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maw [93]
3 years ago
10

Suppose that $a$ is a positive integer for which the least common multiple of $a+1$ and $a-5$ is $10508$. What is $a^2 - 4a + 1$

?
Mathematics
1 answer:
Nana76 [90]3 years ago
4 0

Answer:

21022.

Step-by-step explanation:

Find the prime factors of 10508:

2 ) 10508

2 ) 5254

37 ) 2627

       71.

50208 = 2*2*37*71.

Now there is no integer value for a that would fit  (a+ 1)(a - 5) = 10508 .

But we could try multiplying the LCM by 2:-

= 21016  = 2*2*2*37*71.

= 2*2*37 multiplied by 2 * 71

= 148 * 142.

That looks promising!!

a - 5 = 142 and

a + 1 = 148

This gives  2a - 4 = 290

2a = 294

a = 147.

So substituting a = 147 into a^2 - 4a + 1 we get:

= 21022.

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First you would start getting the denominators to the same number and you could do this by multiplying 9/10 by 4, and 7/8 by 5 to get the denominators to 40 and when you add the fractions you get 71/40 so the answer would be D. About 2
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3 years ago
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Hope this helps u pls mark me brainlist

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2 years ago
The midpoint of AB is M(3,3). If the coordinates of A are (2,-8), what are the coordinates of B?
Lyrx [107]

Step-by-step explanation:

MID POINT =[(X1 +X2)/2 , (Y1 +Y2)/2]

WE KNKW THAT A(2,–8) AND THE MID POINT IS (3,3)

SUBSTITUTING INTO THE EQUATION ABOVE

(3,3) = [(2+ X2)/2 ,(–8+ Y2)/2]

EQUATING THE X COORDINATES

=> 3 = (2+ X2)/2 (CROSS MULTIPLY)

=> 6 = 2 + X2

X(subscript 2)= 4

EQUATING THE Y COORDINATES

=> 3 =(–8 +Y2)/2 (CROSS MULTIPLY)

6 = –8 +Y2

=> Y(subscript 2)= 14

THEREFORE THE COORDINATES OF B ARE (4 ,14)

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4 0
3 years ago
Verify the following identity: (csc theta -cot theta )/(sec theta -1) A. sec theta B. cos theta C. cot theta D. sin theta
alexdok [17]

Answer:

C. cot theta

Step-by-step explanation:

(csc theta -cot theta )/(sec theta -1)

csc = 1/ sin

cot = cos / sin

sec = 1 / cos

Let x = theta

(1/ sin x -cos x / sin x )/(1/ cos x -1)

Getting a common denominator in the denominator and combining terms

(1- cos x)/ sinx  / ( 1 - cos x) / cos x

(1- cosx)      (1- cosx)

----------- ÷ ------------

sinx            cos x

Copy dot flip

(1- cosx)       cosx

----------- * ------------

sinx            1 -cos x

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3 0
3 years ago
Find the domain of the function y = 3 tan(2/3x)
Damm [24]

Answer:

{x∈R | \frac{2x}{3\pi } +\frac{1}{2}, x∉Z}

Step-by-step explanation:

Given the function y=3tan(2/3x)

We know that tangent is a function that's continuous within it's domain but not continuous on all real numbers

Also, the roots of y=3tan(2/3x) is 3\pi n/2 where n is an integer

Note that the domain of the function cannot be within 3\pi n/2

Therefore, {x∈R | \frac{2x}{3\pi } +\frac{1}{2}, x∉Z}

5 0
2 years ago
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