Y=x^2+3x+4
y-x=7
x^2+3x+4-x=7
x^2+2x+4=7
(factor) x^2+2x-3=0
(x+3)(x-1)=0
X= -3 and X=1
(Plug x in for y)
Y= 1^2+3(1)+4
Y=8
(Check your answer on the second equation)
8-1=7
7=7 (Which is the solution)
Answer:
B
Step-by-step explanation:
From what we have here;
if a implies b and b implies c
It simply means that we have a implying c
the correct representation here is given in the second option
And thus, we have it that;
a => c
Since T is the midpoint of PQ, this means that PT and TQ must be equal to each other. Make them equal to each other in an equation.
PT = TQ
4x + 2 = 7x - 7
- Subtract 2 from both sides.
4x = 7x - 9
- Subtract 7x from both sides.
-3x = -9
<u>x = 3</u>
- Now substitute 3 for x into PT.
PT = 4(3) + 2
<h3>PT = 14</h3>
Answer:
$180000
Step-by-step explanation:
Let's c be the number of chair and d be the number of desks.
The constraint functions:
- Unit of wood available 4d + 3c <= 2000 or d <= 500 - 0.75c
- Number of chairs being at least twice of desks c >= 2d or d <= 0.5c
c >= 0
d >= 0
The objective function is to maximize the profit function
P (c,d) = 400d + 250c
We draw the 2 constraint functions (500 - 0.75c and 0.5c) on a c-d coordinates (witch c being the horizontal axis and d being the vertical axis) and find the intersection point 0.5c = 500 - 0.75c
1.25c = 500
c = 400 and d = 0.5c = 200 so P(400, 200) = $250*400 + $400*200 = $180,000
The 500 - 0.75c intersect with c-axis at d = 0 and c = 500 / 0.75 = 666 and P(666,0) = 666*250 = $166,500
So based on the available zones in the chart we can conclude that the maximum profit we can get is $180000
Z - (-9) is the same as z + 9. Subtracting a negative is the same as adding.
Therefore
17 = z - (-9)
is the same as
17 = z + 9
To get 'z' all by itself, we need to subtract 9 from both sides. We subtract 9 from both sides to undo the "plus 9" occurring to the 'z' on the right side.
17 = z + 9
17-9 = z + 9=9 ... subtracting 9 from both sides
8 = z
z = 8
So the answer is z = 8
---------------------------
Check:
17 = z - (-9)
17 = 8 - (-9) ... replace z with 8
17 = 8 + 9
17 = 17
Answer checks out
