Answer:
b
Step-by-step explanation:
Standard form =
ax + by = c
y = -5x + 3
Add 5x to both sides.
5x + y = 3
And this is your answer.
You need to fill the cup up 4 times since there are 4 cups in a quart.
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
Given:
Original or base : 40
New amount : 72
We need to find the difference of the new amount and the original amount
72 - 40 = 32
We then divide the difference by the original amount
32/40 = 0.80
We multiply the quotient by 100%
0.80 x 100% = 80%
The percentage of change is 80%
