Answer:

Step-by-step explanation:
Assuming the given logarithmic equation is

We interchange x and y to get:

We solve for y now:

We add 4 to both sides to get;

Divide through by 4:

Answer:
Smaller number: 12
Larger number: 34
Step-by-step explanation:
Let x represent the smaller number.
Let 3x - 2 represent the larger number (The larger number is two less than three times the smaller number, or x)
x + 3x -2 = 46
Add 3x + x:
4x - 2 = 46
Add 2 to both sides:
4x = 46 + 2
Add 46 + 2:
4x = 48
Divide both sides by 4:
4x/4 = 48/4
x = 12 is the smaller number
Since 12 is the smaller number, and the sum of the two numbers is 46, than the larger number must be 34.
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The first one is the answer
Answer:
∠Q = 75°
Step-by-step explanation:
Start by recognizing that the triangle is isosceles (the long sides are marked as being equal-length). That means angles Q and R have the same measure.
Next, you use the fact that the sum of angles is 180° to write an equation.
∠R +∠P +∠Q = 180°
(2x +15)° +x° +(2x +15)° = 180° . . . . substitute the known values
5x +30 = 180 . . . . . . . . . . . . . . . . divide by °, collect terms
5x = 150 . . . . . . . . subtract 30
x = 30 . . . . . . . divide by 5
Then angle Q is ...
∠Q = (2x +15)° = (2×30 +15)°
∠Q = 75°
We have the following function that is a
quadratic function:
So the graph of this function is shown in the figure below. This is a <em>parabola</em> as you can see. The roots of this functions, that is, the x-intercepts are:

As you can see in the figure. This function decreases from

and increases from

Finally, another thing we can see from the graph is that the vertex is the point: