Answer:
if marcus ran 1,600 meters that means he walked 400 meters
Step-by-step explanation:
Answer:
- b/a
- 16a²b²
- n¹⁰/(16m⁶)
- y⁸/x¹⁰
- m⁷n³n/m
Step-by-step explanation:
These problems make use of three rules of exponents:
![a^ba^c=a^{b+c}\\\\(a^b)^c=a^{bc}\\\\a^{-b}=\dfrac{1}{a^b} \quad\text{or} \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%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D%5C%5C%5C%5Ca%5E%7B-b%7D%3D%5Cdfrac%7B1%7D%7Ba%5Eb%7D%20%5Cquad%5Ctext%7Bor%7D%20%5Cquad%20a%5Eb%3D%5Cdfrac%7B1%7D%7Ba%5E%7B-b%7D%7D)
In general, you can work the problem by using these rules to compute the exponents of each of the variables (or constants), then arrange the expression so all exponents are positive. (The last problem is slightly different.)
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1. There are no "a" variables in the numerator, and the denominator "a" has a positive exponent (1), so we can leave it alone. The exponent of "b" is the difference of numerator and denominator exponents, according to the above rules.
![\dfrac{b^{-2}}{ab^{-3}}=\dfrac{b^{-2-(-3)}}{a}=\dfrac{b}{a}](https://tex.z-dn.net/?f=%5Cdfrac%7Bb%5E%7B-2%7D%7D%7Bab%5E%7B-3%7D%7D%3D%5Cdfrac%7Bb%5E%7B-2-%28-3%29%7D%7D%7Ba%7D%3D%5Cdfrac%7Bb%7D%7Ba%7D)
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2. 1 to any power is still 1. The outer exponent can be "distributed" to each of the terms inside parentheses, then exponents can be made positive by shifting from denominator to numerator.
![\left(\dfrac{1}{4ab}\right)^{-2}=\dfrac{1}{4^{-2}a^{-2}b^{-2}}=16a^2b^2](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B1%7D%7B4ab%7D%5Cright%29%5E%7B-2%7D%3D%5Cdfrac%7B1%7D%7B4%5E%7B-2%7Da%5E%7B-2%7Db%5E%7B-2%7D%7D%3D16a%5E2b%5E2)
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3. One way to work this one is to simplify the inside of the parentheses before applying the outside exponent.
![\left(\dfrac{4mn}{m^{-2}n^6}\right)^{-2}=\left(4m^{1-(-2)}n^{1-6}}\right)^{-2}=\left(4m^3n^{-5}}\right)^{-2}\\\\=4^{-2}m^{-6}n^{10}=\dfrac{n^{10}}{16m^6}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B4mn%7D%7Bm%5E%7B-2%7Dn%5E6%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%284m%5E%7B1-%28-2%29%7Dn%5E%7B1-6%7D%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%284m%5E3n%5E%7B-5%7D%7D%5Cright%29%5E%7B-2%7D%5C%5C%5C%5C%3D4%5E%7B-2%7Dm%5E%7B-6%7Dn%5E%7B10%7D%3D%5Cdfrac%7Bn%5E%7B10%7D%7D%7B16m%5E6%7D)
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4. This works the same way the previous problem does.
![\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}=\left(x^{-4-(-9)}y^{1-5}\right)^{-2}=\left(x^{5}y^{-4}\right)^{-2}\\\\=x^{-10}y^{8}=\dfrac{y^8}{x^{10}}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7Bx%5E%7B-4%7Dy%7D%7Bx%5E%7B-9%7Dy%5E5%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%28x%5E%7B-4-%28-9%29%7Dy%5E%7B1-5%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%28x%5E%7B5%7Dy%5E%7B-4%7D%5Cright%29%5E%7B-2%7D%5C%5C%5C%5C%3Dx%5E%7B-10%7Dy%5E%7B8%7D%3D%5Cdfrac%7By%5E8%7D%7Bx%5E%7B10%7D%7D)
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5. In this problem, you're only asked to eliminate the one negative exponent. That is done by moving the factor to the numerator, changing the sign of the exponent.
![\dfrac{m^7n^3}{mn^{-1}}=\dfrac{m^7n^3n}{m}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm%5E7n%5E3%7D%7Bmn%5E%7B-1%7D%7D%3D%5Cdfrac%7Bm%5E7n%5E3n%7D%7Bm%7D)
Answer:
the cheapest cost would be to buy the large pack as there's a 25% discount resulting in tim only having to pay 38.25 rather than 60 for the small pack
Step-by-step explanation:
Answer:
![\boxed{ \bold{ \huge{\boxed{ \sf{62}}}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Chuge%7B%5Cboxed%7B%20%5Csf%7B62%7D%7D%7D%7D%7D)
Step-by-step explanation:
![\sf{x ° + 118 ° = 180 ° }](https://tex.z-dn.net/?f=%20%5Csf%7Bx%20%C2%B0%20%2B%20118%20%C2%B0%20%3D%20180%20%C2%B0%20%7D)
( Sum of angle in straight line )
Move 118 to right hand side and change it's sig
⇒![\sf{x ° = 180 ° - 118 °}](https://tex.z-dn.net/?f=%20%5Csf%7Bx%20%C2%B0%20%3D%20180%20%C2%B0%20%20-%20%20118%20%C2%B0%7D)
Calculate
⇒![\sf{x = 62 °}](https://tex.z-dn.net/?f=%20%5Csf%7Bx%20%3D%2062%20%C2%B0%7D)
Hope I helped!
Best regards!!
Answer:
1. heights
2. blood pressure
3 . measurement error
4. IQ scores
Step-by-step explanation:
hope this will help you