All categories

3 years ago

How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

Mathematics

1 answer:

MAVERICK [17]3 years ago

8 0

Answer: The correct option is

(E) 70.

Step-by-step explanation: We are given to find the number of triangles and quadrilaterals altogether that can be formed using the vertices of a 7-sided regular polygon.

To form a triangle, we need any 3 vertices of the 7-sided regular polygon. So, the number of triangles that can be formed is

$n_t=^7C_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}=35.$

Also, to form a quadrilateral, we need any 4 vertices of the 7-sided regular polygon. So, the number of quadrilateral that can be formed is

$n_q=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.$

Therefore, the total number of triangles and quadrilaterals is

$n=n_t+n_q=35+35=70.$

Thus, option (E) is CORRECT.

You might be interested in

Eight friends share two pizzas equally. How much of a pizza does each friend get?

My name is Ann [436]

2/8.

You take two pizzas and divide them by 8.

3 0

3 years ago

Read 2 more answers

Parabolas y=−2x^2 and y=2x^2 +k intersect at points A and B that are in the third and the fourth quadrants respectively. Find k

OverLord2011 [107]

Answer:

-25

Step-by-step explanation:

(1) y = -2x²

(2) y = 2x² + k Subtract (1) from (2)

0 = 4x² + k Subtract 4x² from each side

k = -4x²

The parabolas are <em>symmetrical about the y-axis.</em>

Segment AB = 5, so x = +2.5 and x = +2.5.

k = -4(±2.5)² = -4 × 6.25 = -25

8 0

3 years ago

A certain scale has an uncertainty of 4 g and a bias of 2 g. A single measurement is made on this scale. What are the bias and u

Fed [463]

Answer: 0.8

Step-by-step explanation:

given data:

uncertainity = 4g

bias = 2g

solution:

σX =0.2 and σY = 0.4

σcX

= 3σX

= 4(0.2)

= 0.8

6 0

4 years ago

(6•11)2 •2-4(-2+14)2-12 simplest terms

Ksju [112]

Answer:

\frac{13+\left(-3\right)^2+4\left(-3\right)+1-\left[-10-\left(-6\right)\right]}{\left[4+5\right]\div \left[4^2\:−\:3^2\left(4−3\right)−8\right]+12}

Step-by-step explanation:

\frac{13+\left(-3\right)^2+4\left(-3\right)+1-\left(-10-\left(-6\right)\right)}{\frac{4+5}{\left(4^2-3^2\left(4-3\right)-8\right)+12}}

8 0

4 years ago

I really need help with this

zysi [14]

Answer:

Our system of equations is:

y+2x+1=0
4y-4x²-12x = -7

We are looking for x

Let's express y using x

y+2x+1=0
y= -2x-1

Replace x in the second equation with the result

4y-4x²-12x = -7
4(-2x-1)-4x²-12x = -7
-8x-4-4x²-12x = -7
-8x-4x²-12x = -7+4
-4x²-20x = -3
-4x²-20x+3 = 0 multiply by -1 to get rid of the - signs with x
4x²+20x-3=0

4x²+20x+3=0 is a quadratic equation

Let Δ be our discriminant

a= 4
b= 20
c= -3

Δ= 20²-4*4*(-3)

Δ=448 > 0 so we have two solutions for x

let x and x' be the solutions

x = $\frac{-20-\sqrt{448} }{8}$ = -5.145 ≈ -5.15
x'= $\frac{-20+\sqrt{448} }{8}$ = 0.145≈ 0.15

so the solutions are:

-5.15 and 0.15

7 0

3 years ago