Find the Difference 9,052-7,391

Two more than the square of a number is 123 what is the number? Can someone please explain to me how to do this

max2010maxim [7]

Give the number a label. That can be anything you want. A lot of people will use 'x' every single time they do a math problem,but there's no reason to do that and it's boring. Let's call our number ' M ' for 'Mystery number'. OK ?

The number . . . M
The square of the number . . . M²
Two more than the square of the number . . . M² + 2

You said that this is equal to 123, so we can write  M² + 2 = 123

That's the equation we have to take and solve for ' M '.

Subtract 2 from each side of the equation, and you have M² = 121 .

Take the square root of each side: M = √121 .

The Mystery number is the square root of 121.

If you don't happen to know what that is, then you can use your pocket
calculator, or the calculator that comes with your computer (if you know
how to find it). They will all tell you that the square root of 121 is 11 .

That's a fine and wonderful answer, but technically, it's only half of the
answer. Any equation that has something squared in it almost always
has two solutions, and this one does.

The square root of 121 is a number that gives you 121 when you
multiply it by itself. ' 11 ' does that: (11 x 11) = 121 . Is there another
number that does the same thing ?

How about ' -11 ' ? Look at this: ( -11 x -11 ) = 121 . (Remember that
if both numbers being multiplied have the same sign, then their product
is positive.)

The bottom line is: The mystery number is +11 and also -11 .
Either one does what you want . . . When you square it and then
add 2 more, you get 123 either way.

6 0

4 years ago

Homework problem #7: 24567389+35432611=what there is soo much regrouping, could someone show me how to do it?

Natasha_Volkova [10]

Answer:

$24567389+35432611 =60000000$

Step-by-step explanation:

Given

$24567389+35432611 =$

Required

Solve

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

The numbers in parentheses are carried from previous sum

Start from the right

$9 + 1 = 10 \to$ Write 0, carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0

$8 + 1 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0

$6 +3 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0

$7+2 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0

$6 +3 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0 0

$5 +4 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0 0 0

$4 +5 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0 0 0 0

$2 +3 + (1) = 6 \to$ Write 6

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

6 0 0 0 0 0 0 0

Hence:

$24567389+35432611 =6 0 0 0 0 0 0 0$

8 0

3 years ago

The system of equations is given:

Nutka1998 [239]

Answer:

x=-1/85; y=-283/85; z=2/17

Step-by-step explanation:

Using an algebraic method like elimination or substitution would take a lot of steps which could lead to mistake the calculations. In this case, I decided to use the Gaussian elimination. We can express the system in matrix form as follows:

$\left[\begin{array}{ccc}2&-4&6\\9&-3&1\\5&0&9\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}14\\10\\1\end{array}\right]$

To begin the calculations, we write the system in augmented matrix form and use the Gaussian elimination:

$\left[\begin{array}{ccccc}2&-4&6&|&14\\9&-3&1&|&10\\5&0&9&|&1\end{array}\right]$

By applying the Gaussian elimination, the final matrix is the following:

$\left[\begin{array}{ccccc}1&0&0&|&-1/85\\0&1&0&|&-283/85\\0&0&1&|&2/17\end{array}\right]$

In order to verify the results, it´s enough to substitute the calculated values in the original equations to see if the equalities are correct. Here you can see the verification for all of the equations:

$2(-1/85)-4(-283/85)+6(2/17)=14\\9(-1/85)-3(-283/85)+1(2/17)=10\\5(-1/85)+9(2/17)=1$