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

1 answer:

max2010maxim [7]3 years ago

6 0

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.

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Answer:

24 m^2

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2 years ago

Help please if anyone knows

larisa86 [58]

Part A
To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case, $\frac{3}{5}$ and $\frac{2}{3}$ equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about 3 gallons.

Part B
To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.

$1 \frac{3}{5} \\ \\ (5*1)+3 =8 \\ \\ \frac{8}{5} \\ \\ \\ \\ 1 \frac{2}{3} \\ \\ (3*1)+2=5 \\ \\ \frac{5}{3} 
$

Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.

Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.

$\frac{8}{5} *3 = \frac{24}{15} \\ \\ \frac{5}{3} *5 = \frac{25}{15}$

Now, we can simply add our numerators.

$25+24=49$

We know that he needs $\frac{49}{15}$ gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.

$\frac{49}{15} \\ \\ 49 / 15 = 3(Remainder: 4) \\ \\ 3\frac{4}{15}$

Using that logic, we can see that the painter needs exactly $3 \frac{4}{15}$ gallons of paint.

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