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kykrilka [37]
2 years ago
14

Given that the expression 2x² -2.9x-3.6 can be factorized into the form 0.1(px+q)(rx+s), where p, q, r and s are integers, find

the value of p + q + r + s. ​
Mathematics
1 answer:
Nonamiya [84]2 years ago
3 0

~~2x^2-2.9x-3.6\\\\=\dfrac{20}{10}x^2 - \dfrac{29}{10} x-\dfrac{36}{10}  \\\\=\dfrac 1{10} (20x^2 -29x -361)\\\\=0.1(20x^2-29x-36)\\\\=0.1(20x^2-45x+16x-36)\\\\=0.1[5x(4x-9)+4(4x-9)]\\\\=0.1(5x+4)(4x-9)\\\\\text{Where,}~ p=5, ~ q=4,~ r=4~,s=-9\\\\\text{Hence,}~ \\\\p+q+r+s \\\\ = 5+4+4 -9 \\\\=13-9 \\\\ =4

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Step-by-step explanation:

Equation of given line is:

y =  -  \frac{1}{2} x + 5 \\  \\ equating \: it \: with \: y =m_1x + c  \\ we \: find \:  \\ m_1 = -  \frac{1}{2} \\ let \: m_2 \: be \: the \: slope \: of \: required \: line \\  \\  \therefore \: m_1 \times m_2 =  - 1( \because \: lines \: are \:  \perp) \\  \\ \therefore \: -  \frac{1}{2} \times m_2 =  - 1\\  \\ \therefore \: m_2 = 2 \\

Thus, the slope of required line is 2.

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2 years ago
If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ first, find
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Given

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Step One

Find the center

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Step Two

Find the radius squared using the distance formula. Use (5,2) as the second point. The other point is the center.

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Step Three

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Answer:

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