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2 years ago

Prove each of the following identities.

Mathematics

1 answer:

Fittoniya [83]2 years ago

6 0

Prove of the following identity is given below in photo.

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Elly's room measures 78 inches by 96 inches. Sarah's room measures 66 inches by 108 inches. They want to combine their rooms. Ho

frozen [14]

Okay add 78 and 66. Then add 96 and 108. It should be 144 by 204. I know math is hard, but when you work at it you can do amazing things! I hope that helps you.

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3 years ago

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In a recent 82-game season, Dwight Hoard averaged 20.7 points per game. His approximate total points scored p(g) is a function o

ankoles [38]

20.7(82)=1697.4
20.7(9)=186.3

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3 years ago

What is k if : k!+48=48((k+1)^m)

lys-0071 [83]

Answer:

The value of k is greater than or equal to 0, i.e. k≥7.

Step-by-step explanation:

The given equation is

$k!+48=48((k+1)^m)$

The value of k must be a positive integer because k! is defined for k≥0, where k∈Z.

Subtract 48 from both the sides.

$k!=48((k+1)^m)-48$

$k!=48((k+1)^m-1)$

$k!=48(k+1-1)(\frac{(k+1)^m-1}{(k+1)-1})$

Using $[\frac{r^m-1}{r-1}=r^{m-1}+r^{m-2}+...+1]$ , we get

$k!=48k((k+1)^{m-1}+(k+1)^{m-2}+...+1)$

Divide both sides by 48k.

$\frac{k!}{48k}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

$\frac{k(k-1)!}{48k}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

$\frac{(k-1)!}{48}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

Note: The value of m can be 0 or 1.

The value of k is positive integer, so the right hand side of the above equation must be a positive integer.

Since RHS of the equation is positive integer, therefore (k-1)! is completely divisible by 48.

$k-1\geq 6$

Add 1 on both sides.

$k\geq 6+1$

$k\geq 7$

Therefore the value of k is greater than or equal to 0.

4 0

4 years ago

you sell tickets for admission school play and collect a total of $21. admission prices are $3 for adults and $2 for children. y

noname [10]

There is more then one answer, but one answer is 5 adult tickets and 3 children tickets. (5×3)+(3×2)=21

5 0

3 years ago

If the area of the trapezoid below is 98 square units,what is the value of x?<br>Plz help!

aleksandrvk [35]

Area of Trapezoid is = 1/2 x height x (base1 + base2)

Here, Area = 98, base1 = 8, base2 = 20 and height = unknown (x)

So, 1/2 x height x (8+20) = 98
==> 1/2 x height x 28 = 98
==> height x 14 = 98
==> height = 98/14
==> height = 7 units

So, the final answer is --> the value of x = 7 units

4 0

3 years ago

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