11a. I can't show the workings because I don't have pie on my keyboard. am so sorry but number 11a's answer is 6
11b = 10
Answer:
x = 5
Step-by-step explanation:
A quadratic equation:
f(x) = y = a*x^2 + b*x + c
Has a vertex in a point:
(h, k) such that:
h = -b/2a
and:
k = f(-b/2a)
And the axis of symmetry (this is the line that cuts the graph in two halves) is:
x = h.
In this case, the vertex is (5, -6)
Then the axis of symmetry is:
x = 5.
Answer:
Step-by-step explanation:
2x + z = 9.....z = -2x + 9
so we r gonna sub in -2x + 9 for z in our other 2 equations
3x + 2y + z = 9 -3x - y + 3z = -7
3x + 2y + (-2x + 9) = 9 -3x - y + 3(-2x + 9) = -7
3x + 2y - 2x + 9 = 9 -3x - y - 6x + 27 = -7
x + 2y = 9 - 9 - 9x - y = -7 - 27
x + 2y = 0 -9x - y = - 34
now we take our results and eliminate a variable
x + 2y = 0
-9x - y = -34.....multiply by 2
-------------------
x + 2y = 0
-18x - 2y = - 68 (result of multiplying by 2)
------------------add
-17x = -68
x = -68/-17
x = 4
now we sub 4 in for x in either of our resulting equations
x + 2y = 0
4 + 2y = 0
2y = 0 - 4
2y = -4
y = -4/2
y = -2
now that we know x and y, sub these values in to any of the original equations to find z
z = -2x + 9
z = -2(4) + 9
z = -8 + 9
z = 1
check it...
3x + 2y + z = 9
3(4) + 2(-2) + 1 = 9
12 - 4 + 1 = 9
8 + 1 = 9
9 = 9 (correct)...and it checks out
solution is : (4,-2,1) <====
Answer:
2 left out, with 333 boxes
Step-by-step explanation:
2000/6=333.333333 ()
of 6 is 2. Therefore, there would be 333 boxes, with two left unboxed.
9514 1404 393
Answer:
- 246 products in year 5
- 2017 products over 5 years
Step-by-step explanation:
The n-th term of the geometric series is ...
an = a1(r^(n-1))
for first term a1 and common ratio r. The common ratio here is the growth factor: 1 -20% = 0.8. This means the 5th term (5th year sales) will be ...
a5 = 600(0.8^(5-1)) ≈ 246 . . . . . products sold in year 5
The sum is given by ...
sn = a1(1 -r^n)/(1 -r) = 600(1 -0.8^5)/(1-0.8) = 2017
The company will have sold about 2017 products over 5 years.