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3 years ago

Select the statement that describes the expression 5 x (8 − 5) ÷ 3.

Mathematics

1 answer:

lys-0071 [83]3 years ago

8 0

Step-by-step explanation:

Substitution: ‘Find the value of 2x + 3 if x = 4.’ In this case the pronumeral is given the value 4.

Solving an equation: ‘Find x if 2x + 3 = 8.’ Here we are seeking the value of the pronumeral that makes the sentence true.

Identity: ‘The statement of the commutative law: a + b = b + a.’ Here a and b can be any real numbers.

Formula: ‘The area of a rectangle is A = lw.‘ Here the values of the pronumerals are connected by the formula.

Equation of a line or curve: ‘The general equation of the straight line is y = mx + c.’

Here m and c are parameters. That is, for a particular straight line, m and c are fixed.

In some languages other than English, one distinguishes between ‘variables’ in functions and ‘unknown quantities’ in equations (‘incógnita’ in Portuguese/Spanish, ‘inconnue’ in French) but this does not completely clarify the situation. The terms such as variable and parameter cannot be precisely defined at this stage and are best left to be introduced later in the development of algebra.

An algebraic expression is an expression involving numbers, parentheses, operation signs and pronumerals that becomes a number when numbers are substituted for the pronumerals. For example 2x + 5 is an expression but +) × is not.

Examples of algebraic expressions are:

3x + 1 and 5(x2 + 3x)

As discussed later in this module the multiplication sign is omitted between letters and between a number and a letter. Thus substituting x = 2 gives

3x + 1 = 3 × 2 + 1 = 7 and 5(x2 + 3x) = 5(22 + 3 × 2) = 30.

In this module, the emphasis is on expressions, and on the connection to the arithmetic that students have already met with whole numbers and fractions. The values of the pronumerals will therefore be restricted to the whole numbers and non-negative fractions.

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Answer:

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Step-by-step explanation:

6 0

3 years ago

(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

3 years ago

I really need help quickly please!!!!

Vladimir [108]

Answer:The third one is!!

Step-by-step explanation:

The commutative property of addition says that changing the order of addends does not change the sum. Here's an example: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+4

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3 years ago

Read 2 more answers

The hight of Niagara Falls is 56 meters. How many kilometers hight is Niagara Falls?

charle [14.2K]

One kilometer=1000 meters

1 meter= 0.001 kilometer

56 meters = 0.056 kilometers

Therefore, the height of Niagara falls is 0.056 kilometers

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4 years ago

If the point (-1/2, y ) lies on the line whose equation is 2 x - 3 y = 6, what is the value of y ?

Ghella [55]

The answer is -7/3. First put -1/2 for 2x {2(-1/2)} and multiply that should give you -1. Then you do the opposite of -1 which is +1 and add that to 6 which is 7. After you’re going to divide -3y from 7. Which should give you -7/3. Hopes this helps:)

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3 years ago