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3 years ago

15

Two students are going to guess on their next quiz. Adam has two multiple choice questions, each with five options: A, B, C, D a

nd E. Zach has three TRUE/FALSE questions. Who has the better
chance of doing well? Explain your thought process.

1 answer:

Artyom0805 [142]3 years ago

7 0

Answer:

Zach

Step-by-step explanation:

it's most likely Zach will be able to get the right answer

more easily then Adam since he can try to guess it more easily???

I'm not good at explaining but yeah -

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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:

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

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2 years ago

Factor the quadratic expression completely 15x^-4x-4

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Answer:

(5x+2)(3x-2)

Step-by-step explanation:

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2 years ago

Find the values of x and y

eimsori [14]

Answer:

y = 70 and x = 20

Step-by-step explanation:

180 - 40 = 140

140/2 = 70

70 + 90 = 160

180 - 160 = 20

3 0

3 years ago

Point B has coordinates (1,2). The x-coordinate of point A is -8. The distance between point A and point B is 15 units. What

Xelga [282]

Answer:

The possible coordinates of point A are $A_{1} (x,y) = (-8, 14)$ and $A_{2} (x,y) = (-8, -10)$ , respectively.

Step-by-step explanation:

From Analytical Geometry, we have the Equation of the Distance of a Line Segment between two points:

$l_{AB} = \sqrt{(x_{B}-x_{A})^{2} + (y_{B}-y_{A})^{2}}$ (1)

Where:

$l_{AB}$ - Length of the line segment AB.

$x_{A}, x_{B}$ - x-coordinates of points A and B.

$y_{A}, y_{B}$ - y-coordinates of points A and B.

If we know that $l_{AB} = 15$ , $x_{A} = -8$ , $x_{B} = 1$ and $y_{B} = 2$ , then the possible coordinates of point A is:

$\sqrt{(1+8)^{2}+(2-y_{A})^{2}} = 15$

$81 + (2-y_{A})^{2} = 225$

$(2-y_{A})^{2} = 144$

$2-y_{A} = \pm 12$

There are two possible solutions:

1) $2-y_{A} = -12$

$y_{A} = 14$

2) $2 - y_{A} = 12$

$y_{A} = -10$

The possible coordinates of point A are $A_{1} (x,y) = (-8, 14)$ and $A_{2} (x,y) = (-8, -10)$ , respectively.

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3 years ago

CAN SOMEONE HELP ME WITH THIS PLEASE!!

Delvig [45]

Answer:

B

Step-by-step explanation:

the money increases hourly so A and C are wrong. and it is constant so the answer is B

4 0

3 years ago