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natita [175]
3 years ago
5

Which of the following equations shows the correct way to apply the Commutative Property of Addition?

Mathematics
1 answer:
o-na [289]3 years ago
4 0

Answer:

Commutative Property of Addition: a + b = b + a

Step-by-step explanation:

The Commutative Property of Addition implies that even on changing the order of addition the final result (i.e. the sum) remains the same.

  • Consider the addition of two numbers, say <em>a</em> and <em>b</em>:

a + b = b + a

Suppose <em>a</em> = 5 and <em>b</em> = 6, then:

<em>a</em> + <em>b</em> = 5 + 6 = 11

<em>b</em> + <em>a</em> = 6 + 5 = 11.

Thus, a + b = b + a.

  • Consider the addition of three numbers, say <em>a, b</em> and <em>c</em>:

a + b + c= a + c + b = b + a + c = c + a + b

Suppose <em>a</em> = 4, <em>b</em> = 3 and <em>c</em> = 6, then:

a + b + c = 4 + 3 + 6 = 13

a + c + b = 4 + 6 + 3 = 13

b + a + c = 3 + 4 + 6 = 13

c + a + b = 6 + 4 + 3 = 13.

Thus, a + b + c= a + c + b = b + a + c = c + a + b.

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What is the enlargement ratio if you enlarge the figure to have a width of 16 units and length of 12 units
Fantom [35]

Answer:

The enlargement ratio is 3:4

Step-by-step explanation:

We are given

a width of 16 units and length of 12 units

so,

W=16

and

L=12

now, we can find enlargement ratio

we can use formula

enlargement ratio = (length)/(width)

=\frac{L}{W}

now, we can plug values

=\frac{12}{16}

now, we can simplify it

=\frac{3}{4}

So,

The enlargement ratio is 3:4

6 0
3 years ago
Differentiating a Logarithmic Function In Exercise, find the derivative of the function.
sp2606 [1]

Answer:

\dfrac{d(f(x))}{dx} = \dfrac{2}{x}

Step-by-step explanation:  

We are given the following function in the question:

f(x) = \ln (3x^2)

We have to derivate the given function.

Formula:

\dfrac{d(\ln x)}{dx} = \dfrac{1}{x}\\\\\dfrac{d(x^n)}{dx} = nx^{n-1}

The derivation takes place in the following manner

f(x) = \ln (3x^2)\\\\\dfrac{d(f(x))}{dx} = \displaystyle\frac{d(\ln(3x^2))}{dx}\\\\=\frac{1}{3x^2}\times \frac{d(3x^2)}{dx}\\\\= \frac{1}{3x^2}\times (6x)\\\\=\frac{6x}{3x^2}\\\\=\frac{2}{x}

\dfrac{d(f(x))}{dx} = \dfrac{2}{x}

5 0
3 years ago
The residual plot for a data set is shown.
BaLLatris [955]
The correct answer is: <span>D. The regression line is not a good model because the points in the residual plot form a curve.  (i know this because i just passed the test ;) )</span>
5 0
3 years ago
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A parabola with the vertex at (1.5, 12.5) inscribes a segment of length 5 on x-axis. What is the area of the triangle formed by
damaskus [11]

Answer:

  20 units²

Step-by-step explanation:

The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at

  1.5 ± 5/2 = {-1, 4}

Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...

  0 = a(4 -1.5)² +12.5

  0 = 6.25a +12.5 . . . . . simplify

  0 = a +2 . . . . . . . . . . . divide by 6.25

  -2 = a

Then the standard-form equation of the parabola is ...

  y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5

  y = -2x² +6x +8

This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...

  A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²

5 0
3 years ago
Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album o
sammy [17]

He took 36 weeks to compose 12 songs.

Unit rate : Divide total weeks by total songs:

Unit Rate = 36 / 12 = 3 weeks per song.

5 0
3 years ago
Read 2 more answers
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