Answer:
The average rate of change cover the given interval is -6
Step-by-step explanation:
The average rate of change of a function over a range can be calculated by;
f(b) - f(a)/b-a
f(b) and f(a) refers to the respective y values of the x values a and b
Since we have a and b, we can get f(a) and f(b) from the plot
From the graph, since a = 0, f(a) is the y-intercept = 6
b = 1
f(b) = 0
So we have the slope as
= (0-6)/(1-0) = -6/1 = -6
<h3>Answer:</h3>
a) l = 5 + 2w
b) P = 2(l +w) = 2(5 +2w +w)
c) w = 8 cm, l = 21 cm
<h3>Explanation:</h3>
a) Using w for width, twice the width is 2w, and 5 more than that is 5+2w. This is your expression for l:
... l = 5 + 2w
b) The perimeter is the sum of the lengths of all sides, so is the sum of twice the length and twice the width.
... P = 2(l +w) = 2(5 +2w + w) . . . . substituting for l using the expression of (a)
c) Substituting the given perimeter, we have ...
... 58 = 2(5 +3w) = 10 + 6w . . . . . collect terms, eliminate parentheses
... 48 = 6w . . . . . . . . . . . . . . . . . . subtract 10
... 8 = w . . . . . . . . divide by 6
... l = 5 + 2·8 = 21 . . . . . find length using the formula for it
Dimensions are in centimeters, so we can write the solution as ...
- width = 8 cm
- length = 21 cm
Step-by-step explanation:
x + y ≤ 6
You'll have to express the linear inequality into an equality statement (in slope-intercept form, y = mx + b) in order to graph. You'll have to use a solid line because of the "≤ " symbol.
y = - x + 6
Next, you'll have to choose two points to use for graphing. It's always safe to start with the y-intercept, (0, 6).
From there, you could use the slope (m = -1) and do the "rise over run" technique to plot your next point. Going up 1, left 1 will get you to (-1, 7); going down 1 right 1 will get you to point (1, 5). Connect your points and create a straight line.
Next, to determine which region to shade, you must choose a convenient test point (that's not on the line) to see whether the given test point will satisfy the inequality statement.
Let's choose the point of origin, (0, 0), and plug its values into the inequality statement:
x + y ≤ 6
0 + 0 ≤ 6
0 ≤ 6 (True statement). This means that you should shade the half-plane region where the test point is located (left side of the plane).
The first screenshot shows how I created the lines by plotting the first three points. The second screenshot shows the actual graph with the shaded region.
Please mark my answer as the Brainliest if you find this explanation helpful :)
Answer:
The correct answer is B. -3.
Step-by-step explanation:
To solve this problem, we need to plug in -3 for all of the values of x in the equation. If we do this, we get:
f(x) = 2x + 3
f(-3) = 2(-3) + 3
Now, we can just simplify the expression found on the right side of the equation using PEMDAS. First, we should perform the multiplication.
f(-3) = -6 + 3
Next, we should add our final two terms together.
f(-3) = -3
Therefore, the correct answer is -3.
Hope this helps!
3. g(x) = (x-3)^2 -5
Replace g(x) with y
y = (x-3)^2 -5
Switch the x and the Y:
x = (y-3)^2 -5
Solve for y:
Add 5 to both sides:
x + 5 = (y-3)^2
Take the square root of both sides:
+ /- SQRT(x+5) = y -3
Add 3 to both sides:
y = +/- SQRT(x +5) +3
The solution is both the positive and negative:
SQRT(x +5) +3 and -SQRT(x+5) +3
7. Following the same steps as 3
The answer is SQRT(x-2) -6 and -SQRT(X-2) -6
9. Following thw same steps as 3.
The answer is SQRT(2(x+4)) +2 and - SQRT(2(x+4))
