Answer:
24
Step-by-step explanation:
Based on the logarithmic expressions given 
, we need to identify the value of 
By substituting x = a³, y = a⁷, and z = a⁻² into the logarithmic function , we will derive;
Therefore, the result of the logarithmic expression is 24
Manuel has opted to construct a fence to define a play area for his dogs, which will be a rectangular shape. Since only three sides require fencing because his house acts as one side of the rectangle, we conclude that the optimal area configuration will consist of two shorter sides each measuring 20 feet and a longer side measuring 40 feet.
The complete question reads:
Peter created two rays, AC and AP, sharing a common vertex at point A. Which of the following statements
might accurately describe Peter's drawing?
I. AC and AP are parallel.
II. PAC represents an angle.
III. AC and AP are at right angles.
A. I and II
B. II and III
C. I and III
D. I, II, and III
Answer:
Option B: II & III
Step-by-step explanation:
We know Peter has drawn rays AC and AP.
Since the point A is shared as the endpoint, it indicates an angular relationship at this common point.
This angle could potentially be 90°, suggesting that rays AC and AP may be perpendicular.
Thus, the valid statements that characterize his drawing are: II & III.
Answer:
x = 11.33 years
Step-by-step explanation:
The equation for rainbow smelt is Y1 = −19.76x + 227
For bloater fish, the equation is Y2 = –92.57x + 1052
To find where these populations are equal:
–19.76x + 227 = –92.57x + 1052
Combine like terms:
-19.76x + 92.57x = 1052 - 227
72.81x = 825
Now divide by 72.81:
x = 825 / 72.81
Thus,
x = 11.33 years
<span>To find out how much she makes weekly, we must multiply her hourly wage of $7 by the total hours she worked throughout the week. When determining how many hours she worked, we need to rearrange the formula:
Salary per week = hourly wage x hours worked
In this case, we already know two pieces of information: hourly wage and total weekly salary.
Hours worked = weekly salary / hourly wage
Hours worked = 143.50 / 7
Hours worked = 20.5
Therefore, the maximum hours she can work is 20h30.</span>
