What is the y-intercept of f(x)=(3/5)^x
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Hello,
To solve this problem we want to use the Pythagorean Theorem.
The pythagorean theorem states that for a 90° triangle,
where a and b represent the two legs of the triangle, and c represents the hypotenuse.
Let a = the longer leg and b = the shorter leg.
If the longer leg of the triangle is 1 foot longer than the shorter leg, then
a = b +1.
If the hypotenuse is 9 feet longer than the shorter leg, then c = b + 9.
Using the equations we created, we can plug them into the Pythagorean Theorem to solve for a, b, and c.
Doing this, we have:
Expanding this, we get
Solving for b, we get b = 20, and b = -4.
The length of the side of a triangle cannot be negative, so we know that b = 20.
However, we should check this with the original question to make sure it checks out.
a = b + 1
a = 20 + 1 = 21
c = b + 9
c = 20 + 9 = 29
So, we have a = 21, b = 20, and c = 29. (Also, 20-21-29 is a well known Pythagorean triple)
Using the Pythagorean Theorem, we have:
441 + 400 = 841
841 = 841, checks out.
So, the shorter leg is 20 feet, the longer leg is 21 feet, and the hypotenuse is 29 feet.
Hope this helps!
To solve this problem we want to use the Pythagorean Theorem.
The pythagorean theorem states that for a 90° triangle,
where a and b represent the two legs of the triangle, and c represents the hypotenuse.
Let a = the longer leg and b = the shorter leg.
If the longer leg of the triangle is 1 foot longer than the shorter leg, then
a = b +1.
If the hypotenuse is 9 feet longer than the shorter leg, then c = b + 9.
Using the equations we created, we can plug them into the Pythagorean Theorem to solve for a, b, and c.
Doing this, we have:
Expanding this, we get
Solving for b, we get b = 20, and b = -4.
The length of the side of a triangle cannot be negative, so we know that b = 20.
However, we should check this with the original question to make sure it checks out.
a = b + 1
a = 20 + 1 = 21
c = b + 9
c = 20 + 9 = 29
So, we have a = 21, b = 20, and c = 29. (Also, 20-21-29 is a well known Pythagorean triple)
Using the Pythagorean Theorem, we have:
441 + 400 = 841
841 = 841, checks out.
So, the shorter leg is 20 feet, the longer leg is 21 feet, and the hypotenuse is 29 feet.
Hope this helps!
The inscribed angle theorem says that
Triangle AOC is isosceles because both AO and CO are radii of the circle and have the same length. This means angles CAO and ACO have the same measure and are congruent.
Angles ACO and COD are congruent because they form an alternating interior pair between the parallel lines AC and OD.
Taking all these facts together, we have
and since angle COB is made up of angles COD and DOB, these angles must be congruent, and so the arcs they subtend (CD and DB, respectively) must also congruent.