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:
{290,315,340, 365, 390, 415, 440, 465} That's the answer. Its hard for me to explain how i got it.
Distributive property :
a (b+c) = ab + bc
Try writing 47 = 50-3 or 47 = 40+7.
11 x 47 = 11 x (50-3) = 11 x 50 - 11 x 3 = 550 - 33 = 517
or
11 x 47 = 11 x (40+7) = 11 x 40 + 11 x 7 = 440 + 77 = 517
Answer:
38
Step-by-step explanation:
Let SUV be a triangle
Perimeter of SUV = SU+SV + UV
102 = 38 + 26 + UV
102 = 64 + UV
UV = 102 - 64
UV = 38
Hence the length of UV is 38
Answer: Rob ate more crackers.
Symbol answer: 6/12 < 9/12
Step-by-Step explanation:
Common knowledge: Anytime you have the same numerator, with a different denominator, the one with the bigger denominator is always smaller. For example, if had a pizza with 6 slices and a pizza with 4 slices, the one with 6 slices and smaller and the one with 4 slices and bigger. Even though 6>4 that mindset has to change when thinking about a problem like this.
<em>Another explanation: </em>
<em>If you still don’t get it, simply find a common denominator, so we’ll choose 12. Take 3/6 and multiply that by 2/2 so you get 6/12 and then take 3/4 and multiply that by 3/3 on both the (numerator and denominator) and that equals 9/12.</em>
<em>So now you have the expression: 6/12<9/12.</em>
