(a) Complementary angles
(b) Vertical angles
(c) Supplementary angles
<u>Explanation:</u>
Complementary angles are those two angles whose sum is 90 degrees.
Supplementary angles are those two angles whose sum is 180 degrees.
Vertical angles are the angles opposite each other when two lines cross.
(a)
Angles 1 and 5 are complementary angles
(b)
Angles 3 and 5 are vertical angles
(c)
Angles 3 and 4 are supplementary angles
Answer: in 95% of races, his finishing time will be between 62 and 64 seconds.
Step-by-step explanation:
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 63 seconds and the standard deviation is 5 seconds.
2 standard deviations = 2 × 0.5 = 1
63 - 1 = 62 seconds
63 + 1 = 64 seconds
Therefore, in 95% of races, his finishing time will be between 62 and 64 seconds.
Using translation concepts, the change of f(x) = x to g(x) = x - 90 can be described as follows:
The base graph has been shifted down 90 units.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have that g(x) = f(x) - 90, that is, the base graph was shifted down 90 units.
More can be learned about translation concepts at brainly.com/question/4521517
#SPJ1
The first step for solving this expression is to distribute
through the first set of parenthesis.
× (x - 9)
Now use the FOIL method to multiply each term in the first parenthesis by each term in the second parenthesis. This will look like the following:
x × x -
x × 9 -
x -
× (-9)
Remember that multiplying two negatives together equals a positive,, so the expression changes to:
x × x -
x × 9 -
x +
× 9
Calculate the product of all of the sets of multiplication to make the expression become:
x² -
x -
x +
Lastly,, calculate the difference of -
x -
x to find your final answer.
x² -
x +
Let me know if you have any further questions.
:)