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Algebra 2

Class 9 Algebra 2 Questions asked by Filo students

Question 1

A kilobyte is a thousand = 103 bytes, usually abbreviated KB.

A megabyte is a million = 106 bytes, usually abbreviated MB or meg.
A gigabyte is a billion = 109 bytes, usually abbreviated GB or gig.
A terabyte is a trillion = 1012 bytes, usually abbreviated TB.
Determine how many kilobytes are in 1.2 terabytes.

Topic:

Algebra 2

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Question 2

The circumference of a circle = (where r is the radius of the circle) Area of a circle = (where r is the radius of the circle) Surface Area of a sphere = (where r is the radius of the sphere) Surface Area of a cube = (where x is the length of the cube) Volume of a sphere = (where r is the radius of the sphere) Volume of a cube = (where x is the length of the cube) The volume of a cube with length x is proportional to the cube of its length. What is the constant of proportionality?

Topic:

Algebra 2

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Question 3

The triangles in the figure below are similar. Find the length of the side labeled x. Round your answer to two decimal places, if necessary. Screen Shot 2020-05-14 at 5.37.30 PM.png If your browser will not let you see the figures. Use this description: The smaller top triangle has sides labeled "6.4 cm" and "12 cm". The larger lower triangle has sides labeled "x cm" and "15 cm". The side labeled "6.4 cm" from the top triangle corresponds to the side labeled "x cm" from the lower triangle. The side labeled "12 cm" from the top triangle corresponds to the side labeled "15 cm' from the lower triangle.

Topic:

Algebra 2

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Question 4

An important part in many applications such as optimization, mechanics, and partial differential equations (PDE) is taking derivatives with respect to vectors. By definition, if \( \boldsymbol{y}=\left[\begin{array}{llll}y_{1} & y_{2} & \ldots & y_{n}\end{array}\right]^{T} \) and \( \boldsymbol{x}=\left[\begin{array}{llll}x_{1} & x_{2} & \ldots & x_{n}\end{array}\right]^{T} \) are two vectors and \( \boldsymbol{y}=f(\boldsymbol{x}) \), which means \( \boldsymbol{y} \) is dependent on \( \boldsymbol{x} \), then \[ \frac{\partial \boldsymbol{y}}{\partial \boldsymbol{x}}=\left[\begin{array}{cccc} \frac{\partial y_{1}}{\partial x_{1}} & \frac{\partial y_{1}}{\partial x_{2}} & \cdots & \frac{\partial y_{1}}{\partial x_{n}} \\ \frac{\partial y_{2}}{\partial x_{1}} & \frac{\partial y_{2}}{\partial x_{2}} & \cdots & \frac{\partial y_{2}}{\partial x_{n}} \\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial y_{n}}{\partial x_{1}} & \frac{\partial y_{n}}{\partial x_{2}} & \cdots & \frac{\partial y_{n}}{\partial x_{n}} \end{array}\right] . \] 1. Using the definition, determine \( \frac{\partial \boldsymbol{y}}{\partial \boldsymbol{x}} \) if \( \boldsymbol{y}=A \boldsymbol{x} \), when \[ A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right], \quad A=\left[\begin{array}{lll} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right] \] Make a guess: what if \( A \) is a general \( n \times n \) matrix? 2. The definition also holds even when \( \boldsymbol{y} \) is a scalar (a vector of length 1 ). What is \( \frac{\partial \boldsymbol{y}}{\partial \boldsymbol{x}} \), if \( \boldsymbol{y}=\boldsymbol{x}^{T} \boldsymbol{x} \) (Hint: you can try with \( \boldsymbol{x} \) has length 2,3 , and generalize)?

Topic:

Algebra 2

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Question 5

Use your own words to describe this equation where

n

is a number:

5 (n + 3) = 2 n

Topic:

Algebra 2

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Question 6

For the following exercises, simplify the given expression.

(4 + 5)^{2} \div 3

Topic:

Algebra 2

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Question 7

For the following exercises, simplify the given expression.

9 - 18 \div 3^{2}

Topic:

Algebra 2

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Question 8

For the following exercises, simplify the given expression.

(15 - 7) \cdot (3 - 7)

Topic:

Algebra 2

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Question 9

For the following exercises, simplify the given expression.

2 \cdot 4 - 9 (- 1)

Topic:

Algebra 2

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Question 10

For the following exercises, solve for the variable.

8 (x + 3) = 64

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Algebra 2

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Question 11

For the following exercises, solve for the variable.

4 (3 - 1) x = 4

Topic:

Algebra 2

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Question 12

For the following exercises, simplify the expression.

5 l \div 3 l \cdot (9 - 6)

Topic:

Algebra 2

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Question 13

For the following exercises, simplify the expression.

5^{2} - 4 (3 x)

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Algebra 2

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Question 14

For the following exercises, solve the given problem.Jessica and her roommate, Adriana, have decided to share a change jar for joint expenses. Jessica put her loose change in the jar first, and then Adriana put her change in the jar. We know that it does not matter in which order the change was added to the jar. What property of addition describes this fact?

Topic:

Algebra 2

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Question 15

For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel. Write the equation that describes the situation.

Topic:

Algebra 2

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Question 16

The division of two whole numbers will always result in what type of number?

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Algebra 2

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Question 17

What property of real numbers would simplify the following expression:

4 + 7 (x - 1)?

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Algebra 2

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Question 18

When can you add two exponents?

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Algebra 2

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Question 19

Explain what a negative exponent does.

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Algebra 2

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Question 20

Simplify the given expression. Write answers with positive exponents.

1 1^{3} \div 1 1^{4}

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Algebra 2

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Class 9 Algebra 2 Questions asked by Filo students

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