Please help I am confused
1 answer:
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The true statement about the function f(x) = -x² - 4x + 5 is that:
- The range of the function is all real numbers less than or equal to 9.
The domain of a function is the set of given values of input for which the function is valid and true.
The range is the dependent variable of a given set of values for which the function is defined.
- The domain of the function: f(x) = -x² - 4x + 5 are all real number from -∞ to +∞
For a parabola ax² + bx + c with the vertex
- If a < 0, then the range is f(x) ≤
- If a > 0, then the range f(x) ≥
- Here; a = -1,
The vertex for an up-down facing parabola for a function y = ax² + bx + c is:
Thus,
- vertex
= (-2, 9)
Range: f(x) ≤ 9
Therefore, we can conclude that the range of the function is all real numbers less than or equal to 9.
Learn more about the domain and range of a function here:
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Answer:
a = 1
Step-by-step explanation:
Given the point (a, 3) is on the line: 5x + y = 8.
Any point on the line satisfies the equation.
So, (a, 3) should satisfy the equation 5x + y = 8
Substituting x = a and y = 3, we get:
5(a) + 3 = 8
⇒ a = 1
Therefore, (1, 3) is the point on the line.
Answer:
Variables:
→ The number of hours the worker worked
→ The number of shirts the worker made.
System fo equations:
Step-by-step explanation:
Let be the number of hours the worker worked and
the number of shirts the worker made.
Since:
- Jason must pay the worker $25 per hour (which can be represented with
).
- He must pay $1.75 per shirt for material costs (which can be represented with
).
- The total expenses were $270.
You can write the following equation:
Knowing that the worker created an average of 5 shirts per hour, you can write the other equation:
Therefore, with this equations you can set up the following system of equations, which could be used to determine the number of hours the worker worked and the number of shirts the worker made: