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nalin [4]
2 years ago
12

Which expression correctly represents the perimeter of a rectangle that is 12 centimeters long and 7 centimeters wide?

Mathematics
1 answer:
Goryan [66]2 years ago
3 0

Answer:

The expression for the perimeter of the rectangle is:

P = 2*(12 cm) + 2*(7 cm)

And the perimeter is:

P = 38cm

Step-by-step explanation:

We know that for a rectangle of length L and width W, the perimeter is given by:

P = 2*L + 2*W

So, if we have a rectangle that is 12 cm long,  we have L = 12cm

and if the rectangle is 7cm wide, we have W = 7cm

Now we can replace these in the perimeter equation to get:

P = 2*(12 cm) + 2*(7 cm)

P = 24cm + 14cm

P = 38cm

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The table includes points on a quadratic function used to model the shape of a hole for one support beam at a new building site.
erastovalidia [21]

The hole is 8 feet deep at ground level ⇒ 3rd answer

Step-by-step explanation:

The form of the quadratic function is y = ax² + bx + c, where

  • a is the coefficient of x²
  • b is the coefficient of x
  • c is the y-intercept (at x = 0)

The vertex point of the quadratic is (h , k), where h=\frac{-b}{2a}

and k is the value of y when x = h

The table:

→  x  :  -2   ,  0  ,  2

→  y  :  -6   , -8  ,  -6

∵ x represents distance from hole's center in feet

∵ y represents the depth from level ground

∴ The quadratic function is y = ax² + bx + c

∵ c is the value of y at x = 0 ⇒ y-intercept

- From the table at x = 0 ⇒ y = -8

∴ c = -8

- Substitute its value in the function model

∴ y = ax² + bx - 8

- To find the values of a and b substitute x and y in the model by

   the coordinates of the point in the table

∵ x = -2 and y = -6

∴ -6 = a(-2)² + b(-2) - 8

∴ -6 = 4a - 2b - 8

- Add 8 to both sides

∴ 2 = 4a - 2b

- Switch the two sides

∴ 4a - 2b = 2 ⇒ (1)

∵ x = 2 and y = -6

∴ -6 = a(2)² + b(2) - 8

∴ -6 = 4a + 2b - 8

- Add 8 to both sides

∴ 2 = 4a + 2b

- Switch the two sides

∴ 4a + 2b = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equations(1) and (2) to eliminate b

∵ 8a = 4

- Divide both sides by 8

∴ a = 0.5

- Substitute value of a in equation (1) or to to find b

∵ 4(0.5) + 2b = 2

∴ 2 + 2b = 2

- Subtract 2 from both sides

∴ 2b = 0

- Divide both sides by 2

∴ b = 0

Substitute the values of a and b in the function model

∴ y = 0.5x² + (0)x - 8

∴ y = 0.5x² - 8

∵ y represents the depth from level ground

∵ The vertex of the function model is (h , k)

∴ The deep of the hole at ground level is the value of k

∵ h=\frac{-b}{2a}

∴ h=\frac{-(0)}{2(0.5)}

∴ h = 0

∵ k is the value of y when x = h

- From the table at x = 0 ⇒ y = -8

∴ k = -8

- Ignore the sign (-) because the k represents the depth of the

  hole in feet

∴ The deep of the hole at ground level is 8 feet

The hole is 8 feet deep at ground level

Learn more:

You can learn more about the quadratic function in brainly.com/question/1332667

#LearnwithBrainly

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If the average of x and y is 11 and the average of x, y and z is 5, then the value of z is -7

Given,

The average of x and y = 11

We know average = Sum of the terms / Number of terms

Then, the equation will become

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x+y =22

Average of x, y and z = 5

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x+y+z = 5×3

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Substitute the value of x+y

22+z=15

z =15-22

x = -7

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