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4 years ago

This figure is made up of a rectangle and

Mathematics

1 answer:

pishuonlain [190]4 years ago

4 0

Answer:

Area = 51 square units

Step-by-step explanation:

Area of the figure given in the attachment = Area of a parallelogram ABEF + Area of a rectangle BCDE

Area of the parallelogram = Base × Height

= AB × GE

= 4 × 3

= 12 square unit

Area of rectangle BCDE = Length × Height

= BC × CD

= $(\sqrt{9^2+6^2})\times (\sqrt{2^2+3^2} )$ [By Pythagoras theorem]

= (√117) × (√13)

= √1521

= 39 square units

Now total area of the figure = 12 + 39 = 51 units²

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Sphere with a volume of 1767.1 . what is the radius?

Llana [10]

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3 years ago

ZEFG and ZGFH are a linear pair, mZEFG = 2n + 16, and mZGFH = 3n+24. What are mZEFG and mZGFH?

liubo4ka [24]

Answer:

m<EFG = 72°

m<GFH = 108°

Step-by-step explanation:

m<EFG = 2n + 16

m<GFH = 3n + 24

Linear pairs are supplementary, therefore,

m<EFG + m<GFH = 180°

Substitute

2n + 16 + 3n + 24 = 180

Add like terms

5n + 40 = 180

5n + 40 - 40 = 180 - 40 (subtraction property of equality)

5n = 140

5n/5 = 140/5 (division property of equality)

n = 28

✔️m<EFG = 2n + 16

Plug in the value of n

m<EFG = 2(28) + 16 = 72°

✔️m<GFH = 3n + 24

Plug in the value of n

m<GFH = 3(28) + 24 = 108°

4 0

3 years ago

Which expression is equivalent to 1 4 ( 3 x + 4 y ) + 3 ( 1 4 x + 2 3 y ) ? 3 2 x + 3 y 3 halves x plus 3 y 3 2 x + 2 y 3 halves

Nat2105 [25]

Answer:

3x/2 + 3y

Step-by-step explanation:

Given the expression 1/4 ( 3x + 4y ) + 3 ( 1/4 x + 2/3 y)

Open the parentheses

= 1/4(3x) + 1/4(4y) + 3(1/4x) +3(2/3y)

= 3/4 x + y + 3/4 x +2y

Collect like terms

3/4 x +3/4 x +y+2y

6/4 x + 3y

3x/2 + 3y

Hence the correct expression is 3x/2 + 3y

8 0

3 years ago

Angle Terminology with Equations

Sergeeva-Olga [200]

Answer:

∠ B = 54°

Step-by-step explanation:

Supplementary angles sum to 180°.

Sum A and B and equate to 180, that is

7x + 14 + 5x - 26 = 180, that is

12x - 12 = 180 ( add 12 to both sides )

12x = 192 ( divide both sides by 12 )

x = 16

Thus

∠ B = 5x - 26 = 5(16) - 26 = 80 - 26 = 54°

5 0

4 years ago

Approximate the change in the volume of a sphere when its radius changes from r = 40 ft to r equals 40.05 ft (Upper V (r )equal

alexgriva [62]

Answer:

The change in the volume of a sphere whose radius changes from 40 feet to 40.05 feet is approximately 1005.310 cubic feet.

Step-by-step explanation:

The volume of the sphere ( $V$ ), measured in cubic feet, is represented by the following formula:

$V = \frac{4\pi}{3}\cdot r^{3}$

Where $r$ is the radius of the sphere, measured in feet.

The change in volume is obtained by means of definition of total difference:

$\Delta V = \frac{\partial V}{\partial r}\Delta r$

The derivative of the volume as a function of radius is:

$\frac{\partial V}{\partial r} = 4\pi \cdot r^{2}$

Then, the change in volume is expanded:

$\Delta V = 4\pi \cdot r^{2}\cdot \Delta r$

If $r = 40\,ft$ and $\Delta r = 40\,ft-40.05\,ft = 0.05\,ft$ , the change in the volume of the sphere is approximately:

$\Delta V \approx 4\pi\cdot (40\,ft)^{2}\cdot (0.05\,ft)$

$\Delta V \approx 1005.310\,ft^{3}$

The change in the volume of a sphere whose radius changes from 40 feet to 40.05 feet is approximately 1005.310 cubic feet.

7 0

3 years ago