Claire is 18 years old and her mother is 40 years old.
-2/3x + 5 = 20 - x
subtract 5 from each side
-2/3 x = 15 -x
add x to each side
-2/3 x +x = 15
get a common denominator of 3 for the x terms
-2/3x + 3/3 x =15
combine like terms
1/3 x = 15
multiply by 3 on each side
x = 45
Answer: x=45
Answer:
-3.5 meters per second
Step-by-step explanation:
Divide the distance by the time.
-17.5 meters / 5 seconds = -3.5 meters per second
First you must find the tenths place
7 .8 3 9
O T H Th
So, the 8 is in the tenths place. Now look at the number to it's right, 3.
Since 3 is less than 5, you just turn everything behind the 8, including the 3, into a zero, giving you 7.800 or 7.8
Answer:
1/2, 3
Step-by-step explanation:
This is a pretty involved problem, so I'm going to start by laying out two facts that our going to help us get there.
- The Fundamental Theorem of Algebra tells us that any polynomial has <em>as many zeroes as its degree</em>. Our function f(x) has a degree of 4, so we'll have 4 zeroes. Also,
- Complex zeroes come in pairs. Specifically, they come in <em>conjugate pairs</em>. If -2i is a zero, 2i must be a zero, too. The "why" is beyond the scope of this response, but this result is called the "complex conjugate root theorem".
In 2., I mentioned that both -2i and 2i must be zeroes of f(x). This means that both and are factors of f(x), and furthermore, their product, , is <em>also</em> a factor. To see what's left after we factor out that product, we can use polynomial long division to find that
I'll go through to steps to factor that second expression below:
Solving both of the expressions when f(x) = 0 gets us our final two zeroes:
So, the remaining zeroes are 1/2 and 3.