Math Simplify the expression

Mathematics

1 answer:

djyliett [7]3 years ago

4 0

$\bf \cfrac{1}{x-10}\div\cfrac{9x}{x^2-9x-10}\implies \cfrac{1}{x-10}\cdot \cfrac{x^2-9x-10}{9x} \\\\\\ \cfrac{1}{\begin{matrix} x-10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \cfrac{\begin{matrix} (x-10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+1)}{9x}\implies \cfrac{x+1}{9x}$

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Question 10: If the product of all the numbers from 1 to 100 is divisible by 2^n, then what is the maximum possible value for n:

Klio2033 [76]

Answer: D

Step-by-step explanation:

100!=2*3*4*...*100

Counting which numbers are divisible by 2:

2,4,6,8,10,12,14,...,96,98,100 : 50 numbers (100/2=50)

Counting which numbers are divisible by 4=2²:

4,8,12,16,20,...96,100: 25 numbers (100/4=25)

Counting which numbers are divisible by 8=2³:

8,16,24,32,40,...,96: 12 numbers (100/8=12.5 ==> 12)

Counting which numbers are divisible by 16=2⁴:

16,32,48,...,96: 6 numbers (100/16=6.25 ==> 6)

Counting which numbers are divisible by 32=2⁵:

32,64,96 : 3 numbers(100/32=3.125 ==>3)

Counting which numbers are divisible by 64=2⁶:

64 : 1 number (100/64=1.5625 ==>1)

Sum of those numbers= 50+25+12+6+3+1=97

100! is divisible by 2⁹⁷.

Answer D

4 0

3 years ago

Read 2 more answers

15 less than twice a number is less than or equal to -23. Into an equation

Dafna1 [17]

I hope it’s correct!

4 0

3 years ago

Plz solve this if u know plz

salantis [7]

<h3>Solution:</h3>

${64}^{ - \frac{1}{3} } ( {64}^{ \frac{1}{3} } - {64}^{ \frac{2}{3} } ) \\ {64}^{ \frac{1}{3} - \frac{1}{3} } - {64}^{ \frac{2}{3} - \frac{1}{3} } \\ {64}^{0} - {64}^{ \frac{1}{3} } \\ 1 - \sqrt[3]{64} \\ 1 - 4 \\ - 3$