Answer:
We have the system of equations:
y = -2*x
y = 2*x + 4.
To solve it by graphing, you need to graph both lines and see in which point the lines intersect each other.
You can see it in the image below. (blue is y = 2*x + 4, and green is y = -2*x)
We also can calculate the solution with math, let's do that:
y = -2*x
y = 2*x + 4.
We can replace the first equation in the second one, to get:
-2*x = 2*x + 4
Now let's solve this for x
-2*x -2*x = 4
-4*x = 4
x = 4/-4 = -1
Evaluating this in one of the equations we get:
y = -2*-1 = 2
Then the solution is the point (-1, 2), exactly what we can see in the graph.
We can see a right triangle here.
Diagonal is a hypotenuse of the right triangle. Two legs are equal 102 yards each.
We can use Pythagorean theorem
hypotenuse² = leg² + leg² = 2leg²
hypotenuse² = 2leg²
√hypotenuse² = √(2leg²)
hypotenuse = leg*√2
hypotenuse = 102*√2≈144.25 yards
the diagonal ≈144.25 yards
Answer:
Step-by-step explanation:
Natsano can satisfy his constraints by investing the first $20,000 in Company A, then splitting the remaining $35,000 evenly between the companies. For best return, he needs to invest as much as possible in Company B, but each such dollar (after the first 20k) must be matched by a dollar invested in Company A. That is, his investments should be ...
- Company A: $37,500
- Company B: $17,500
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The attached graph shows the feasible region of investments (doubly shaded). The vertex that maximizes the objective function (return on investment) is the one highlighted. (It puts the objective function line as far as possible from the origin.)
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Sometimes graphing the constraints is more work than necessary if there is some simple logic that quickly identifies the solution.
Answer:972
Step-by-step explanation:
Divide both numbers by 972 and they both go into each other
Look to the right of the number with the line under it. If it is 5 or up then the number with the line goes up by one.
