2
Then divide the two equations:
750/ 48 = (a * b5) / (a * b2)
So:
15.625 = b3
Take the cube root of both sides:
2.5 = b
Now, substitue b into one of the equations (the one with 48 has smaller numbers and is easier to work with.)
48 = a * 2.52
Simplify.
48 = a * 6.25
Divide both sides by 6.25
7.68 = a
Now substitute in a and b to write the exponential function:
y = 7.68 * 2.5x
