If f(x)=3^x and g(x)=2x+5, at which value of x is f(x)
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<h2>Answer</h2>
Draw a graph which joins the points (100, 120) and (50, 95) and has a slope = 0.50
<h2>Explanation</h2>A graph of y against x means that x is the independent variable and y is the dependent variable. Notice that the charge (y) depends on the number of minutes (x). Therefore, the points that we are going to join to make our graph will have coordinates (x, y)
We know that the company charges $120 for 100 minutes, so x=100 and y=120. Therefore, our first point will be (100, 120)
We also know that the company charges $95 for 50 minutes, so x=95 and y=50. Therefore, our second point will be (50, 95)
Now, to find the slope between our tow points, we are going to use the slope formula:
where
are the coordinates of the first point
are the coordinates of the second point
We know from our points that ,
,
, and
. So let's replace those values in our formula to find
Now that we have our slope, we can use the point-slope formula to complete the equation of the line joining our two points
Answer: hypotenuse =
Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side () of the right triangle, .i.e.:
In this question:
=
2bc
Substituing and taking square root to find hypotenuse:
Calculating:
=
, then:
Hypotenuse for the right-angled triangle is units