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3 years ago

HELP QUICK TIMED!!!!!!Drag the expressions into the boxes to correctly complete the table.

Mathematics

2 answers:

ValentinkaMS [17]3 years ago

5 0

Answer:

The following expressions are polynomials:

$3x^2-5x^4+2x-12$

$x^5-5x^4+4x^3-3x^2+2x-1$

$x^3-7x^2+9x-5x^4-20$

The following expressions are not polynomials:

$\frac{4}{x^4}+\frac{3}{x^3}-\frac{2}{x^2}-1$

$x^{-5}-5x^{-4}+4x^{-3}-3x^{-2}+2x^{-1}-1$

$\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16$

Step-by-step explanation:

We are required to differentiate the expressions as polynomials and non-polynomials.

Since, we know,

A polynomial is an expression that involves variables and their coefficients separated by mathematical operations with the variables having non-negative integer values.

i.e. A polynomial is of the form, $a_{n}x^{n}+a_{n-1}x^{n-1}+.....+a_{1}x+a_{0}$ , with 'n' being non-negative integer.

Thus, according to the definition, we have that,

The following expressions are polynomials:

$3x^2-5x^4+2x-12$

$x^5-5x^4+4x^3-3x^2+2x-1$

$x^3-7x^2+9x-5x^4-20$

The following expressions are not polynomials:

$\frac{4}{x^4}+\frac{3}{x^3}-\frac{2}{x^2}-1$

$x^{-5}-5x^{-4}+4x^{-3}-3x^{-2}+2x^{-1}-1$

$\sqrt[4]{x}-\sqrt[3]{x}+4\sqrt{x}-8x+16$

a_sh-v [17]3 years ago

3 0

To qualify as a polynomial, the expression in question:
* Consists of one or more terms
* Variables are only with positive whole exponents
* No variables in the denominator of any term.

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Answer:

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Step-by-step explanation:

Given the equation of the height expressed ad;

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Given that initial height = 400feet

h(t) = - 16t^2 + 400

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Hello,

<span>SA = s^2 + 2 × s × l

Base = 4

SA= 4^2 + 2 x 4 x l
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Answer:

g) $u^{4}\cdot v^{-1}\cdot z^{3}$ , h) $\frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}$

Step-by-step explanation:

We proceed to solve each equation by algebraic means:

g) $\frac{u^{5}\cdot v}{z}\div \frac{u\cdot v^{2}}{z^{4}}$

1) $\frac{u^{5}\cdot v}{z}\div \frac{u\cdot v^{2}}{z^{4}}$ Given

2) $\frac{\frac{u^{5}\cdot v}{z} }{\frac{u\cdot v^{2}}{z^{4}} }$ Definition of division

3) $\frac{u^{5}\cdot v\cdot z^{4}}{u\cdot v^{2}\cdot z}$ $\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}$

4) $\left(\frac{u^{5}}{u} \right)\cdot \left(\frac{v}{v^{2}} \right)\cdot \left(\frac{z^{4}}{z} \right)$ Associative property

5) $u^{4}\cdot v^{-1}\cdot z^{3}$ $\frac{a^{m}}{a^{n}} = a^{m-n}$ /Result

h) $\frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}$

1) $\frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}$ Given

2) $\frac{\frac{x^{2}-16}{x^{2}-10\cdot x+25} }{\frac{3\cdot x - 12}{x^{2}-3\cdot x - 10} }$ Definition of division

3) $\frac{(x^{2}-16)\cdot (x^{2}-3\cdot x -10)}{(x^{2}-10\cdot x + 25)\cdot (3\cdot x - 12)}$ $\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}$

4) $\frac{(x+4)\cdot (x-4)\cdot (x-5)\cdot (x+2)}{3\cdot (x-5)^{2}\cdot (x-4) }$ Factorization/Distributive property

5) $\left(\frac{1}{3} \right)\cdot (x+4)\cdot (x+2)\cdot \left(\frac{x-4}{x-4} \right)\cdot \left[\frac{x-5}{(x-5)^{2}} \right]$ Modulative and commutative properties/Associative property

6) $\frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}$ $\frac{a^{m}}{a^{n}} = a^{m-n}$ / $\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot c}{b\cdot d}$ /Definition of division/Result

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3 years ago