Let x = the shorter leg
2x + 6 is the longer leg
2x + 9 is the hypotenuse
We now do the Pythagorean Theorem of
Multiply out to get:
The
will cancel out each other when you combine like terms to get all the terms on one side of the equal sign.
Combine like terms with the rest to end with
Factor this to get
then set each factor equal to zero.
You end up with two solutions, x = 15 and x = - 3
HOWEVER distance cannot be measure in negatives so that answer will not work so x = 15. Now plug into our given information.
The short leg is 15 cm long.
The longer leg of 2(15) + 6 = 36 cm long
The hypotenuse of 2(15) + 9 = 39 cm long.
You can check your answers by plugging them into the Pythagorean Theorem again.
Answer:
The probability of getting three tails is 1 in 8 or 12.5%.
We are going to use the basic form of an exponential function:
to solve this problem.
Since we have tow points
and
, we are going to have a system of equations:
equation (1)
equation (2)
We know for our problem that
,
,
, and
, so lets replace those values in our equations:
equation (1)
equation (2)
Now, we just need to find
and
:
Dividing equation (2) by equation (1):
equation (3)
Replacing equation (3) in equation (1):
Finally, we can put our function together:
We can conclude that the exponential function whose graph passes through the points (2,8) and (5,512) is
.
Answer:
The mean of the test is 65
Step-by-step explanation:
Let the mean be x and SD be y
3 SD BELOW the mean means that we are taking away 3 SD FROM the mean
Mathematically, we have that as;
x - 3y = 41 •••••(i)
73 is 1 SD above mean
Mathematically;
x + y = 73 ••••••••(ii)
So let us solve both equations simultaneously
Simply multiply equation ii by 3 then add to i
x - 3y = 41
3x + 3y =219
4x = 41 + 219
4x = 260
x = 260/4
x = 65