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9-12 Integrated Math 3 Unit 6 Lesson 1

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 Integrated Math 2 •Integrated Math 3

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7

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•Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20

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Unit 6, Lesson 1

Moving in Circles

$Course Icon$

Integrated Math 3

Practice

Problem 1

Here is a clock face. For each time given, name the number that the second hand points at.

15 seconds after 1:00.
30 seconds after 1:00.
1 minute after 1:00.
5 minutes after 1:00.

<p>A blank clock face with numbers 1 through 12.</p>

Problem 2

At 12:15, the end of the minute hand of a clock is 8 feet above the ground. At 12:30, it is 6.5 feet off the ground.

How long is the minute hand of the clock? Explain how you know.
How high is the clock above the ground?

Problem 3

Here is a point on a circle that is centered at \((0,0)\).

Which equation defines the circle?

<p>A circle on a coordinate plane, center at the origin. The point 6 comma 8 lies on the circle.</p>

\(x + y = 10\)
\(x^2 + y^2 = 10\)
\(x^2 + y^2 = 100\)
\((x-6)^2 + (y-8)^2 = 100\)

Problem 4

The point \((3,4)\) is on a circle that is centered at \((0,0)\). Which of these points lie on the circle? Select all that apply.

\((\text-3,\text-4)\)
\((4,3)\)
\((0,5)\)
\((0,0)\)
\((\text-5,0)\)

Problem 5

ForLesson 4: End Behavior of Rational Functions

Match each rational function with its end behavior as \(x\) gets larger and larger in the positive and negative directions. (Note: Some of the answer choices are not used and some answer choices may be used more than once.)

\(f(x)=\dfrac{6}{x-6}\)
\(g(x)=\dfrac{3x}{x-6}\)
\(h(x)=\dfrac{3x-18}{x-6}\)
\(k(x)=\dfrac{3x^2-16x-12}{x-6}\)
\(m(x)=\dfrac{(x+5)(x-4)(x-6)}{x-6}\)

The graph approaches \(y=6\).
The graph approaches \(y=3\).
The graph approaches \(y=0\).
The graph approaches \(y=x^2+x-20\).
The graph approaches \(y =3x^2+16x-12\).
The graph approaches \(y=3x+2\).
The graph approaches \(y=x-3\).

Problem 6

ForLesson 14: Transforming Circles

Here is an equation of a transformed circle: \(x^2+14x+y^2+6y-86=0\)

Rewrite an equation for the circle by completing the square.
What transformations would take the circle \(x^2+y^2=1\) to this transformed circle?
What is the center and radius of the transformed circle?