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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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Step-by-step explanation:

2*5=10

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Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 ki
kramer

Samantha and Mia are 13 km apart from each other.

<h3>What is Pythagorean ?</h3>

A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.

Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.

Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.

A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.

Hypotenuse of the triangle, which measures distance between the females

the Pythagorean theorem,

H² = P² + B²

H² = 7² + 11²

H² = 49 + 121

H = √170

H = 13.038

H = 13km

Between them, there is a 13 kilometer distance.

To know more about Pythagorean Theorem visit:

brainly.com/question/2245624

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7 0
1 year ago
David bought a used Dodge Challenger for $14,000. The value of the car depreciates 11% per year from the time he bought the car.
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Answer:

V(t) = 14,000(0.89)^t

Step-by-step explanation:

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Depreciation value = 11%

Number of years = t

Future value = V(t)

V(t) = Present value of the Dodge Challenger(Present percentage value - Depreciation value)^t

= 14,000(100% - 11%)^t

= 14,000(89%)^t

= 14,000(0.89)^t

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Step-by-step explanation:

1.) First, you need to take the whole numbers (9 and 1) and set them aside.

2.) Multiply the numerators from each fraction by one another. The numerators are the numbers on the top of the fraction. (Whatever you get on that will be the numerator of the answer!)

3.) Multiply the denominators by each other as well. The denominators are the numbers on the bottom. This will be the denominator of your answer.

4.) Now, you need to multiply your whole numbers (9 and 1) together.

5.) Then, simplify or reduce your answer. (this can't be simplified, as it is already in its simplest form)

Your answer will be 9 1/66.

Your work should look like this in the end:

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