Hi there!
The range of a function describes its possible y-values. For example, y=x produces a linear graph. Its range is all real numbers, meaning that for any value of y, the function is defined.
However, for y=x², for example, the range is y>0, since there the graph doesn't travel to y-values less than 0. The function is only defined when y>0.
To find the range of the given functions, you can try graphing them. Or, if you've memorized the ranges of their parent functions, you can try to take that and apply transformations.
Answer for the first question:
f(x)=-√x
The parent function is f(x)=√x. The range of this is y≥0.
f(x)=-√x
Adding a negative in front of the square root reflects the function across the x-axis, meaning the range is therefore flipped too:
y≤0
I hope this helps!
The two expressions are not equal
You can solve this problem by creating a system of equations and solving by substitution. This allows you to solve for one of the unknown values (in this case, the number of short answer and number of multiple choice) and you can then solve for both, if you would like.
The two variables in your equations standing in for these missing values represent the number of short answer (s) and the number of multiple choice questions (m).
First create an equation for the number of total questions on the test. The total number of multiple choice and short answer questions is 45:
m + s = 45
Then create an equation with these variables representing the number of points on the test. The point values for each question will be the variable coefficients (numbers that the variables are multiplied by in this problem).
2m + 5s = 120
Now you can take the first equation - since it is simpler, the variables don't have coefficients so it only requires subtraction to get one variable by itself - solve for one of the variables, and substitute the result into the second equation in place of that variable. You will then be able to solve for that variable!
First, solve for m in the first equation by moving the m to one side of the equals sign by itself. It then becomes 45 - s = m
Now put (45-s) into the second equation in place of m.
120 = 2(45-s) + 5s
Distribute the 2(45-s)
120 = 90 - 2s + 5s
Add the "s" expressions together. Subtract 90 from both sides.
30 = 3s
Divide by 3 and find that s = 10
There are 10 short answer questions on the test.
Answer:
Step-by-step explanation:
11x - 2° = 75° ( being corresponding angles )
11x = 75° + 2°
11x = 77°
x = 77°/ 11
x = 7°
hope it helps :)
