Product means the sum of two things i.e. the product of 1 and 2 is 3 <span>(1 + 2 = 3)
So the product of 3x and (3x+1) can be written as:
35 < 3x + 3x + 1
^ Greater than 35 i.e. at least 35
35 < 6x + 1
34 < 6x
34/6 < x
17/3 < x
5.67 (2dp) < x
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The complete question is
A fence must be built to enclose a rectangular area of 5000ft^2. Fencing material costs $1 per foot for the two sides facing north and south and 2$ per foot for the other two sides. Find the cost of the least expensive fence.
Answer:
Total cost will be $400
Step-by-step explanation:
Let x = be other side
y = north and south side
Area = x*y = 5000
Perimeter of the rectangle = 2x + 2y
cost of fencing = 2(1)*5000/x + 2*2x
= 10000/x + 4x
now to get the least we will take the derivative of this
C'(x) = 10000(-1/x^2) + 4 =0
x^2 = 2500
x= 50ft cost = 2*$2*50 = $200
y= 100ft cost = 2*$1*100 = $200
Total cost = $400
Answer:
(2,4)
Step-by-step explanation:
Add the X-coordinates for both points and divide by 2
which now becomes 6+(-2)=4
Now divide 4 by 2 : 4/2 = 2
Add the Y-coordinates for both points and divide by 2
which now becomes 6+2=8
Divide 8 by 2 : 8/2 = 4
Bring the X and the Y together which becomes (2,4)
Answer:
The amount invested at 4.5% was 
The amount invested at 5% was 
Step-by-step explanation:
we know that
The simple interest formula is equal to
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x -----> the amount invested at 4.5%
9,000-x -----> the amount invested at 5%
in this problem we have
substitute
so
therefore
The amount invested at 4.5% was
The amount invested at 5% was
Even without doing the math, (and without having the requisite diagram to view), it seems likely that the rectangle was simply divided along the diagonal. And, if that's the case then the two triangles formed would have the same area. So, if one triangle's area ABC is 600 sq. yds. as the problem states, then the other triangle ACD also would be 600 sq. yds.
But if we do the math anyway, we can get the same result.
Keep in mind that:
P of rectangle = 2 ( l + w)
A of rectangle = (l x w)
A of triangle = h x b divided by 2
I'd say that the length of the rectangle is 40 and the width is 30.
P of rectangle is 2 (30 + 40) = 140 .... check
A of rectangle is 30 x 40 = 1,200 .... check
A of triangle is 30 x 40 divided by 2 = 600 ...... check
