Simplify completely the quantity x squared plus x minus 12 over quantity x squared minus x minus 20 divided by the quantity 3 x squared minus 24 x plus 45 over quantity 12 x squared minus 48 x minus 60.

Answers

Answer 1

Answer: x² + x - 12 / x² - x - 20 ÷ 3x² - 24x + 45 / 12x² - 48x - 60

x² + x - 12 / x² - x - 20 * 12x² - 48x - 60 / 3x² - 24x + 45

(x² + x - 12)(12x² - 48x - 60)
(x² - x - 20)(3x² - 24x + 45)

12x^4 - 48x³ - 60x² + 12x³ - 48x² - 60x - 144x² + 576x + 720
3x^4 - 24x³ + 45x² - 3x³ + 24x² - 45x - 60x² + 480x - 900

12x^4 - 48x³ + 12x³ - 60x² - 48x² - 144x² - 60x + 576x + 720
3x^4 - 24x³ - 3x³ + 45x² + 24x² - 60x² - 45x + 480x - 900

12x^4 - 36x³ - 252x² + 516x + 720
3x^4 - 27x³ + 9x² + 435x - 900

12(x^4 - 3x³ - 21x² + 43x + 60)
3(x^4 - 9x³ + 3x² + 145x + 300)

4(x^4 - 3x³ - 21x² + 43x + 60)
(x^4 - 9x³ + 3x² + 145x + 300)

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2. Over five years, Jerome grew from a height of 47 inches to a height of 66 inches. Which ofthe following represents Jerome's growth rate during these five years?

(1) 3.8 inches per year
(2) 4.25 inches per year
(3) 4.6 inches per year
(4) 4.75 inches per year

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Answer:

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Answers

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Answers

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Step-by-step explanation:

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3. Determine whether or not AB is tangent to circle O. Show your work.

Answers

The line AB touching the circle at point B in the considered diagram is not tangent to the circle O.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

$|AC|^2 = |AB|^2 + |BC|^2$

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

How are radius and tangent to a circle related?

There is a theorem in mathematics that:

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.

So, if AB is a tangent, then ∠ABO = 90° and therefore satisfies Pythagoras theorem.

Assuming AB is tangent, then ABO is right angled we should get:

$H^2 = P^2 + B^2\n30^2 = 16^2 + 12^2\n900 = 256 + 144\n900= 500$

This statement is false, and therefore, so as our assumption is false that ABis tangent to circle O. Thus, AB is not tangent to circle O.

(so it might be that even if AB looks like touching at one point the circle O, but AB might be intersecting the circle at two points, or not touching it at all)

Thus, the line AB touching the circle at point B in the considered diagram is not tangent to the circle O.

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brainly.com/question/7942024

Answer:

not tangent

Step-by-step explanation:

two reasons, first

Triangle AOB is not a right triangle

line AB intersects the circle O at two points.

- 5x = -x - 48
x = -11
X = 12

Answers

Answer:

B- x=12

Step-by-step explanation:

-5x=-x-48

-12+-48

-12. -12

-60=-5x

-5. -5

x=12

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Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table.

Answers

Remember that a quadratic with two real zeroes can be written as $a(x - r_1)(x - r_2)$ , where $a$ is a constant and $r_1$ and $r_2$ are the zeroes (or roots) of the function. Since the graph shows that the two zeroes are at -6 and 6, the equation has to be of the form

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$m = (y_2 - y_1)/(x_2 - x_1) = \frac{35 - 32}{1 - ({-2})} = 1$
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