Could a triangle have lengths of the sides of 4,8,6,2

A leprechaun places a magic penny under a girls pillow. The next night there are 2 magic pennies under her pillow. The following

kiruha [24]

Answer:

After 47 days she will have more than 90 trillion pennies.

Step-by-step explanation:

At the beginning there was 1 penny. At the second day the amount of pennies under the pillow became 2.

The amount of pennies doubled each day. So the series is,

$1,2,4,8,16,32,.....$

This series is in geometric progression.

As the pennies from each of the previous days are not being stored away until more pennies magically appear so the sum of series will be,

$S_n=\dfrac{a(r^n-1)}{r-1}$

where,

a = initial term = 1,

r = common ratio = 2,

As we have find the number of days that would elapse before she has a total of more than 90 trillion, so

$\Rightarrow 90\times 10^{12}\le \dfrac{1(2^n-1)}{2-1}$

$\Rightarrow 90\times 10^{12}\le \dfrac{2^n-1}{1}$

$\Rightarrow 90\times 10^{12}\le 2^n-1$

$\Rightarrow 2^n\ge 90\times 10^{12}+1$

$\Rightarrow \log 2^n\ge \log (90\times 10^{12}+1)$

$\Rightarrow n\times \log 2\ge \log (90\times 10^{12}+1)$

$\Rightarrow n \ge \dfrac{\log (90\times 10^{12}+1)}{\log 2}$

$\Rightarrow n \ge 46.4$

$\Rightarrow n\approx 47$

8 0

3 years ago

Estimate 76.216+66.36 by first rounding each number to the nearest whole number.

xeze [42]

Answer:

142

Step-by-step explanation:

Round the numbers to their nearest WHOLE NUMBER.

$76.216=76\\66.36=66$

Then ADD

$76+66=142$

6 0

3 years ago

Can someone please explain how to do this.

lutik1710 [3]

Set the to equal:

x^2 - 4x+4 = 2x-4
solve for X

subtract 2x from each side:
x^2 -6x + 4 = -4

subtract 4 from each side:

x^2 -6x = -8

add 8 to both sides:

x^2 -6x +8 = 0

factor the polynomial:

x = 4 and x = 2

using the line equation replace x with 2 and 4 and solve for y

y = 2(2) - 4 = 0
y = 2(4)-4 = 4

so the 2 points the line crosses the curve is (2,0) and (4,4)

using those 2 points you can calculate the length:
distance = sqrt((x2-x1)^2 +(y2-y1)^2

distance = sqrt( (4-2)^2 + (4-0)^2)

distance = sqrt (2^2 + 4^2)
distance = sqrt (4+16)
= sqrt 20
= 2 sqrt(5) EXACT LENGTH

4 0

3 years ago

How to add fractions with unlike denominators?

Ainat [17]

Change the fractions so they have common denominators. For example. If adding 4/8 + 2/3, a common denominator of the two could be 24. Change both fractions to have a denominator of 24. To do this:

(4/8)×(3/3)= 12/24
(2/3)×(8/8)=16/24

Now that both fractions have denominators of 24, you can simply add the numerators to get your answer. in this case, it would be 28/24

5 0

3 years ago

Read 2 more answers

In a chess club the probability that Shaun will beat Mike is 3/8 .

romanna [79]

Answer:

$\frac{10}{56} = 0.1786$ probability that Shaun loses both games