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1 year ago

Find the surface area of the composite figure.

Mathematics

1 answer:

Sloan [31]1 year ago

7 0

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

<h3>What is the surface area of a truncated prism?</h3>

The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:

A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)

A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²

A = 276 cm²

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Simplify the rational Expression

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Answer:

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Step-by-step explanation:

We need to factor out numerator and denominator in order to simplify the rational expression by cancelling common factors.

Numerator : x^3 - 4 x = x (x^2 - 4) = x (x - 2) (x + 2)

Denominator (factoring by grouping):

x^2 - 5 x + 6 = x^2 - 3 x - 2 x + 6 = x (x - 3) - 2 (x - 3) = (x - 3) (x - 2)

Then we can cancel out the common factor (x - 2) in both numerator and denominator, leading to:

x (x + 2) / (x - 3) = (x^2 + 2)/ (x-3)

$\frac{x^2+2x}{x-3}$

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9,899 = 206x
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My using the equation, we can see that he is correct.

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3 years ago

Please helpp . What is the area of the blue figure? *

antiseptic1488 [7]

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465.5

Step-by-step explanation:

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3 years ago

Read 2 more answers

Tony is training to run a marathon. He has already run 2 miles today and is running additional miles at 6 miles per hour. Write

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4 years ago

Triangle X Y Z is cut by line segment C D. Line segment C D goes from side X Y to side Y Z. The length of C D is 15, the length

Marizza181 [45]

The length of DZ is 4 units ⇒ 3rd answer

Step-by-step explanation:

Triangle X Y Z is cut by line segment C D, where

C lies on side XY and D lies on the side YZ
The length of C D is 15
The length of X Z is 18
The length of C Y is 25
The length of Y D is 20
C D and X Z are parallel
CX = 5 units

We need to find the length of DZ

In Δ XYZ

∵ C ∈ XY and D ∈ YZ

∵ CD // XZ

∴ m∠YCD = m∠YXZ ⇒ alternate angles

∴ m∠YDC = m∠YZX ⇒ alternate angles

In Δs YCD and YXZ

∵ m∠YCD = m∠YXZ

∵ m∠YDC = m∠YZX

∵ ∠Y is a common angle

∴ Δ YCD is similar to Δ YXZ by AAA postulate

- There is a constant ratio between their corresponding sides

∴ $\frac{YC}{YX}=\frac{CD}{XZ}=\frac{YD}{YZ}$

∵ YC = 25 units

∵ CX = 5 units

∵ YX = YC + CX

∴ YX = 25 + 5 = 30 units

∵ YD = 20 units

∵ YZ = YD + DZ

∴ YZ = 20 + DZ

Let us use the ratio of the corresponding side

∵ $\frac{YC}{YX}=\frac{YD}{YZ}$

∴ $\frac{25}{30}=\frac{20}{20+DZ}$

- Simplify $\frac{25}{30}$ by dividing up and down by 5

∵ $\frac{25}{30}=\frac{5}{6}$

∴ $\frac{5}{6}=\frac{20}{20+DZ}$

- By using cross multiplication

∴ 5(20 + DZ) = 6(20)

∴ 100 + 5 DZ = 120

- Subtract 100 from both sides

∴ 5 DZ = 20

- Divide both sides by 5

∴ DZ = 4 units

The length of DZ is 4 units

Learn more:

You can learn more about triangles in brainly.com/question/3202836

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