For y=ax²+bx+c
if a>0 then it opens up
if a<0 then it opens down
hmm, y intercept is where x=0
x intercept is where y=0
so
f(x)=3x²+4x+16
3>0 so opens up
y intercep
x=0
3(0)²+4(0)+16
16
y intercept is y=16
x intercept
0=f(x)=3x²+4x+16
there are no real solutions since the discriminant is negative
no x intercepts or no zeroes
so
opens up
y intercept of 16
no zeroes
Answer:
The company can manufacture 135 boxes of stuffed animals for $5000
Step-by-step explanation:
To find b, substitute $5000 for c(x), so
Then subtract 2300 from both sides of the equation, so
- 5000 (-2300) = 20b + 2300 (-2300)
- 2700 = 20b
Finally divide both sides of the equation by 20, so
To check your answer substitute 135 in as b...
- c(x) = 20(135) + 2300
- c(x) = 5000
<u>Answer:</u>
There are infinite solutions to the system of equations given
<u>Solution:
</u>
The given equations given are,
------ (i)
---- (ii)
Now putting the value of (i) in (ii) we get,





So, there are <em>infinite solutions</em> to the system.
1. Let x be a length of square side, then the square perimeter is 4x (you need to cut 4x from 16 in. to make a square with side x in.). Then 16-4x is remained length of wire and you have to make form this piece a rectangle with sides one of which is twice bigger than another. If y is length of the smaller side, then 2y is length of the bigger side and rectangle perimeter is y+2y+y+2y=6y. You have 16-4x in. of wire left, so 6y=16-4x and

.
2.

.
3. Find the derivative of the function A(x):

.
4. Solve the equation A'(x)=0:

5. Since

you have

.
Answer: <span>the width of the rectangle is

</span>