Given that f(x) is a function that represents number of hours required to travel, the domain of the function is: distance travelled in miles (x)
<em><u>Recall:</u></em>
- In a relation that is a function, the domain of the function is the set of input values (x-values).
- The range of the function is the set of output values (y-values or f(x)).
Thus, given that f(x) is a function that represents number of hours required to travel, therefore:
- x = input values (domain) = distance travelled in miles
- f(x) = output values (range) = number of hours.
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Hello!
We know that the sum of the three angles of a triangle is equal to 180 degrees. This can be represented using the following formula:
A1 + A2 + A3 = 180
With this knowledge, we can successfully find the missing measurements.
We’ll begin with the large right triangle. Because it is a right triangle, we know that one of its angles is equal to 90 degrees. We are also given that its second angle has a measure of 65 degrees. Insert this information into the formula above and combine like terms:
(90) + (65) + A3 = 180
155 + A3 = 180
Now subtract 155 from both sides of the equation:
A3 = 25
We have now proven that the third angle has a measure of 25 degrees. Looking at the provided image, you’ll notice that this 25 degree angle is adjacent to the 80 degree angle. We can add these neighboring angles to find one of the missing angles of the medium triangle:
25 + 80 = 105
We have now proven that this larger angle has a measure of 105 degrees. Looking again at the provided image, you’ll notice that this triangle also contains a 50 degree angle. Using the “three-angles” formula, we can find the remaining angle of the medium triangle. Insert any known values and combine like terms:
(105) + (50) + A3 = 180
155 + A3 = 180
Now subtract 155 from both sides of the equation:
A3 = 25
We have now proven the third angle of the medium triangle to have a measure of 25 degrees. Consequently, we now have now proven two of the three angles of the smallest triangle. Again using the “three-angles” formula, we can find the measure of the missing angle (x). Insert any known values (using the variable “x” to represent the missing angle) and combine like terms:
(25) + (25) + (x) = 180
50 + x = 180
Now subtract 50 from both sides:
x = 130
we have now proven that the missing angle (x) has a measure of 130 degrees.
I hope this helps!
second angle which has a value of 65 degrees.
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Answer: (6,13)
Work:
- set them equal to each other
2x + 1 = 1/2x + 10
- multiply both sides by 2 to get rid of fraction
4x + 2 = x + 20
- solve for x and you get x = 6
- plug in to solve for y
2(6) + 1 = y
13 = y
When you add any fractions, you need to find a common denominator. In this case they have no common factors so you just multiply them together. First multiply the first fraction by
which gets you
. Then multiply the second fraction by
to get
. Now you can add them together to get
.
(b)
now you can pull out root 2 and get
which equals
