pH = f(x) = -log₁₀x
1. Graphs
I used Excel to calculate the pH values and draw the graphs (see the Figure).
f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.
The points at which pH = 0 and pH = 1 are indicated by the large red dots.
2. x = 0.5
When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.
3. Transformations
(a) ƒ(x) = -log(x) + 1
This function has no y-intercept, because log(0) is undefined.
(b) ƒ(x +1) = -log(x + 1)
f(0) = -log(0 + 1) = -log(1) = 0
This function has a y-intercept at (0,0).
hope this helps please mark me brainliest!
Since 1 lap I every 6 minutes then 30\6 is 5 so the answer is 5 LAPS
Answer:
<em><u>z = -3</u></em>
Step-by-step explanation:
<u>Step 1: Simplify both sides of the equation.
</u>
z+7=−z+1
<u>Step 2: Add z to both sides.
</u>
z+7+z=−z+1+z
2z+7=1
<u>Step 3: Subtract 7 from both sides.
</u>
2z+7−7=1−7
2z=−6
<u>Step 4: Divide both sides by 2.
</u>
<u>2z</u> = <u>−6
</u>
2 2
z=−3
Because I see a graph in the picture, I am assuming you need to graph the equations. The two equations are in slope-intercept form. They are in the form
y = mx + b
Where m is the slope and b is the y-intercept. That is why it is called the slope-intercept form.
If you want to graph a slope-intercept form equation, first plug in a value for x then compute it to get the y-coordinate.
First, let's get some points with the equation y = 4x + 3
We will plug in three values for x. 0, 1, and 2.
When x = 0
y = 4(0) + 3
y = 3
When x = 1
y = 4(1) + 3
y = 7
When x = 2
y = 4(2) + 3
y = 11
Now we have the points (0, 3), (1, 7), and (2, 11)
These points are called ordered pairs. Where the first number is the x-coordinate and the second number is the y-coordinate.
The ordered pairs tell you how many times you move your point away from the origin. The origin is (0, 0).
The first number of an ordered pair tells you how many times to move in the x direction and the second number how many times in the y direction.
Now graph the second equation. y = -x - 2
Just plug in some values for x.
I picked 0, 1, and 2.
When x = 0
y = 0 - 2
y = -2
When x = 1
y = -1 - 2
y = -3
When x = 2
y = -2 - 2
y = -4
Now we have the points (0, -2), (1, -3), and (2, -4)
Now plot those points and draw a line through them.
If you need to find the intersection of the equations y = 4x + 3 and y = -x - 2 you need to find where they intersect. Or in other words, share a common point.
After playing around with the numbers, I got the intersection point for the both of the equations.
It is the ordered pair (-1, -1). This the solution to both of the equations. If you plug in the ordered pairs into both of the equations, they will show it belongs to their graphs.
Plug in the values for y = 4x + 3
-1 = 4(-1) + 3
-1 = -4 + 3
-1 = -1
Plug in the values for y = -x - 2
-1 = -(-1) - 2
-1 = 1 - 2
-1 = -1
So, this ordered pair is on both equations!
Answer: 25 and 49
Explanation:
25: 1,5,25
49: 1,7,49
