Triangle abc is such that ab=4 and ac=8 if m is the midpoint of bc and am=3, what is the length of bc?
1 answer:
This is an interesting question. I chose to tackle it using the Law of Cosines.
AC² = AB² + BC² - 2·AB·BC·cos(B)
AM² = AB² + MB² - 2·AB·MB·cos(B)
Subtracting twice the second equation from the first, we have
AC² - 2·AM² = -AB² + BC² - 2·MB²
We know that MB = BC/2. When we substitute the given information, we have
8² - 2·3² = -4² + BC² - BC²/2
124 = BC² . . . . . . . . . . . . . . . . . . add 16, multiply by 2
2√31 = BC ≈ 11.1355
AC² = AB² + BC² - 2·AB·BC·cos(B)
AM² = AB² + MB² - 2·AB·MB·cos(B)
Subtracting twice the second equation from the first, we have
AC² - 2·AM² = -AB² + BC² - 2·MB²
We know that MB = BC/2. When we substitute the given information, we have
8² - 2·3² = -4² + BC² - BC²/2
124 = BC² . . . . . . . . . . . . . . . . . . add 16, multiply by 2
2√31 = BC ≈ 11.1355
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Answer:
The common factor is 5x.
The factored polynomial is:
Step-by-step explanation:
Factor of the numbers:
The common factor of the numbers 5, 30 and 10 is 5, as it is the greater common divisor of them, as found below:
5 - 30 - 10|5
1 - 6 - 2
Factor of the exponents:
Between and
, the common factor is the x with the lowest exponent. So x
Common factor
Number multiplied by exponents, so 5x.
Factoring the polynomial:
The factored polynomial is:
Answer:
Step-by-step explanation:
To find g(-4) , substitute the value of x that's - 4 into g(x). That is for every x in g(x) , replace it with - 4
We have
We have the final answer as
<h3>g(-4) = 14</h3>Hope this helps you