Answer:
(a) m = 10
(b) n = 160
Step-by-step explanation:
To rewrite the expression in the manner indicated, write an equation that sets the given expression equal to the desired expression. Then solve for the variable value. The distributive property and the usual rules of exponents apply.
The rules of exponents you can use here are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^0 = 1
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(a) 2^101 +2^103 = m×2^100
2^(101-100) +2^(103-100) = m × 2^(100-100) . . . . . . . multiply by 2^(-100)
2^1 +2^3 = m
2 + 8 = m
m = 10
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(b) 2^101 +2^103 = n×4^48
2^101 +2^103 = n×(2^2)^48 . . . . . substitute 4 = 2^2
2^101 +2^103 = n×2^96 . . . . . . . . simplify
2^5 +2^7 = n . . . . . . . . . . . . . . . . . as above, multiply by 2^(-96)
32 +128 = n
n = 160
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<em>Additional comment</em>
The rules of exponents tell you that ...
(m × 2^100) × 2^-100 = m × 2^(100 -100) = m × 2^0 = m
This is effectively the same as dividing by 2^100. You're doing the same thing you would do to solve any linear equation: divide by the coefficient of the variable.
Answer:
True
Step-by-step explanation:
1+2*1=3
5*1-3*1=2
--------
1+2=3
5-3=2
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3=3
2=2
Answer:
Step-by-step explanation:
By inscribed angle theorem:
![m\angle R = \frac{1}{2} [360 \degree - (120 \degree + 140 \degree)] \\ \\ m\angle R = \frac{1}{2} [360 \degree -260 \degree] \\ \\ m\angle R = \frac{1}{2} \times 100 \degree \\ \\ m\angle R = 50 \degree \\ \\](https://tex.z-dn.net/?f=m%5Cangle%20R%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%5B360%20%5Cdegree%20-%20%28120%20%5Cdegree%20%2B%20140%20%5Cdegree%29%5D%20%20%5C%5C%20%20%5C%5C%20m%5Cangle%20R%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%5B360%20%5Cdegree%20-260%20%5Cdegree%5D%20%20%5C%5C%20%20%5C%5C%20%20m%5Cangle%20R%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20100%20%5Cdegree%20%20%5C%5C%20%20%5C%5C%20%20m%5Cangle%20R%20%20%3D%2050%20%5Cdegree%20%20%5C%5C%20%20%5C%5C%20)
<span>There are different coordinate systems the commonest being the system of latitudes, longitudes, and ellipsoidal heights, and the situation is complicated because the latitudes and longitudes of the same point differ slightly depending on the geodetic coordinate system of a nation,the result being that different system of latitude and longitude in use for the same point can disagree in coordinates sometimes by more than 200 meters.</span>
Answer:
Step-by-step explanation:
So, when we dilate a triangle, it affects side measures.
So let's find it!
So, the sides of our new triangle is 4 and 12.
Let's find the area!
So, it is the first option! Hope this helps!
P.S. Stay Safe
