You want to know the favorite band of the 25 students in your math class. Should you survey the whole class, which is the entire population or a sample of students from the class. Explain.

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:

B) 5 and 13/15 servings

Step-by-step explanation:

Divide 8 4/5 by 1 1/2 to get 5 and 13/15

Answer:

-(x - 7)(x + 6)

Step-by-step explanation:

Step 1: Factor GCF

-1(x² - x - 42)

Step 2: Factor quadratic

-1(x - 7)(x + 6)

Answer:

C

Step-by-step explanation:

-x²+x+42

=-(x²-x-42)

[7-6=1,7×-6=-42]

=-(x²-(7-6)x-42)

=-(x²-7x+6x-42)

=-[x(x-7)+6(x-7)]

=-(x-7)(x+6)

As per linear equation, Donald can go with the given gallons of gas is 276 miles.

The total cost of the gas used is $28.98.

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. When this equation is graphed, it always results in a straight line."

Given, Donald's car gets about 30 miles per gallon.

Donald drive on 9.2 gallons of gas.

Therefore, total distance that Donald can go with the given gas is

= mileage of the car × total amount of gas

= 30 × 9.2 miles

= 276 miles

Again, cost of gas per gallon is $3.15.

The total cost

= total gallons of gas used × cost of gas per gallon

= $(9.2 × 3.15)

= $28.98

Learn more about a linear equation here: brainly.com/question/14498830

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