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3 years ago

What is the HCF of 27 and 42

Mathematics

1 answer:

hichkok12 [17]3 years ago

6 0

Answer: 3

Explanation:

27 = 3^3
42 = 2 x 3 x 7

So the HCF of (27,42) = 3

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Alexxandr [17]

I would say number 2 but dont take my word for it

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3 years ago

2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

ratelena [41]

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

$x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29$

The associated matrix to the system is

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]$

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]$

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]$

Using backward substitution we have that

$0x_5=-140$ , then $0=-140$ and this is absurd. Then The system is inconsistent.

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4 years ago

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goldenfox [79]

Answer:NIce

Step-by-step explanation:

5 0

3 years ago

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Round 43,951,842 to the nearest hundred-thousand

GrogVix [38]

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3 years ago

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What is the equation of the line that passes through the point (-2,5) and has a<br> slope of -4?

adoni [48]

Answer:

$\boxed {\boxed {\sf y= -4x -3}}$

Step-by-step explanation:

We are asked to find the equation of a line given a point and the slope. We will use the point-slope formula.

$y-y_1= m(x-x_1)$

In this formula, m is the slope and (x₁, y₁) is the point the line passes through. The slope of this line is -4 and the line passes through (-2,5).

m= -4
x₁= -2
y₁ = 5

Substitute the values into the formula.

$y-5 = -4 (x--2)$

$y-5 = -4 (x+2)$

We are finding the equation of the line, so we should find the slope-intercept form or y=mx+b ( where m is the slope and b is the y-intercept).We must isolate the variable y on one side of the equation.

First, distribute the -4 on the right side of the equation. Multiply each term inside the parentheses by -4.

$y-5=( -4 *x ) + (-4* 2 )$

$y-5 =(-4x)+ (-8)\\y-5= -4x -8$

5 is being subtracted from y. The inverse operation of subtraction is addition, so we will add 5 to both sides of the equation.

$y-5 =-4x -8 + 5$

$y= -4x -3$

The equation of the line is y= -4x -3. The slope of the line is -4 and the y-intercept is -3.

6 0

3 years ago

What is the HCF of 27 and 42​

What is the HCF of 27 and 42