Hi,
Divide using Copy Dot Flop,
2/3 ÷ 4/5 = 2/3 x 5/4
Multiply,
2 x 5 = 10
3 x 4 = 12
= 10/12
Simplify,
10/12 = 5/6
Answer - 5/6
Answer:
1) 11.581
2) 10.78
3) 14.8
4) 3.5
5) 16.28
6) .64
7) 23.3
8) 1.24
9) 6.53
10) 1.59
11) 8.79
12) 27.7919
Step-by-step explanation:
Ur smarter than u think. ^_^
Answer:
see below
Step-by-step explanation:
For simplifying expressions of this sort, there are four rules of exponents that come into play;
![a^ba^c=a^{b+c}\\\\(ab)^c=a^cb^c\\\\(a^b)^c=a^{bc}\\\\\dfrac{1}{a^b}=a^{-b}\ \quad\text{which means}\quad a^b=\dfrac{1}{a^{-b}}](https://tex.z-dn.net/?f=a%5Eba%5Ec%3Da%5E%7Bb%2Bc%7D%5C%5C%5C%5C%28ab%29%5Ec%3Da%5Ecb%5Ec%5C%5C%5C%5C%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D%5C%5C%5C%5C%5Cdfrac%7B1%7D%7Ba%5Eb%7D%3Da%5E%7B-b%7D%5C%20%5Cquad%5Ctext%7Bwhich%20means%7D%5Cquad%20a%5Eb%3D%5Cdfrac%7B1%7D%7Ba%5E%7B-b%7D%7D)
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I find it convenient to eliminate the fractions by adding the exponents, then rewrite any negative exponents as denominator factors.
![23. \quad\dfrac{1}{x^{-2}}=x^2\\\\24. \quad\dfrac{mn}{m^2n^3}=m^{1-2}n^{1-3}=m^{-1}n^{-2}=\dfrac{1}{mn^2}\\\\25. \quad\dfrac{k^{-2}}{k^{-3}}=k^{-2-(-3)}=k\\\\26. \quad\left(\dfrac{m^2}{n^3}\right)^3=\dfrac{m^{2\cdot 3}}{n^{3\cdot 3}}=\dfrac{m^6}{n^9}\\\\27. \quad\dfrac{x^2y^3z^4}{x^{-3}y^{-4}z^{-5}}=x^{2-(-3)}y^{3-(-4)}z^{4-(-5)}=x^5y^7z^9](https://tex.z-dn.net/?f=23.%20%5Cquad%5Cdfrac%7B1%7D%7Bx%5E%7B-2%7D%7D%3Dx%5E2%5C%5C%5C%5C24.%20%5Cquad%5Cdfrac%7Bmn%7D%7Bm%5E2n%5E3%7D%3Dm%5E%7B1-2%7Dn%5E%7B1-3%7D%3Dm%5E%7B-1%7Dn%5E%7B-2%7D%3D%5Cdfrac%7B1%7D%7Bmn%5E2%7D%5C%5C%5C%5C25.%20%5Cquad%5Cdfrac%7Bk%5E%7B-2%7D%7D%7Bk%5E%7B-3%7D%7D%3Dk%5E%7B-2-%28-3%29%7D%3Dk%5C%5C%5C%5C26.%20%5Cquad%5Cleft%28%5Cdfrac%7Bm%5E2%7D%7Bn%5E3%7D%5Cright%29%5E3%3D%5Cdfrac%7Bm%5E%7B2%5Ccdot%203%7D%7D%7Bn%5E%7B3%5Ccdot%203%7D%7D%3D%5Cdfrac%7Bm%5E6%7D%7Bn%5E9%7D%5C%5C%5C%5C27.%20%5Cquad%5Cdfrac%7Bx%5E2y%5E3z%5E4%7D%7Bx%5E%7B-3%7Dy%5E%7B-4%7Dz%5E%7B-5%7D%7D%3Dx%5E%7B2-%28-3%29%7Dy%5E%7B3-%28-4%29%7Dz%5E%7B4-%28-5%29%7D%3Dx%5E5y%5E7z%5E9)
Answer:
1. isosceles because two of the sides are equal
2. right because there is a right angle
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
AEF is a similar triangle to ABC. that means it has the same angles, and the sides (and all other lines in the triangle) are scaled from the ABC length to the AEF length by the same factor f.
now, what is f ?
we know this from the relation of AC to FA.
FA = 12 mm
AC = 12 + 28 = 40 mm
so, going from AC to FA we multiply AC by f so that
AC × f = FA
40 × f = 12
f = 12/40 = 3/10
all other sides, heights, ... if ABC translate to their smaller counterparts in AEF by that multiplication with f (= 3/10).
the area of a triangle is
baseline × height / 2
aABC = 500
and because of the similarity we don't need to calculate the side and height in absolute numbers. we can use the relative sizes by referring to the original dimensions and the scaling factor f.
baseline small = baseline large × f
height small = height large × f
we know that
baseline large × height large / 2 = 500
baseline large × height large = 1000
aAEF = baseline small × height small / 2 =
= baseline large × f × height large × f / 2 =
= baseline large × height large × f² / 2 =
= 1000 × f² / 2 = 500 × f² = 500 ×(3/10)² =
= 500 × 9/100 = 5 × 9 = 45 mm²