It is true because a rational function is defined as those functions where the variable is placed in the denominator, which must be restricted, because all denominators cannot be equal to zero, other wise it would be undetermined
Answer:
42, 138, 138
Step-by-step explanation:
the line not adjacent to the 42 degree angle is also 42 by the vertical angles theorem. Then you find the measure of the other 2 by x+42=180 so x=138.
The first way:
1. Reflect the figure I across the x-axis.
2. Translate the figure I and its reflection and rotate them 90 degrees.
The second way:
1. Reflect the figure I across the x-axis.
2. Rotate 90 degrees counterclockwise.
3. Rotate it across the y-axis.
Answer:
The range is the difference between the biggest and smaller values of a set. The median is the middle value of a set. So we cannot say were the lowest score was found, comparing the median and ranges, because it could be that some repeated value very low or high is biasing the median, we could do it with the mean perhaps. So the proposal is false.
The series' value is maximized if the sum only consists of positive terms. Notice that each term in the sum takes the form 4<em>n</em> + 1 for integer <em>n</em>. This means the smallest positive integer that the sum can involve is 1, so the maximum value is
<em>S</em> = 29 + 25 + 21 + … + 9 + 5 + 1
Reversing the order of terms gives the same sum,
<em>S</em> = 1 + 5 + 9 + … + 21 + 25 + 29
Adding terms in the same positions gives us twice this sum,
2<em>S</em> = (29 + 1) + (25 + 5) + (21 + 9) + … + (1 + 29)
Notice how each grouped sum adds to 30. There are 8 terms in the sum, since 4<em>n</em> + 1 = 29 when <em>n</em> = 8. So
2<em>S</em> = 8 × 30 = 240 ===> <em>S</em> = 120
