*falls on floor crying*❤️❤️❤️❤️

Which statements are true about the lines of symmetry of a regular pentagon? Select three options

Sav [38]

Complete question is;

Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.

A) Every line connects two vertices.

B) Every line connects the midpoints of 2 sides.

C) Every line bisects a vertex angle.

D) Every line bisects a side.

E) Every line is perpendicular to a side.

Answer:

C: Every line bisects a vertex angle.

D: Every line bisects a side.

E: Every line is perpendicular to a side.

Step-by-step explanation:

A shape will have a line of symmetry when after the perpendicular line is drawn through from one vertex to the centre of one side, it can be folded and the folded part will sit perfectly on top in such a way that all the edges match.

Now, a pentagon has 5 sides and by implication from the explanation of line of symmetry above, it has 5 lines of symmetry.

Attached below is an image showing the 5 lines of symmetry of a pentagon.

From the attached image, we can see that the lines of symmetry bisects a vertex angle, it bisects a side and is perpendicular to a side.

Thus correct answer is Options C, D & E

7 0

3 years ago

A light bulb is designed by revolving the graph of:

nadya68 [22]

Answer:

$\displaystyle 0.251327 \ in. \ of \ glass$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Expand by FOIL (First Outside Inside Last)
Factoring

Calculus

Differentiation

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integration Property: $\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx$

Fundamental Theorem of Calculus: $\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)$

Area between Two Curves

Volumes of Revolution

Arc Length Formula: $\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx$

Surface Area Formula: $\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}]$

Step 2: Differentiate

Basic Power Rule: $\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}$
[Derivative] Simplify: $\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}$
[Derivative] Simplify: $\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}$

Step 3: Integrate Pt. 1

Substitute [Surface Area]: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx$
[Integral - √Radical] Expand/Add: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx$
[Integral - √Radical] Factor: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx$
[Integral - Simplify]: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx$
[Integral] Integration Property: $\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx$

Step 4: Integrate Pt. 2

[Integral] Define: $\displaystyle \int {|9x + 1|(3x - 1)} \, dx$
[Integral] Assumption of Positive/Correction Factors: $\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx$
[Integral] Expand - FOIL: $\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx$
[Integral] Integrate - Basic Power Rule: $\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)$
[Expression] Multiply: $\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}$

Step 5: Integrate Pt. 3

[Integral] Substitute/Integral - FTC: $\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}$
[Integrate] Evaluate FTC: $\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})$
[Expression] Multiply: $\displaystyle SA = \frac{\pi}{27} \ ft^2$

It is in ft² because it is given that our axis are in ft.

Step 6: Find Amount of Glass

Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.

Convert ft² to in²: $\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2$
Multiply: $\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass$