IDNLearn.com provides a user-friendly platform for finding and sharing accurate answers. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.
Sagot :
Alright, let's evaluate each expression as per the given values.
### 2. Evaluate each expression using [tex]\( p = -\frac{1}{2}, q = -\frac{3}{4}, r = \frac{4}{3} \)[/tex].
#### a) [tex]\( p \cdot q \)[/tex] and [tex]\( q^2 \cdot r \)[/tex]
1. [tex]\( p \cdot q = -\frac{1}{2} \cdot -\frac{3}{4} = 0.375 \)[/tex]
2. [tex]\( q^2 \cdot r = \left(-\frac{3}{4}\right)^2 \cdot \frac{4}{3} = 0.75 \)[/tex]
#### b) [tex]\( r \cdot q \)[/tex]
[tex]\( r \cdot q = \frac{4}{3} \cdot -\frac{3}{4} = -1.0 \)[/tex]
#### c) [tex]\( q \cdot r \cdot p \)[/tex]
[tex]\( q \cdot r \cdot p = -\frac{3}{4} \cdot \frac{4}{3} \cdot -\frac{1}{2} = 0.5 \)[/tex]
#### d) [tex]\( p^2 \cdot r \)[/tex]
[tex]\( p^2 \cdot r = \left(-\frac{1}{2}\right)^2 \cdot \frac{4}{3} = 0.3333333333333333 \)[/tex]
### 3. Simplify each of the following.
#### a) [tex]\( \left(\frac{2}{3}-\left(-\frac{1}{3}\right)\right) \div \left(\frac{-3}{4} - \left(-\frac{2}{3}\right)\right) \)[/tex]
[tex]\( = -11.999999999999995 \)[/tex]
#### b) [tex]\( \left(\frac{-1}{8}+\frac{1}{-4}\right) \left(\frac{-1}{-2}+\frac{1}{-6}\right) \)[/tex]
(first expression labeled as b)
[tex]\( = -0.125 \)[/tex]
#### c) [tex]\( \left(\frac{2}{-3} - \left(-\frac{1}{2}\right)\right) \div \left(\frac{-3}{2} - \frac{3}{2}\right) \)[/tex]
(second expression labeled as b)
[tex]\( = 0.055555555555555546 \)[/tex]
#### d) [tex]\( \left(\frac{4}{5}-\frac{3}{-4}\right) \left(\frac{-1}{3}-\frac{1}{4}\right) \)[/tex]
[tex]\( = -0.9041666666666666 \)[/tex]
### 4. Find the value of the expression [tex]\( x^2 - p \cdot q \)[/tex] for the following.
#### a) [tex]\( x = \frac{1}{2}, p = -\frac{1}{3}, q = -\frac{1}{4} \)[/tex]
[tex]\( x^2 - p \cdot q = \left(\frac{1}{2}\right)^2 - \left(-\frac{1}{3} \cdot -\frac{1}{4}\right) = 0.16666666666666669 \)[/tex]
#### b) [tex]\( x = -\frac{3}{4}, p = \frac{1}{2}, q = -\frac{2}{3} \)[/tex]
[tex]\( x^2 - p \cdot q = \left(-\frac{3}{4}\right)^2 - \left(\frac{1}{2} \cdot -\frac{2}{3}\right) = 0.8958333333333333 \)[/tex]
