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3 years ago

What is the surface area of a square pyramid with a height of 12 mm and a base that measures 8 mm on each side?

Mathematics

1 answer:

Nostrana [21]3 years ago

8 0

Answer:

266.39mm²

Step-by-step explanation:

The formula for surface area of a square based pyramid =

S.A = a² + 2a √a²/4 + h²

Where

a = base length = 8mm

s = Height of the pyramid = 12mm

Hence,

S.A = 8² + 2 × 8 × √8²/4 + 12²

S.A = 64 + 16 ×√64/4 + 144

S.A = 80 × √16 + 144

S.A = 80 × √160

S.A = 266.39 mm²

Therefore, the surface area of a square pyramid is 266.39 mm²

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Solve the following system of equations algebraically:<br> y = x2 - 6x + 9<br> y = -9x + 19

Ratling [72]

{(-5,64), (2,1)}

linear equation: y = -9x + 19
quadratic equation: y = x² - 6x + 9

Substitute the y in the quadratic equation by the its value in the linear equation.

-9x + 19 = x² - 6x + 9
      - 19    - 19 *subtract 19 to both sides
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+9x + 9x *add 9x to both sides
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Set each factor = 0 and solve
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Find the corresponding value of y using the linear equation.
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x = -5 x = 2
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(-5,64) (2,1)

Check each value on each equation.
y = x² - 6x + 9
(-5,64) (2,1)
64 = (-5)² - 6(-5) + 9 1 = 2² - 6(2) + 9
64 = 25 + 30 + 9 1 = 4 - 12 + 9
64 = 64    1 = 1

y = -9x + 19
64 = -9(-5) + 19 1 = -9(2) + 19
64 = 45 + 19 1 = -18 + 19
64 = 64 1 = 1

{(-5,64), (2,1)}

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Can you help me to solve this

Ber [7]

Answer:

$\frac{4a-2}{2a+1}$

Step-by-step explanation:

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8a² - 2 ← factor out 2 from each term

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= $\frac{4a-2}{2a+1}$

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