First distribute 1/2 into (9-2x) which would give you:
4.5-1x= x+1
then you add 1x to each side and you will get:
4.5=2x+1
then you subtract 1 from each side and you will get:
3.5=2x
finally divide 3.5 by 2 and you will get:
x = 1.75
Hope this helps
I don't usually do calculus on Brainly and I'm pretty rusty but this looked interesting.
We have to turn K into the limits of integration on our integrals.
Clearly 0 is the lower limit for all three of x, y and z.
Now we have to incorporate
x+y+z ≤ 1
Let's do the outer integral over x. It can go the full range from 0 to 1 without violating the constraint. So the upper limit on the outer integral is 1.
Next integral is over y. y ≤ 1-x-z. We haven't worried about z yet; we have to conservatively consider it zero here for the full range of y. So the upper limit on the middle integration is 1-x, the maximum possible value of y given x.
Similarly the inner integral goes from z=0 to z=1-x-y
We've transformed our integral into the more tractable

For the inner integral we get to treat x like a constant.

Let's expand that as a polynomial in y for the next integration,

The middle integration is



Expanding, that's

so our outer integral is

That one's easy enough that we can skip some steps; we'll integrate and plug in x=1 at the same time for our answer (the x=0 part doesn't contribute).


That's a surprise. You might want to check it.
Answer: 0
Answer:
$37.00
Step-by-step explanation:
Tickets:
4 friends, each ticket costs $8
4*8=32
$32
Sodas:
4 friends, each soda costs $3.75
4*3.75=15
$15
Total:
tickets + sodas
32+15=47
$47
Coupons:
2 friends each had a coupon for $5 off
2*5=10
$10 discount
Grand Total:
total-discount
47-10=37
$37.00
Answer:
(0, -1)
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.
Hence for parallelogram RSTU, RS // TU and RU // ST
Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:
Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5
Slope of ST = (2 - 4) /[6 - 3] = -2/3
Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)
Slope of TU = (y - 2) /[x - 6]
Slope of RU = Slope of ST
(y - 1) / (x + 3) = -2/3
3y - 3 = -2x -6
2x + 3y = -6 + 3
2x + 3y = -3 (1)
Slope of RS = Slope of TU
0.5 = (y - 2) /[x - 6]
0.5x - 3 = y - 2
0.5x - y = 1 (2)
Solving 1 and 2 simultaneously gives:
x = 0, y = -1
Therefore the coordinates of U = (0, -1)