Let h be the height of the tree and d the distance to the top of the tree from the point on the ground. Draw a diagram to visualize the situation:
Since the distance to the top of the tree is 11 ft more than two times the height, then:
Use the Pythagorean Theorem to relate the length of the sides of the right triangle:
Notice that we have obtained a quadratic equation in terms of h. Write it in standard form and use the quadratic formula to solve for h:
Since the height of the tree must be positive, the only solution is h=39ft. To the nearest foot, the height of the tree is 39.
Therefore, the height of the tree is 39 ft.
Answer:
x=2
you have to evaluate the numbers to gt to 2
Answer:
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Step-by-step explanation:
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Answer: (x-9)(x+1), so x=9 and x=-1
Step-by-step explanation:
X^2-8x-9=0
-9 times 1 = -9 and -9 plus 1 = -8
So (x-9)(x+1)
X=9, x=-1
A greatest common factor is the largest number that goes into two or more numbers (in this case two). To find the GCF of two numbers, we have to find the prime factorization (how to express a number as a product of prime numbers) and then see which numbers are common in both of the prime factorizations.
11. The prime factorization of 12 is 3 * 2 * 2. The prime factorization of 18 is 3 * 3 * 2. Looking at the prime factorizations, we can see that both of them have 3 and 2. That means that the GCF is 3 * 2 which is 6.
12. The prime factorization of 48 is 2 * 2 * 2 * 2 * 3. The prime factorization of 80 is 2 * 2 * 2 * 2 * 5. We see that the numbers shared are 2, 2, 2, and 2. That means that the GCF is 2 * 2 * 2 * 2 or 16.
