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2 years ago

What is the greatest common divisor of $1665,$ $4554,$ $1683,$ and $4050$?

Mathematics

2 answers:

Tju [1.3M]2 years ago

7 0

9 is the greatest common divisor

Morgarella [4.7K]2 years ago

6 0

Answer:9 good luck

I hope you liked me answer

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Perpendicular bisector theorem

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2 years ago

A^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.

Verdich [7]

Answer:

$2a - 3b + 4c = 1$

Step-by-step explanation:

Given

$a^2 + b^2 + c^2 = 2(a - b - c) - 3$

Required

Determine $2a - 3b + 4c$

$a^2 + b^2 + c^2 = 2(a - b - c) - 3$

Open bracket

$a^2 + b^2 + c^2 = 2a - 2b - 2c - 3$

Equate the equation to 0

$a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0$

Express 3 as 1 + 1 + 1

$a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0$

Collect like terms

$a^2 - 2a + 1 + b^2 + 2b + 1 + c^2 + 2c + 1 = 0$

Group each terms

$(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

Factorize (starting with the first bracket)

$(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$(a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b^2 + b+b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)(b + 1)) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c^2 + c+c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c(c + 1)+1(c + 1)) = 0$

$((a - 1)^2) + ((b + 1)^2) + ((c + 1)(c + 1)) = 0$

$((a - 1)^2) + ((b + 1)^2) + ((c + 1)^2) = 0$

Express 0 as 0 + 0 + 0

$(a - 1)^2 + (b + 1)^2 + (c + 1)^2 = 0 + 0+ 0$

By comparison

$(a - 1)^2 = 0$

$(b + 1)^2 = 0$

$(c + 1)^2 = 0$

Solving for $(a - 1)^2 = 0$

Take square root of both sides

$a - 1 = 0$

Add 1 to both sides

$a - 1 + 1 = 0 + 1$

$a = 1$

Solving for $(b + 1)^2 = 0$

Take square root of both sides

$b + 1 = 0$

Subtract 1 from both sides

$b + 1 - 1 = 0 - 1$

$b = -1$

Solving for $(c + 1)^2 = 0$

Take square root of both sides

$c + 1 = 0$

Subtract 1 from both sides

$c + 1 - 1 = 0 - 1$

$c = -1$

Substitute the values of a, b and c in $2a - 3b + 4c$

$2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)$

$2a - 3b + 4c = 2 +3 -4$

$2a - 3b + 4c = 1$

7 0

3 years ago

HELP PLEASE!! TON OF POINTS. RIGHT ANSWERS ONLY REWARDED. MATH GENIUSES?

Nonamiya [84]

Answer:

The graph is shifted 1 unit right

The graph is shifted 2 units down

Step-by-step explanation:

We are given

Parent function as

$f(x)=2^{x+3}-3$

New function as

$g(x)=2^{x+2}-1$

we can also write as

$g(x)=2^{x+3-1}-3+2$

We can see that

1 is subtracted to x-value

and 2 is added to y-value

So, f(x) is shifted right by 1 unit

and

f(x) is shifted up by 2 unit

3 0

2 years ago

I NEED HELP WITH THIS. PLEASE HELP. I'M GETTING GRADED ON IT TODAY.

choli [55]

Answer:

Point P = (-9,11)

Step-by-step explanation:

Point M: (1,3) X and Y have the 2 on the bottom right of them

Midpoint N: (-5,7)

Point P: (X*2, Y*2)

( 1 + X*2 3 + Y*2 )

( _______ ________ ) = (-5 , 7)

( 2 , 2 )

( 1 + X*2 )

( _____ ) = -5

( 2 )

Then multiply the left equation above by 2, and that cancels out the 2 being

divided on the bottom. Also, multiply the -5 by 2 and you get -10

1 + X*2 = -10

+1 +1

__________

X*2 = -9

X = -9

( 3 + Y*2 )

( ______ ) = 7

( 2 )

Then multiply the left equation above by 2, and that cancels out the 2 being divided on the bottom. Also, multiply the 7 by 2 and you get 14

3 + Y*2 = 14

-3 -3

_________

Y*2 = 11

Y = 11

Hope this helps, good luck! :)

3 0

2 years ago

Read 2 more answers