The answer is <span>A.) F(x) = 10(2.5)^x</span><span>.
</span>Since our base (2.5) is greater than 1, our graph would be increasing, hence it matches the given graph (it increases to the right, or towards quadrant I). Now all we need to do is solve for the y-intercept:
F(x) = 10(2.5)^x
F(0) = 10(2.5)^0 [substitute 0 in for x]
F(0) = 10(1) [any number raised to 0 would always equal 1]
y-intercept: 10
Now does it match the graph? <span><em>Yes, it does.</em>
</span>
Thus, our exponential function for this graph would be F(x) = 10(2.5)^x.
<em /><u>Tip for life</u>: When solving for the y-intercept of exponential functions, our y-intercept is always the number in front of the base (in this case, <u /><u><em>10</em></u>(2.5)^x).
<em>Hope this helps.</em>
Answer:
-2
Step-by-step explanation:
f(-6)=x^2+8x+10
f=(-6)^2+8(-6)+10
f=36-48+10
f(-6)=-2
Answer:
- The graph has a minimum.
- The graph has a y-intercept at (0, -3).
- The solutions ... are -1 and 3.
- The vertex is located at (1, -4).
- In the equation, 'a' would be positive.
Step-by-step explanation:
When the graph has a low point, it has a minimum. 'a' is positive in that case. The coordinates of that low point are (1, -4). That point is the vertex.
The graph crosses the y-axis at y = -3, so the y-intercept is (0, -3).
The graph crosses the x-axis at (-1, 0) and (3, 0). These points represent the solution to the equation y = 0.
- The graph has a minimum.
- The graph has a y-intercept at (0, -3).
- The solutions ... are -1 and 3.
- The vertex is located at (1, -4).
- In the equation, 'a' would be positive.
To find slope, we must find the change in y values divided by the change in x values, also called the rise/run. This is modeled below:
Slope = m = (y1 - y2)/(x1-x2) = (6-(-3))/(1 - (-6)) = (6+3)/(1+6) = 9/7
We can check that this answer is correct by consulting the graph. The graph shows a positive correlation (means that the slope should be positive), and if you count the graph unit squares, you get that the graph moves up 9 squares and over 7 squares between the two points shown, letting us know we got the right answer.
Hope this helps!
Answer:
x = -11
Step-by-step explanation:
Hello There!
create an equation
x + 51 + 60 + 80 = 180
combine like terms
51 + 60 + 80 = 191
x + 191 = 180
subtract 191 from each side
180 - 191 = -11
we're left with
x = -11
