5 cm 7 cm 15 cm What is th5 surface area of the figure?

A stand is a frustum shape, formed by removing a small square-based pyramid from the top of

kupik [55]

The frustum can be considered as consisting of a square pyramid, less the

cut volume.

The mass of the stand, is approximately 18.60905 kg

Reasons:

The given parameter of the frustum are;

The density of the frustum, ρ = 85 g/cm³

Height of pyramid, h = 9 cm

Side length of base = 10 cm

Height of frustum

By proportional shapes, the side length of the top of the frustum can be found as follows;

$\dfrac{4 \, cm}{9 \, cm} = \dfrac{x}{10 \, cm}$

$x = \dfrac{4 \, cm}{9 \, cm} \times 10 \, cm = 4\frac{4}{9} \, cm$

$V = \dfrac{h}{3} \times \left(B_1 + B_2 + \sqrt{B_1 \times B_2} \right)$

B₁ = 10², B₂ = $\left(4\frac{4}{9} \right)^2$

Therefore;

$V = \dfrac{4}{3} \times \left(10^2 + \left(4\frac{4}{9} \right)^2 + \sqrt{10^2 \times \left(4\frac{4}{9} \right)^2} \right) \approx 218.93$

The volume of the stand, V ≈ 218.93 cm³

Mass = Volume × Density

∴ Mass of the stand, m = 218.93 cm³ × 85 g/cm³ = 18,609.05 grams = 18.60905 kg.

Learn more here:

brainly.com/question/24323975

8 0

3 years ago

Solve the following linear system by graphing 4x+5y=10 3x-3y=21

Inga [223]

Answer:

y = 2

x = 5

Step-by-step explanation:

4x + 5y = 10 | ×3 |

3x - 3y = 21 | ×4 |

12x + 15y = 30

12x - 12y = 84

____________--

27y = -54

y = -54/27

y = 2

4x + 5y = 10 | ×3 |

3x - 3y = 21 | ×5 |

12x + 15y = 30

15x - 15y = 105

____________+

27x = 135

x = 135/27

x = 5

6 0

3 years ago

Will give brainless if solved

wel

Answer:

1. 70 2. 85 3. 63 4. 20 5. They are vertical angles

Step-by-step explanation:

6 0

3 years ago

(1/27)^x-6=27 Could I please have a step by step as well? Much appreciated!

Andrei [34K]

Answer:

$x = 7$

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

$\frac{1}{ {27}^{x - 8} } = 27$

2) Multiply both sides by 27^x - 8.

$1 = {27} \times 27^{1 + x - 8}$

3) Use the product rule: x^a x^b = x^a+b.

$1 = {27}^{1 + x - 8}$

4) Simplify 1 + x - 8 to x - 7.

$1 = {27}^{x - 7}$

5) Use Definition of Common Logarithm: b^a = x if and only if logb (x) = a.

$log_{27}1 = x - 7$

6) Use Change of Base Rule.

$\frac{ log_1 }{ log{27} } = x - 7$

7) Use rule of 1: log 1 = 0.

$\frac{0}{ log_{27}} = x - 7$

8) Simplify 0/log_27 to 0.

$0 = x - 7$

9) Add 7 to both sides.

$7 = x$

10) Switch sides.

$x = 7$

Therefor, the answer is x = 7.

5 0

3 years ago

Which of the following is not a true statement about pi?

FinnZ [79.3K]

Answer:

Option D.The ratio of the radius of a circle to its circumference

Step-by-step explanation:

Verify each statement

A) The ratio of the circumference of a circle to its diameter

The statement is True

Because

$C=\pi D$

so

$\pi=C/D$

B) Approximated to be 3.14

The statement is True

Because $\pi=3.14159265...$

C) Approximated to be 22/7

The statement is True

Because

$\frac{22}{7}=3.1423$

D) The ratio of the radius of a circle to its circumference

The statement is not True

Because

$\frac{r}{2\pi r}=\frac{1}{2\pi}$

4 0

3 years ago

5 cm 7 cm 15 cm What is th5 surface area of the figure? _square centimeters