We have to find: Find \(\displaystyle{4}-{1}{\left(\frac{{1}}{{2}}\right)}\)

Notice that Find \(4-1(\frac{1}{2})=4-(1+(\frac{1}{2})) =(4-1)+\frac{1}{2} =3+(\frac{1}{2}) =3(\frac{1}{2})\)

asked 2021-08-17

Find \(\displaystyle{4}-{1}{\left(\frac{{1}}{{2}}\right)}\)

asked 2021-07-30

a) Using the remainder theorem, determine whether \(\displaystyle{\left({x}-{4}\right)}\) and \(\displaystyle{\left({x}-{1}\right)}\) are factors of the expression \(\displaystyle{x}^{{{3}}}+{3}{x}^{{{2}}}-{22}{x}-{24}\).

b) Hence, by use of long division, find all remaining factors of the expression.

b) Hence, by use of long division, find all remaining factors of the expression.

asked 2021-08-03

Simplify.

\(\displaystyle{\frac{{{1}+{\frac{{{2}}}{{{x}+{4}}}}}}{{{1}+{\frac{{{9}}}{{{x}-{3}}}}}}}\)

Step 1: Find the LCM of the denominators of the fractions in the numerator and denominator.

Step 2: Multiply the numerator and denominator of the complex fraction by the LCM.

Step 3: Factor \(\displaystyle{\frac{{{x}-{3}}}{{{x}+{4}}}}\)

Step 4: Divide out common factors.

\(\displaystyle{\frac{{{1}+{\frac{{{2}}}{{{x}+{4}}}}}}{{{1}+{\frac{{{9}}}{{{x}-{3}}}}}}}\)

Step 1: Find the LCM of the denominators of the fractions in the numerator and denominator.

Step 2: Multiply the numerator and denominator of the complex fraction by the LCM.

Step 3: Factor \(\displaystyle{\frac{{{x}-{3}}}{{{x}+{4}}}}\)

Step 4: Divide out common factors.

asked 2021-08-01

Find the least common denominator

1) \(\displaystyle{\frac{{{4}}}{{{5}}}}{\frac{{{5}}}{{{6}}}}\)

2) \(\displaystyle{\frac{{{5}}}{{{8}}}}{\frac{{{1}}}{{{6}}}}\)

3) \(\displaystyle{\frac{{{4}}}{{{5}}}}{\frac{{{1}}}{{{3}}}}\)

1) \(\displaystyle{\frac{{{4}}}{{{5}}}}{\frac{{{5}}}{{{6}}}}\)

2) \(\displaystyle{\frac{{{5}}}{{{8}}}}{\frac{{{1}}}{{{6}}}}\)

3) \(\displaystyle{\frac{{{4}}}{{{5}}}}{\frac{{{1}}}{{{3}}}}\)

asked 2021-10-21

let \(\displaystyle{u}={\left[{2},-{1},-{4}\right]},{v}={\left[{0},{0},{0}\right]}\), and \(\displaystyle{w}={\left[-{6},-{9},{8}\right]}\). we want to determine by inspection (with minimal compulation) if \(\displaystyle{\left\lbrace{u},{v},{w}\right\rbrace}\) is linearly dependent or independent. choose the best answer:

A. The set is linearly dependent because one of the vectors is a scalar multiple of another vector.

B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other.

C. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space.

D. The set is linearly dependent because two of the vectors are the same.

E. The set is linearly dependent because one of the vectors is the zero vector.

F. We cannot easily tell if the set is linearly dependent or linearly independent.

A. The set is linearly dependent because one of the vectors is a scalar multiple of another vector.

B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other.

C. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space.

D. The set is linearly dependent because two of the vectors are the same.

E. The set is linearly dependent because one of the vectors is the zero vector.

F. We cannot easily tell if the set is linearly dependent or linearly independent.

asked 2021-08-08

A sum of scalar multiple of two or more vectors (such as \(\displaystyle{c}_{{{1}}}{u}+{c}_{{{2}}}{v}+{c}_{{{3}}}{w}\), where \(\displaystyle{c}_{{{i}}}\) are scalars) is called a linear combination of the vectors. Let \(\displaystyle{i}={\left\langle{1},{0}\right\rangle},{j}={\left\langle{0},{1}\right\rangle},{u}={\left\langle{1},{1}\right\rangle}\), and \(\displaystyle{v}={\left\langle-{1},{1}\right\rangle}\).

Express \(\displaystyle{\left\langle{4},-{8}\right\rangle}\) as a linear combination of i and j (that is, find scalars \(\displaystyle{c}_{{{1}}}\) and \(\displaystyle{c}_{{{2}}}\) such that \(\displaystyle{\left\langle{4},-{8}\right\rangle}={c}_{{{1}}}{i}+{c}_{{{2}}}{j}\)).

Express \(\displaystyle{\left\langle{4},-{8}\right\rangle}\) as a linear combination of i and j (that is, find scalars \(\displaystyle{c}_{{{1}}}\) and \(\displaystyle{c}_{{{2}}}\) such that \(\displaystyle{\left\langle{4},-{8}\right\rangle}={c}_{{{1}}}{i}+{c}_{{{2}}}{j}\)).

asked 2021-07-31

A number that has exactly 2 factors (1 and itself) a called a _______ number

1) factors

2) prime

3) composite

4) multiplication

1) factors

2) prime

3) composite

4) multiplication