Answer: 4 ounces
Step-by-step explanation:
6 * (2/3) = 12/3 = 4 ounces
Answer:
28. 120 degrees
29. 30 degrees
30. 56 degrees & 124 degrees
31. 72 degrees, 108 degrees, and 18 degrees
Step-by-step explanation:
We assign variable x for the answer we are looking for (28-29).
28.
Supplement means x + y = 180 degrees. We also know x = 2y. Substitution gives us 3y = 180 degrees, so y = 60 degrees and x = 120 degrees.
29.
Complement means x + y = 90 degrees. We are given 2x = y. Substitution brings us 3x = 90 degrees, x = 30 degrees.
30.
Supplement means x + y = 180 degrees. We are told that y = 2x + 12, so we substitute. This gives 3x + 12 = 180 degrees, x = 56 degrees. Substituting that back into the equation for y, we get 124 degrees.
31.
Supplement means x + y = 180 degrees. Complement means x + z = 90 degrees. Using our given info, we know y = 6z. We can substitute that in to get x + 6z = 180. Subtracting our second and third equations, we get 5z = 90, z = 18 degrees. Therefore, x = 72 degrees, y = 108 degrees.
So what we have to do to solve this problem is to write down those values in 2 equations (one that represents what you sold and the other what your friend sold) compare them and find how much each ticket is worth.
First equation : 11x + 8y = 158
Where x = how much each adult ticket is
and y = how much each student ticket is
The second equation is : 5x + 17y = 152
Using the method of substitution , we can compare each equation side by side:
11x + 8y = 158
5x + 17y = 152
Now we need to set one of the variables of both equations so they are equal:
11(5)x + 8(5) = 158(5)
5(11)x + 17(11)x = 152(11)
55x + 40y = 790
55x + 187y = 1672
Then we subtract the second equation by the first one
55x-55x + 187y - 40y = 1672 - 790
147y = 882
y = 6
The we apply y to one of the equations to discover x :
11x + 8y = 158
11x + 8(6) = 158
11x + 48 = 158
11x = 110
x = 10
So the awnser is :
Each adult ticket (x) is $10
And each student ticket (y) is $8
I hope you understood my explanation,
At the start, the tank contains
(0.25 lb/gal) * (100 gal) = 25 lb
of sugar. Let
be the amount of sugar in the tank at time
. Then
.
Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

Separate variables, integrate, and solve for <em>S</em>.







Use the initial value to solve for <em>C</em> :


The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

has passed. At this time, we want the tank to contain
(0.5 lb/gal) * (5 gal) = 2.5 lb
of sugar, so we pick <em>P</em> such that

Answer:
The equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x=-5
Option A is correct.
Step-by-step explanation:
We need to find equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4)
We need a line parallel to x=-2 or x+2=0 it should be of form x+k=0
We need to find k, by putting value of x=-5 as given in question the point(-5,4)
-5+k=0
k=5
So, the equation of line will be found by putting k=5:
x+k=0
x+5=0
x=-5
So, the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x=-5
Option A is correct.