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GrogVix [38]
3 years ago
6

When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

ind the number?
Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
6 0

Let x be the unknown number. So, three times that number means 3x, and the square of the number is x^2

We have to sum 528 and three times the number, so we have 528+3x

Then, we have to subtract this number from x^2, so we have

x^2-(3x+528)

The result is 120, so the equation is

x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0

This is a quadratic equation, i.e. an equation like ax^2+bx+c=0. These equation can be solved - assuming they have a solution - with the following formula

x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

If you plug the values from your equation, you have

x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}

So, the two solutions would be

x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27

x = \dfrac{3-51}{2} = \dfrac{-48}{2} = -24

But we know that x is positive, so we only accept the solution x = 27

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Niccherip5 and 19 more users found this answer helpful

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4 0
2 years ago
What is the lcm of 16, 24 and 40
ivann1987 [24]
The answer is 240

Explanation: The Least Common Multiple (LCM) is the smallest number that two or more numbers will divide into evenly. NOTE: to find LCM you first need to know how to find GCD.

First we will find LCM for first two numbers ( 16 and24 ).

Step 1: Find the GCD (Greatest Common Divisor ) of 16 and 24 which is 8.

Step 2: Multiply the numbers 16 and 24 together ( 16 * 24 = 384 )

Step 3: Divide the 384 with 8. (384/8 = 48)

So, the LCM of 16 and 24 is 48.

Now we will find the LCM of above result (48) and third number ( 40 ) using the same procedure.

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(ps you can also just plug in all of the answer choices to desmos and see which one matches your graph)

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