The diagonal of the square creates two congruent right triangles, which you could see if you drew a picture. The diagonal is the hypotenuse of the triangle, and the sides of the square are the legs of the triangle. Again, a diagram might help.
The pythagorean theorem is (a^2)+(b^2)=(c^2), where c is the hypotenuse and a and b are the legs.
We know that c is 5 square root of 2, so:
(a^2)+(b^2)=((5 square root of 2)^2),
Now, distribute the square (exponent of 2) to both the 5 and the square root of 2. Squaring and the square root cancel each other out, leaving us with 2. 5^2 is 25. Then, both of those are multiplied together, so:
(a^2)+(b^2)=50
Since we are dealing with a square, both side lengths are the same, so a and b are the same number. So, we have two of the same term being added to each other. To eliminate any confusion, let x stand for the length of the sides of the triangle. This is equivalent to:
2(x^2)=50.
Then, we just solve for x.
(x^2)=25
x=5
All sides of the triangle are 5. So, the area is 5*5, or 25 inches.
<em><u>Solution:</u></em>
Given that:
To find: (fog)(2) and (f + g)(2)
By composite function,
( f o g)(x) = f (g(x))
Substitute g(x) = 4x + 9 in above formula,
( f o g)(x) = f(4x + 9)
To find (fog)(2) substitute x = 2 in above formula
( f o g)(2) = f(4(2) + 9)
( f o g)(2) = f(8 + 9) = f(17)
We know that
<em><u>To find (f + g)(2)</u></em>
We know that,
(f + g)(x) = f (x) + g(x)
Therefore,
(f + g)(2) = f(2) + g(2)
Substitute x = 2 in f(x) and g(x)
Answer:
all work is shown and pictured
What numbers did they give you?
Answer:
For every table served, Bradley's pay increases by an average of 4
Step-by-step explanation:
The line of best fit for the graph is y = 4x + 25 ; where, y = total pay and x = tables served
Using the slope intercept relation : y = mx + c ; where, m = slope
y = 4x + 25 ; the slope of the graph is 4
This means the rate of change of x with respect to y is 4 ;
This means for every unit change in x ; y increases by 4
For every table served, total pay increases by 4