How do you write 2y=3(-x+5) in standard form ?

Mathematics

1 answer:

Drupady [299]2 years ago

7 0

2y=3(-x+5)

Distributed property

2y= -3x +15

Move x term to left side to get

3x+2y=15

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A square and a circle intersect so that each side of the square contains a chord of the circle equal in length to the radius of

krek1111 [17]

Answer:

Step-by-step explanation:

it is given that Square contains a chord of of the circle equal to the radius thus from diagram

$QR=chord =radius =R$

If Chord is equal to radius then triangle PQR is an equilateral Triangle

Thus $QO=\frac{R}{2}=RO$

In triangle PQO applying Pythagoras theorem

$(PQ)^2=(PO)^2+(QO)^2$

$PO=\sqrt{(PQ)^2-(QO)^2}$

$PO=\sqrt{R^2-\frac{R^2}{4}}$

$PO=\frac{\sqrt{3}}{2}R$

Thus length of Side of square $=2PO=\sqrt{3}R$

Area of square $=(\sqrt{3}R)^2=3R^2$

Area of Circle $=\pi R^2$

Ratio of square to the circle $=\frac{3R^2}{\pi R^2}=\frac{3}{\pi }$

5 0

2 years ago

Find a number C such that the polynomial p(x)= -x+4x^2+Cx^3-8x^4

Ksenya-84 [330]

Answer:

C = 2

Step-by-step explanation:

$p(x)= -x+4x^2+Cx^3-8x^4 \\ \\ \because \: given \: polynmial \: has \: zero \: at \: \\x = \frac{1}{4} \\ \\ \implies \: p\bigg(\frac{1}{4} \bigg) = 0...(1) \\ \\ plug \: x = \frac{1}{4} \: in \: p(x) \: we \: find \\ \\ p \bigg(\frac{1}{4} \bigg) = - \frac{1}{4} + 4 {\bigg(\frac{1}{4} \bigg)}^{2} + c {\bigg(\frac{1}{4} \bigg)}^{3} - 8 {\bigg(\frac{1}{4} \bigg)}^{4} \\ \\ 0 = - \frac{1}{4} + \cancel 4 \times {\frac{1}{\cancel{16} } } + c {\bigg(\frac{1}{64} \bigg)} - \cancel 8 \times \frac{1}{\cancel{256} } \\ \\0 =\cancel{ - \frac{1}{4}} + \cancel {{\frac{1}{4} }} + c {\bigg(\frac{1}{64} \bigg)} - \times \frac{1}{32} \\ \\0 = c {\bigg(\frac{1}{64} \bigg)} - \frac{1}{32} \\ \\c {\bigg(\frac{1}{64} \bigg)} = \frac{1}{32} \\ \\ c = \frac{1}{32} \times 64 \\ \\ c = 2$