A number is chosen at random from 1 to 25. find the probability of selecting a composite number

Answer:

hello :

the perimeter is : p = 2 ( w + l )

The area is : A= w ×l       w : width       l : length       w ?

2 ( w + l )  = 76

w ×l  = 336

you have the system :

w + l = 38 ...(1)

w ×l  = 336...(2)

by (1) : l = 38 - w

subst in (2) : w ( 38 - w ) =336

38w - w²= 336

w² - 38w +336 = 0

delta = b² -4ac     when : a = 1   and  b= -38      c = 336

delta = (-38)² -4(1)(336) = 1444 - 1344  = 100 = 10²

w1 = (38-10)/2 = 14( the shorter sides length)

w2 = (38+10)/2 = 24( refused  )

The shorter side's length of the rectangle is 24 inches. This is determined by solving the system of equations derived from the area (336 square inches) and perimeter (76 inches) constraints, resulting in a quadratic equation with two possible solutions, and the shorter side being 24 inches.

• To find the shorter side's length of a rectangle with an area of 336 square inches and a perimeter of 76 inches, we'll use a system of equations.
• Let's denote:
• Length of the rectangle as L (in inches).
• Width of the rectangle as W (in inches).
• We have two pieces of information:
• The area of the rectangle is 336 square inches:
• L * W = 336
• The perimeter of the rectangle is 76 inches:
• 2L + 2W = 76
• Now, we can solve this system of equations for L and W.
• First, isolate L in the perimeter equation:
• 2L + 2W = 76
• 2L = 76 - 2W
• L = (76 - 2W) / 2
• L = 38 - W
• Now, substitute this expression for L into the area equation:
• (38 - W) * W = 336
• Expand and rearrange the equation:
• 38W - W^2 = 336
• Move all terms to one side to create a quadratic equation:
• W^2 -
• Now, we can solve this quadratic equation for W. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:
• W = (-b ± √(b² - 4ac)) / (2a)
• Where:
• a = 1 (coefficient of W^2)
• b = -38 (coefficient of W)
• c = 336
• W = (-(-38) ± √((-38)² - 4 * 1 * 336)) / (2 * 1)
• W = (38 ± √(1444 - 1344)) / 2
• W = (38 ± √100) / 2
• W = (38 ± 10) / 2
• Now, we have two possible values for W:
• W = (38 + 10) / 2 = 48 / 2 = 24 inches (shorter side)
• W = (38 - 10) / 2 = 28 / 2 = 14 inches (longer side)
• So, the shorter side's length is 24 inches.

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Answer:

(-3,-3)

Step-by-step explanation:

I think that you meant to put 1/2x^2+3x+3/2. If so, the vertex is at point (-3,-3).

I graphed the equation down below.

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