### 5. Evaluate each expression using [tex]\( x = -\frac{1}{2}, y = -\frac{3}{4}, z = \frac{4}{3} \)[/tex].
#### a) [tex]\( x \cdot y + z \)[/tex]
[tex]\( x \cdot y + z = -\frac{1}{2} \cdot -\frac{3}{4} + \frac{4}{3} = 1.7083333333333333 \)[/tex]
#### b) [tex]\( y - x \cdot z \)[/tex]
[tex]\( y - x \cdot z = -\frac{3}{4} - \left(-\frac{1}{2} \cdot \frac{4}{3}\right) = -0.08333333333333337 \)[/tex]
#### c) [tex]\( y \cdot z \div x \)[/tex]
[tex]\( y \cdot z \div x = \left(-\frac{3}{4} \cdot \frac{4}{3}\right) \div -\frac{1}{2} = 2.0 \)[/tex]
#### d) [tex]\( 2 \cdot x - 3 \cdot y \)[/tex]
[tex]\( 2 \cdot x - 3 \cdot y = 2 \cdot -\frac{1}{2} - 3 \cdot -\frac{3}{4} = 1.25 \)[/tex]
#### e) [tex]\( \frac{1}{2} \cdot y - \frac{2}{3} \cdot x \)[/tex]
[tex]\( \frac{1}{2} \cdot y - \frac{2}{3} \cdot x = \frac{1}{2} \cdot -\frac{3}{4} - \frac{2}{3} \cdot -\frac{1}{2} = -0.041666666666666685 \)[/tex]
#### f) [tex]\( \frac{3}{4} \cdot x - \frac{3}{8} \cdot y \)[/tex]
[tex]\( \frac{3}{4} \cdot x - \frac{3}{8} \cdot y = \frac{3}{4} \cdot -\frac{1}{2} - \frac{3}{8} \cdot -\frac{3}{4} = -0.09375 \)[/tex]
#### g) [tex]\( 2 \cdot x + 3 \cdot y - 2 \cdot z \)[/tex]
[tex]\( 2 \cdot x + 3 \cdot y - 2 \cdot z = 2 \cdot -\frac{1}{2} + 3 \cdot -\frac{3}{4} - 2 \cdot \frac{4}{3} = -5.916666666666666 \)[/tex]
#### h) [tex]\( \frac{1}{4} \cdot x - \frac{2}{3} \cdot y \div (4 \cdot z) \)[/tex]
[tex]\( \frac{1}{4} \cdot x - \frac{2}{3} \cdot y \div (4 \cdot z) = \frac{1}{4} \cdot -\frac{1}{2} - \frac{2}{3} \cdot -\frac{3}{4} \div (4 \cdot \frac{4}{3}) = -0.03125 \)[/tex]
These detailed steps should help you understand the process of evaluating each expression with the given values.
### 2. Evaluate each expression using [tex]\( p = -\frac{1}{2}, q = -\frac{3}{4}, r = \frac{4}{3} \)[/tex].
#### a) [tex]\( p \cdot q \)[/tex] and [tex]\( q^2 \cdot r \)[/tex]
1. [tex]\( p \cdot q = -\frac{1}{2} \cdot -\frac{3}{4} = 0.375 \)[/tex]
2. [tex]\( q^2 \cdot r = \left(-\frac{3}{4}\right)^2 \cdot \frac{4}{3} = 0.75 \)[/tex]
#### b) [tex]\( r \cdot q \)[/tex]
[tex]\( r \cdot q = \frac{4}{3} \cdot -\frac{3}{4} = -1.0 \)[/tex]
#### c) [tex]\( q \cdot r \cdot p \)[/tex]
[tex]\( q \cdot r \cdot p = -\frac{3}{4} \cdot \frac{4}{3} \cdot -\frac{1}{2} = 0.5 \)[/tex]
#### d) [tex]\( p^2 \cdot r \)[/tex]
[tex]\( p^2 \cdot r = \left(-\frac{1}{2}\right)^2 \cdot \frac{4}{3} = 0.3333333333333333 \)[/tex]
### 3. Simplify each of the following.
#### a) [tex]\( \left(\frac{2}{3}-\left(-\frac{1}{3}\right)\right) \div \left(\frac{-3}{4} - \left(-\frac{2}{3}\right)\right) \)[/tex]
[tex]\( = -11.999999999999995 \)[/tex]
#### b) [tex]\( \left(\frac{-1}{8}+\frac{1}{-4}\right) \left(\frac{-1}{-2}+\frac{1}{-6}\right) \)[/tex]
(first expression labeled as b)
[tex]\( = -0.125 \)[/tex]
#### c) [tex]\( \left(\frac{2}{-3} - \left(-\frac{1}{2}\right)\right) \div \left(\frac{-3}{2} - \frac{3}{2}\right) \)[/tex]
(second expression labeled as b)
[tex]\( = 0.055555555555555546 \)[/tex]
#### d) [tex]\( \left(\frac{4}{5}-\frac{3}{-4}\right) \left(\frac{-1}{3}-\frac{1}{4}\right) \)[/tex]
[tex]\( = -0.9041666666666666 \)[/tex]
