Find the maximum value of x+y given thatx>=-3
y>=5x-9
3x+y<=15

Answers

Answer 1

Answer: x ≥ -3
y ≥ 5x - 9
3x + y ≤ 15

3(-3) + (5x - 9) ≤ 15
    -9 + (5x - 9) ≤ 15
    (-9 - 9) + 5x ≤ 15
   -18 + 5x ≤ 15
   + 18    + 18
   5x ≤ 33
      5 5
   x ≤ 6.6
     y ≤ 5(6.6) - 9
   y ≤ 33 - 9
   y ≤ 24
   (x, y) ≤ (6.6, 24)

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Find the equations of the vertical asymptotes of the given rational function f(x)=(x²+9x)(x²-2x-15)

Answers

To find the vertical asymptotic equations of the rational function, we must first find the points of intersection of the function with the x-axis. These points are the solutions of the equation f(x) = 0. We decompose the exponential function into the product of two expressions: f(x) = (x² + 9x)(x² - 2x - 15) Now we can set each of the expressions inside the parentheses equal to zero and solve the vertical asymptotic equations: x² + 9x = 0 or x² - 2x - 15 = 0 To solve the first equation, we can factor x out: x(x + 9) = 0 So the two vertical asymptote equations are x = 0 and x + 9 = 0 (that is, x = -9). To solve the second equation, we can use the analysis method or the quadratic formula. Using the analysis method, we can decompose the expression x² - 2x - 15 in the following form: (x - 5)(x + 3) = 0 Therefore, two vertical asymptote equations equal to x - 5 = 0 (that is, x = 5) and x + 3 = 0 (that is, x = -3). So the vertical asymptotic equations of the rational function f(x) = (x² + 9x)(x² - 2x - 15) are equal to x = 0, x = -9, x = 5 and x = -3.

What is the least common denominator of 3/20 and 8/15?
A.30
B.20
C.5
D.60

Answers

5 since both numbers are divisible by 5 and not by any smaller number

The least common denominator is 5.
This is because all of the other numbers are not divisible by the denominators; they are either greater than one of them or not divisible.

Twenty percent of 150 is

Answers

20% of 150 is 30

Change the percentage into a decimal by dividing it over 100:

20 / 100 = 0.2

Multiply:

0.2 × 150 = 30

Answer: 30

Step-by-step explanation:

Is it possible for an event to have a probability of 1? Explain.

Answers

An event that is certain to happen has a probability of 1(So yes an event can have a probability of 1).
An event that cannot possibly happen has a probability of zero. (examples below)
--If it is Thursday, the probability that tomorrow is Friday is certain, therefore the probability is 1.
--If you are sixteen, the probability of you turning seventeen on your next birthday is 1. It's a certain event.

Mr ramirez bought 1/4 pounds of cashews he divided the cashews equally with 3 childern. how many cashews did each children get