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2 years ago

6

Matthew has 12 pencils . Three of them do not have erasers on the end . 4 are green .2 is orange .4 are brown .What fractions of

the M&Ms are brown

1 answer:

deff fn [24]2 years ago

7 0

You have given us no information whatsoever concerning the distribution
of M&Ms in Matthew's pencil box, so it's quite impossible to formulate any
sort of answer to the question.

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find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

6 0

2 years ago

What is the arc measure, in degrees, of major arc \stackrel{\large{\frown}}{ADC} ADC ⌢ A, D, C, start superscript, \frown, end s

Mrrafil [7]

Answer:

$\stackrel{\large{\frown}}{ADC} = 186^{\circ}$

Step-by-step explanation:

Given

See attachment

Required

Determine the measure of $\stackrel{\large{\frown}}{ADC}$

$The\ sum\ of\ angles\ in\ a\ circle\ is$ $360^{\circ}$ .

So, we have:

$\stackrel{\large{\frown}}{ADC} + \stackrel{\large{\frown}}{APB} + \stackrel{\large{\frown}}{BPC} = 360^{\circ}$

Where:

$\stackrel{\large{\frown}}{APB} = 70^{\circ}$

$\stackrel{\large{\frown}}{BPC} = 104^{\circ}$

Substitute these values in the above equation.

$\stackrel{\large{\frown}}{ADC} + 70^{\circ} +104^{\circ} = 360^{\circ}$

$\stackrel{\large{\frown}}{ADC} + 174^{\circ} = 360^{\circ}$

Collect Like Terms:

$\stackrel{\large{\frown}}{ADC} = 360^{\circ} - 174^{\circ}$

$\stackrel{\large{\frown}}{ADC} = 186^{\circ}$

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Graph the system of equations on graph paper.

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Ths system of equations is

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2x−3y=−6 ..............>y = 6/3 + 2x/3

If we use a graphic tool, we can easily check the solution,
which is (x,y) = (3,4)

The ordered pair lies in Quadrant I</span>

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Which expression is equivalent to

viva [34]

Answer:

C) $x^{27} (\sqrt[3]{y} )$

Step-by-step explanation:

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Find the value of m. A. 32 B. 50 C. 63 D. 74

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Answer:

c

Step-by-step explanation:

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