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Unit Test $\newline$ Unit Test $\newline$ Active $\newline$ $1$ $\newline$ $2$ $\newline$ $3$ $\newline$ $4$ $\newline$ $5$ $\newline$ $6$ $\newline$ $\text{?}$ $\newline$ $8$ $\newline$ $9$ $\newline$ $10$ $\newline$ $2$ $0$ $\newline$ TIME REMAINING $\newline$ $2$ $1$ $\newline$ EFGH is a rhombus. $\newline$ Given $\newline$ $2$ $2$ and $\newline$ $2$ $3$ , what is the length of one side of the rhombus? $\newline$ $6$ units $\newline$ $8$ units $\newline$ $10$ units $\newline$ $2$ $7$ units

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Interpret stem-and-leaf plots

Full solution

Q. Unit Test

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Unit Test

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Active

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1

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2

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3

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4

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5

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6

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\text{?}

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8

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9

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10

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2

0

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TIME REMAINING

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2

1

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EFGH is a rhombus.

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Given

\newline

2

2

and

\newline

2

3

, what is the length of one side of the rhombus?

\newline

6

units

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8

units

\newline

10

units

\newline

2

7

units

Understand Rhombus Properties: Understand the properties of a rhombus and its diagonals. $\newline$ A rhombus is a type of polygon that is a quadrilateral with all four sides of equal length. The diagonals of a rhombus bisect each other at right angles ( $90^\circ$ ). This means that each diagonal cuts the other into two equal parts at the center of the rhombus.
Form Right Triangles: Use the properties of the diagonals to form right triangles. $\newline$ Since the diagonals bisect each other at right angles, we can form four right triangles within the rhombus. Each triangle will have half the length of one diagonal as one leg and half the length of the other diagonal as the other leg.
Calculate Diagonal Halves: Calculate the lengths of the halves of the diagonals. $\newline$ Half of $EG$ ( $16$ units) is $16/2 = 8$ units. $\newline$ Half of $FH$ ( $12$ units) is $12/2 = 6$ units. $\newline$ These are the lengths of the legs of the right triangles formed by the diagonals.
Apply Pythagorean Theorem: Apply the Pythagorean theorem to find the length of one side of the rhombus. $\newline$ The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ : $c^2 = a^2 + b^2$ . $\newline$ Let's denote the length of one side of the rhombus as $s$ . Then, using the lengths of the halves of the diagonals as the legs of the right triangles, we have: $\newline$ $s^2 = 8^2 + 6^2$
Calculate Side Length: Calculate the length of one side of the rhombus. $\newline$ $s^2 = 64 + 36$ $\newline$ $s^2 = 100$ $\newline$ To find $s$ , we take the square root of both sides of the equation: $\newline$ $s = \sqrt{100}$ $\newline$ $s = 10$ units

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The data below shows how old each of Brad's eight kids were when they started kindergarten.

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\begin{tabular}{|l|l|l|l|}

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5

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He predicts that the relationship between

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He predicts that the relationship between

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\begin{tabular}{|c|c|}

\newline

x

y

\newline

k

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k+7

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\newline

\newline

\newline

The table gives the coordinates of two points on a line in the

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k

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\newline

y

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In physics, work is defined as

W = F \cdot d

F

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Newtons, which are

\text{N}

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\text{J}

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