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podryga [215]
3 years ago
8

Sarah has a solid wooden cube with a length of 4/5 centimeter. From each of its 8 corners, she cuts out a smaller cube with a le

ngth of 1/5centimeter. What is the volume of the block after cutting out the smaller cubes?
Mathematics
1 answer:
kobusy [5.1K]3 years ago
5 1
The answer would be the first one and the fourth one.
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F(x)=2x-4. F(x)=2x-4 f-1x=_x+_. Complete the inverse function
natita [175]

Answer:

f^{-1}(x) = \frac{1}{2}(x +4)

Step-by-step explanation:

Given

f(x) = 2x - 4

Required

Determine the inverse function

Start by replacing f(x) with y

y = 2x - 4

Swap the positions of y and x

x = 2y - 4

Make y the subject: <em>Add 4 to both sides</em>

x+4 = 2y - 4+4

x+4 = 2y

Make y the subject: <em>Divide through by 2</em>

<em></em>\frac{1}{2}(x + 4) = y<em></em>

<em></em>y = \frac{1}{2}(x + 4)<em></em>

<em></em>

Replace y with f-1(x)

f^{-1}(x) = \frac{1}{2}(x +4)

3 0
2 years ago
What is the exact area and circumference?
Rudik [331]

Answer:

Step-by-step explanation:

The area of a circle is calculated using the formula: πr^2

The circumference of a circle is calculated using: 2πr

We are given 8 questions, So by addressing them individually

1) Area of Circle 1:

Radius = r = 12 mi

Total angle in a circle = 360°

Given angle = 90

Ratio of given circle to complete circle = 90/360

=> 1/4

Therefore, the circle 1 is 1/4 of the complete circle with r = 12.

In this way, its area will be 1/4 of the complete circle.

Hence

Area = 1/4 (πr^2)

=> 1/4 (π*12^2 )

=> 1/4 (144π)

=> 36π   Hence option C

2) Area of Circle 2:

Radius = r = 19 in

Total angle in a circle = 360°

Given angle = 315

Ratio of given circle to complete circle = 315/360

=> 7/8

Therefore, the circle 2 is 7/8 of the complete circle with r = 19.

In this way, its area will be 7/8 of the complete circle.

Hence

Area = 7/8 (πr^2)

=> 7/8 (π*19^2 )

=> 7/8 (361π)

=> 315.8π   Hence answer is not provided that is option f

3) Area of Circle 3:

Radius = r = 15 km

Total angle in a circle = 360°

Given angle = 270

Ratio of given circle to complete circle = 270/360

=> 3/4

Therefore, the circle 3 is 3/4 of the complete circle with r = 15.

In this way, its area will be 3/4 of the complete circle.

Hence

Area = 3/4 (πr^2)

=> 3/4 (π*15^2 )

=> 3/4 (225π)

=> 168.75π   Hence answer is not provided that is option f

4) Area of Circle 4:

Radius = r = 6 km

Total angle in a circle = 360°

Given angle = 270

Ratio of given circle to complete circle = 90/360

=> 3/4

Therefore, the circle 4 is 3/4 of the complete circle with r = 6.

In this way, its area will be 3/4 of the complete circle.

Hence

Area = 3/4 (πr^2)

=> 3/4 (π*6^2 )

=> 3/4 (36π)

=> 27π   Hence answer is not provided that is option f

5) Circumference of Circle 1:

Radius = r = 12 mi

Total angle in a circle = 360°

Given angle = 90

Ratio of given circle to complete circle = 90/360

=> 1/4

Therefore, the circle 1 is 1/4 of the complete circle with r = 12.

In this way, its circumference will be 1/4 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.

Hence

Circumference = 1/4 (2πr) + 2r

=> 1/4 (2π12) + 2*12

=> 1/4 (24π) + 24

=> 6π + 24 Hence answer is not provided that is option f

6) Circumference of Circle 2:

Radius = r = 19 in

Total angle in a circle = 360°

Given angle = 315

Ratio of given circle to complete circle = 315/360

=> 7/8

Therefore, the circle 2 is 7/8 of the complete circle with r = 19.

In this way, its circumference will be 7/8 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.

Hence

Circumference = 7/8 (2πr) + 2r

=> 7/8 (2π19) + 2*19

=> 7/8 (38π) + 38

=> 33.25π + 38 Hence answer is not provided that is option f

7) Circumference of Circle 3:

Radius = r = 15 km

Total angle in a circle = 360°

Given angle = 270

Ratio of given circle to complete circle = 270/360

=> 3/4

Therefore, the circle 3 is 3/4 of the complete circle with r = 15.

In this way, its circumference will be 3/4 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.

Hence

Circumference = 3/4 (2πr) + 2r

=> 3/4 (2π19) + 2*15

=> 3/4 (38π) + 38

=> 28.5π + 38 Hence answer is not provided that is option f

8) Circumference of Circle 4:

Radius = r = 6 km

Total angle in a circle = 360°

Given angle = 270

Ratio of given circle to complete circle = 270/360

=> 3/4

Therefore, the circle 3 is 3/4 of the complete circle with r = 6.

In this way, its circumference will be 3/4 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.

Hence

Circumference = 3/4 (2πr) + 2r

=> 3/4 (2π6) + 2*6

=> 3/4 (12π) + 12

=> 9π + 12 Hence answer is not provided that is option f

6 0
3 years ago
Answer asap please will mark as brainlist
Leona [35]

Answer:

Exact Form:

√ 30

Decimal Form:

5.47722557 …

Step-by-step explanation: i would go with D

6 0
3 years ago
Solve and type in a different form by using the given theorems of logarithms
scoray [572]

\log\left(\frac{10}{y}\right) = \log(10) - \log(y)

The general rule is

\log\left(\frac{A}{B}\right) = \log(A) - \log(B)

Other log rules are

\log(AB) = \log(A) + \log(B)

B\log(A) = \log(A^B)

4 0
3 years ago
Which of the following is a solution to the inequality 3x-y&lt;5
Ne4ueva [31]

Answer:

not possible

Step-by-step explanation:

they are all greater than 5

7 0
2 years ago
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