### 4. Find the value of the expression [tex]\( x^2 - p \cdot q \)[/tex] for the following.
#### a) [tex]\( x = \frac{1}{2}, p = -\frac{1}{3}, q = -\frac{1}{4} \)[/tex]
[tex]\( x^2 - p \cdot q = \left(\frac{1}{2}\right)^2 - \left(-\frac{1}{3} \cdot -\frac{1}{4}\right) = 0.16666666666666669 \)[/tex]
#### b) [tex]\( x = -\frac{3}{4}, p = \frac{1}{2}, q = -\frac{2}{3} \)[/tex]
[tex]\( x^2 - p \cdot q = \left(-\frac{3}{4}\right)^2 - \left(\frac{1}{2} \cdot -\frac{2}{3}\right) = 0.8958333333333333 \)[/tex]
### 5. Evaluate each expression using [tex]\( x = -\frac{1}{2}, y = -\frac{3}{4}, z = \frac{4}{3} \)[/tex].
#### a) [tex]\( x \cdot y + z \)[/tex]
[tex]\( x \cdot y + z = -\frac{1}{2} \cdot -\frac{3}{4} + \frac{4}{3} = 1.7083333333333333 \)[/tex]
#### b) [tex]\( y - x \cdot z \)[/tex]
[tex]\( y - x \cdot z = -\frac{3}{4} - \left(-\frac{1}{2} \cdot \frac{4}{3}\right) = -0.08333333333333337 \)[/tex]
#### c) [tex]\( y \cdot z \div x \)[/tex]
[tex]\( y \cdot z \div x = \left(-\frac{3}{4} \cdot \frac{4}{3}\right) \div -\frac{1}{2} = 2.0 \)[/tex]
#### d) [tex]\( 2 \cdot x - 3 \cdot y \)[/tex]
[tex]\( 2 \cdot x - 3 \cdot y = 2 \cdot -\frac{1}{2} - 3 \cdot -\frac{3}{4} = 1.25 \)[/tex]
#### e) [tex]\( \frac{1}{2} \cdot y - \frac{2}{3} \cdot x \)[/tex]
[tex]\( \frac{1}{2} \cdot y - \frac{2}{3} \cdot x = \frac{1}{2} \cdot -\frac{3}{4} - \frac{2}{3} \cdot -\frac{1}{2} = -0.041666666666666685 \)[/tex]
#### f) [tex]\( \frac{3}{4} \cdot x - \frac{3}{8} \cdot y \)[/tex]
[tex]\( \frac{3}{4} \cdot x - \frac{3}{8} \cdot y = \frac{3}{4} \cdot -\frac{1}{2} - \frac{3}{8} \cdot -\frac{3}{4} = -0.09375 \)[/tex]
#### g) [tex]\( 2 \cdot x + 3 \cdot y - 2 \cdot z \)[/tex]
[tex]\( 2 \cdot x + 3 \cdot y - 2 \cdot z = 2 \cdot -\frac{1}{2} + 3 \cdot -\frac{3}{4} - 2 \cdot \frac{4}{3} = -5.916666666666666 \)[/tex]
#### h) [tex]\( \frac{1}{4} \cdot x - \frac{2}{3} \cdot y \div (4 \cdot z) \)[/tex]
[tex]\( \frac{1}{4} \cdot x - \frac{2}{3} \cdot y \div (4 \cdot z) = \frac{1}{4} \cdot -\frac{1}{2} - \frac{2}{3} \cdot -\frac{3}{4} \div (4 \cdot \frac{4}{3}) = -0.03125 \)[/tex]
These detailed steps should help you understand the process of evaluating each expression with the given values.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.
