Answer:
ABOVE the x-axis
Step-by-step explanation:
Please use "^" to denote exponentiation: y = x^2 + 2x + 3
To find the vertex, we must complete the square of y = x^2 + 2x + 3, so that we have an equivalent equation in the form f(x) = (x - h)^2 + k.
Starting with y = x^2 + 2x + 3,
we identify the coefficient of x (which is 2), take half of that (which gives
us 1), add 1 and then subtract 1, between "2x" and "3":
y = x^2 + 2x + 1 - 1 + 3
Now rewrite x^2 + 2x + 1 as (x + 1)^2:
y = (x + 1)^2 - 1 + 3, or y = (x + 1)^2 + 2. Comparing this to f(x) = (x - h)^2 + k, we see that h = 1 and k = 2. This tells us that the vertex of this parabola is at (h, k): (1, 2), which is ABOVE the x-axis.
Step-by-step explanation:
Word Problems are mathematical problems presented in complete languages, rather than in mathematical notations.
Example:
A certain number is divided by half, the result is added to itself to give 6, what is the number?
Solution:
- Let the number be x
- Divide x by half:
In word problem, extra caution is to be taken, as misinterpretation can be very chaotic. Dividing a number by 2, is totally different from dividing the number by half.
4 divided by 2 is 4÷2 = 2
4 divided by half is 4÷½ = 4×2/1 = 8
2 and 8 are different, reason to be cautious.
So dividing x by half, we have:
x ÷ 1/2 = x × 2/1 = 2x.
- Now, what we have is
2x + x = 6
Solving this equation, we can obtain the value of x.
2x + x = 6
3x = 6
Dividing both sides by 3
3x/3 = 6/3
x = 2.
Therefore, the solution to the word problem is x = 2.
Answer:
The equation's result: 32,000 (Rounded)
Goal: Find the closest or equivalent result in another expression
Step-by-step explanation:
<h3>A)</h3>
How we got to 31,636 was by dividing from left to right.
Remember: When dividing decimals, it's like multiplying whole numbers in a way. The number(the quotient, also) ends up bigger instead of being smaller like when dividing whole numbers. If you multiply decimals, they(the product) end up smaller.
Therefore, A is the correct answer.
Answer:
Q1: $1.2 Q2: 5 pens
Step-by-step explanation:
