Question

throwback thursday
which statement is true?
a. $10^{-2}=\frac{1}{20}=0.05$
b. $10^{-2}=\frac{1}{200}=0.02$
c. $10^{-2}=\frac{1}{100}=0.01$
d. $10^{-3}=-\frac{1}{100}=-0.01$

1. which line has a negative slope and a positive y - intercept?

a. a
b. b
c. c
d. d

Explanation:

Step1: Evaluate negative exponents

Recall $10^{-n}=\frac{1}{10^n}$.

• $10^{-2}=\frac{1}{10^2}=\frac{1}{100}=0.01$

Step2: Match to correct option

Compare with choices:

• A: $10^{-2}=\frac{1}{20}=0.05$ (incorrect)
• B: $10^{-2}=\frac{1}{200}=0.002$ (incorrect)
• C: $10^{-2}=\frac{1}{100}=0.01$ (correct)
• D: $10^{-2}=\frac{1}{100}=-0.01$ (incorrect)

Step3: Analyze line slope/y-intercept

• Positive y-intercept: line crosses y-axis above origin.
• Negative slope: line falls left to right.
• Line C: crosses y-axis above origin, falls left to right.

Answer:

1. C. $10^{-2} = \frac{1}{100} = 0.01$
2. C. C