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
Answer:
1/4
Step-by-step explanation:
rise: 1, run: 4
Answer:
13
Step-by-step explanation:
Given number = -48
Listing out the possible factors of -48 in pairs along with their difference:
Factors (
) Difference (
) Difference (
)
-26 26
26 -26
-19 19
19 -19
-16 16
16 -16
-14 14
14 -14
On listing out the factors we find out that two of the pairs have difference = 19
The pairs are 
and 
It is given that the factor with greater absolute value is positive. This means 16 would be positive while 3 would be negative.
So, our factors are
The sum of the factors is = 
(Answer)
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