Answer:
- g(x) = x^2 – 4x – 21
- g(x) = 3x^2 – 12x – 63
- g(x) = –(x + 3)(x – 7)
Step-by-step explanation:
When r is an x-intercept of the function, (x -r) is a factor. The two given x-intercepts mean that two factors of the function are (x -(-3))(x -7). There may be a vertical scale factor that is not necessarily positive.
These factors multiply out to give ...
(x +3)(x -7) = x^2 -4x -21 . . . . . . matches the first choice
When this expression is multiplied by 3, it matches the third choice:
3(x +3)(x -7) = 3x^2 -12x -63
When the factored form is multiplied by -1, it matches the fourth choice:
-(x +3)(x -7)
Answer:
<MLJ and <NOQ
Step-by-step explanation:
Alternate exterior angles are angles that lie outside of the two parallel lines that are cut across by the transversal line, and are also alternating each other along the transversal
Considering the image and the options given, <MLJ and <NOQ are exterior angles that alternate each other. Therefore, they are alternate exterior angles.
Answer:
The problem implies that we want to write the (average) amount of natural sweeteners consumed per person as a function of time. Let y represent the (average) amount of natural sweeteners consumed per person (in pounds), and let x represent the time measured in years since 1990. That is, x = 0 represents 1990. If y is a linear function of x, then we can use the slope-intercept form y = mx + b (where m is the slope and b is the y-intercept) to write the function.
The slope can be interpreted as the rate of change of y with respect to x, which in this case means the change in consumption of natural sweeteners per year. The statement that consumption has decreased by 0.6 pounds per year tells us that the slope is m = -0.6 Also, the y-intercept is the same as the y-value of the function when x = 0. (In our case, that means time 0, that is, 1990.) Therefore the y-intercept is b = 133. Hope that helps! Let me know if you have any further questions.
Step-by-step explanation:
