The correct answer for the inequality 2x > 7 is 9. For the slope calculation, the answer is approximately 4.5. In standard notation, numbers are written without exponents, such as 7.11 × 10^-2 becoming 0.0711.
Understanding Inequalities, Slope Calculation, and Standard Notation
To answer the first question regarding the inequality 2x > 7, we need to solve for x to determine which of the given options is a solution. We divide both sides of the inequality by 2 and find that x > 3.5. Therefore, the correct answer is d. 9, since 9 is greater than 3.5.
For the question about the slope, we use the formula (y2 - y1)/(x2 - x1) to calculate the slope between two points. Substituting the given points (1, 0.1) and (7, 26.8) we get (26.8 - 0.1)/(7 - 1) which simplifies to 26.7/6, or approximately 4.45. Hence, the closest answer is b. 4.5.
Expressing numbers in standard notation simply means writing them in normal number form without the exponent. For example:
a. 7.11 × 10^-2 is 0.0711
b. 9.18 × 10^2 is 918
c. 3.09 x 10^7 is 30,900,000
The probable question may be:
Which value of x satisfies the inequality 2x > 7?
a. -9
b. 0
c. 4
d. 9