Answer:
Sometimes
Step-by-step explanation:
I’ll give you an example so you can understand:
Let’s say x is 4. So plug 4 into the problem:
|4|=4 → This is a very true statement, where the absolute value of 4 is equal to 4.
Now, let’s say x is -7. So plug -7 into the problem:
|-7|=-7 → This is a false statement because it’s saying that the absolute value of -7 is -7 which is very untrue.
So |x|=x only works for positive numbers, but not negative numbers. Therefore, |x|=x is the absolute value of x <u>sometimes.</u>
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Hope this helps and answers your question! :)
Answer:
49/8 is the value of k
Step-by-step explanation:
We have the system
x = -2y^2 - 3y + 5
x=k
We want to find k such that the system intersects once.
If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.
This equation has one solution when it's discriminant is 0.
Let's first rewrite the equation in standard form.
Subtracting k on both sides gives
0=-2y^2-3y+5-k
The discriminant can be found by evaluating
b^2-4ac.
Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that
a=-2, b=-3, and c=5-k.
So we want to solve the following equation for k:
(-3)^2-4(-2)(5-k)=0
9+8(5-k)=0
Distribute:
9+40-8k=0
49-8k=0
Add 8k on both sides:
49=8k
Divide both sides by 8"
49/8=k
