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2 years ago

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Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the c

enter of the circle and the length of the radius? A. (-7, -1), 36 units B. (7, 1), 36 units C. (7, 1), 6 units D. (-7, -1), 6 units

1 answer:

son4ous [18]2 years ago

4 0

Answer:

The correct answer is D.

Step-by-step explanation:

Given:

General equation of second degree

x² + y² + 14 x + 2 y + 14 = 0

We must transform given equation to the canonical form from which we will read requested data.

The canonical form of the circle equation is:

(x - p)² + (y - q)² = r²

Where p and q are the coordinates of the center of the circle and r are radius. (p,q) = (x,y)

x² + 2 · x ·7 + 7² - 7² + y² + 2 · y · 1 + 1 - 1 + 14 = (x+7)² + (y+1) - 49 - 1 + 14 = 0

(x + 7)² + (y + 1)² = 36

We see that p = - 7 , q = - 1 and r = 6

God with you!!!

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3 years ago

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What is an equation of the line that is parallel to y=3x-8 and passes through the point, (4,-5)

VladimirAG [237]

Answer:

y= 3x-17

Step-by-step explanation:

When finding a parallel equation to y=mx+b, mx will always stay the same. So we have to find b.

In order to do this you plug the parallel lines passing point into the equation.

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2 years ago

A biology test is worth 100 points and has 36 questions.

Ad libitum [116K]

Answer:

(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

$M + E= 36$ --- Number of questions

$2M + 6E = 100$ --- Points

Solving (a): Number of question of each type.

Make E the subject of formula in $M + E= 36$

$E = 36 - M$

Substitute 36 - M for E in $2M + 6E = 100$

$2M + 6(36 - M) = 100$

$2M + 216 - 6M = 100$

Collect Like Terms

$2M - 6M = 100 - 216$

$-4M = - 116$

Divide both sides by -4

$M = \frac{-116}{-4}$

$M = 29$

Substitute 29 for M in $E = 36 - M$

$E = 36 - 29$

$E = 7$

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

$2M + 6E = 100$ would be:

$4M + xE = 100$

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

$4 * 29 + x * 7 = 100$

$116 + 7x = 100$

Subtract 116 from both sides

$116-116 + 7x = 100 -116$

$7x = 100-116$

$7x = -16$

Make x the subject

$x = -\frac{16}{7}$

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

<em>Your friend is incorrect.</em>

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2 years ago

which shows one way to determine the factors of 12x^3 - 2x^2 + 18x - 3 by grouping? A) 2x^2(6x - 1) + 3(6x - 1) B) 2x^2(6x - 1)

Eva8 [605]

Answer:

$2x^2(6x - 1) + 3(6x - 1)$

Step-by-step explanation:

Given

$12x^3 - 2x^2 + 18x - 3$

Required

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To start with; we need to group the expression into two

$(12x^3 - 2x^2) + (18x - 3)$

Factorize each grouped expression, using their common factor

$2x^2(6x - 1) + 3(6x - 1)$

From the list of given options;

Option A is correct

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3 years ago

Give answer in standard form for part a and b

aniked [119]

a) (23000) × (0.015)

=345

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