That's a question about the Pythagorean Theorem.
We use the Pythagorean Theorem to find the value of one side in a right triangle.
This theorem says that:
- <em>a</em> is the hypotenuse (It's the opposite side the right angle).
- <em>b</em> and <em>c </em>are cathetus (They're the adjacent sides the right angle).
Okay, now, let's go to solve this problem! In our figure, we have two cathetus. Their values are 10 and 7 and we have to find the value of <em>x </em>(the hypotenuse). Let's change this information in that formula.
Therefore, the value of <em>x </em>is 
.
I hope I've helped. :D
Enjoy your studies! \o/
A.) To find the maximum height, we can take the derivative of h(t). This will give us the rate at which the horse jumps (velocity) at time t.
h'(t) = -32t + 16
When the horse reaches its maximum height, its position on h(t) will be at the top of the parabola. The slope at this point will be zero because the line tangent to the peak of a parabola is a horizontal line. By setting h'(t) equal to 0, we can find the critical numbers which will be the maximum and minimum t values.
-32t + 16 = 0
-32t = -16
t = 0.5 seconds
b.) To find out if the horse can clear a fence that is 3.5 feet tall, we can plug 0.5 in for t in h(t) and solve for the maximum height.
h(0.5) = -16(0.5)^2 + 16(-0.5) = 4 feet
If 4 is the maximum height the horse can jump, then yes, it can clear a 3.5 foot tall fence.
c.) We know that the horse is in the air whenever h(t) is greater than 0.
-16t^2 + 16t = 0
-16t(t-1)=0
t = 0 and 1
So if the horse is on the ground at t = 0 and t = 1, then we know it was in the air for 1 second.
Answer:
I believe it's a reflection. I'm doing these in Geometry class right now too.
Step-by-step explanation:
The squares points are all opposite/flipped.
We have the expression 4(x + 8) + 5(x - 3).
First, expand the parentheses by using the distributive property.
4(x + 8) + 5(x - 3) = 4x + 32 + 5x - 15
Now combine like terms.
4x + 32 + 5x - 15 = 9x + 17
So, C 9x + 17 is the answer.
It is 121 x 10^12 so the answer is A.
