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Mars2501 [29]
3 years ago
9

Select the two values of x that are roots of this equation. 2x^2+ 1 = 5x

Mathematics
1 answer:
iren [92.7K]3 years ago
8 0

Answer:

\frac{5+\sqrt{17}}{4},      \frac{5-\sqrt{17}}{4}

Step-by-step explanation:

One is asked to find the root of the following equation:

2x^2+1=5x

Manipulate the equation such that it conforms to the standard form of a quadratic equation. The standard quadratic equation in the general format is as follows:

ax^2+bx+c=0

Change the given equation using inverse operations,

2x^2+1=5x

2x^2-5x+1=0

The quadratic formula is a method that can be used to find the roots of a quadratic equation. Graphically speaking, the roots of a quadratic equation are where the graph of the quadratic equation intersects the x-axis. The quadratic formula uses the coefficients of the terms in the quadratic equation to find the values at which the graph of the equation intersects the x-axis. The quadratic formula, in the general format, is as follows:

\frac{-b(+-)\sqrt{b^2-4ac}}{2a}

Please note that the terms used in the general equation of the quadratic formula correspond to the coefficients of the terms in the general format of the quadratic equation. Substitute the coefficients of the terms in the given problem into the quadratic formula,

\frac{-b(+-)\sqrt{b^2-4ac}}{2a}

\frac{-(-5)(+-)\sqrt{(-5)^2-4(2)(1)}}{2(2)}

Simplify,

\frac{-(-5)(+-)\sqrt{(-5)^2-4(2)(1)}}{2(2)}

\frac{5(+-)\sqrt{25-8}}{4}

\frac{5(+-)\sqrt{17}}{4}

Rewrite,

\frac{5(+-)\sqrt{17}}{4}

\frac{5+\sqrt{17}}{4},      \frac{5-\sqrt{17}}{4}

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The diagram shows a sector of a circle radius 10 cm. the angle is 135 degrees
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Answer:

The perimeter is 43.6 cm

Step-by-step explanation:

In this question, we are tasked with calculating the perimeter of the sector.

Firstly, we define what a sector is. A sector is part of a circle which is is blinded by two radii and an arc. Hence we say a sector contains two radii.

Thus, to calculate the perimeter of the sector, we need the length of the arc added to 2 * length of the radius

Let’s calculate the length of the arc.

Mathematically, this is theta/360 * 2 * pi * r

where theta is the angle subtended at the middle of the circle which is 135 according to the question, and our radius is 10cm

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135/360 * 2 * 22/7 * 10 = 23.57 cm

Adding two radii to this, we have;

23.57 + 2(10)

= 23.57 + 20 = 43.57 = 43.6 cm to 1 decimal place

5 0
3 years ago
b. Tyler practiced the clarinet for 64% as much time as Han practiced the piano. How long did he practice?
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Answer: 48 minutes

Step-by-step explanation:

Han spent 75 minutes practicing the piano.

Tyler spent only 64% as much as that. How long did Tyler practice:

= 75 * 64%

= 48 minutes

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The correct answer is below:

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Harman [31]

Answer:

  1 hour

Step-by-step explanation:

I find these easiest to work by considering the initial difference in distance and the speed at with that gap is closing.

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The gap is 15 miles, the distance the first ship is from harbor when the second ship starts.

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2 years ago
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