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umka2103 [35]
2 years ago
8

Choose Yes or No to tell if each pair of expressions is equivalent. 3x + 14 – x + 112 and 4x + 134 Choose... 2 + 6x and 2(3x + 1

) Choose... 3(x + 1) – (1 + x) and 2x + 3 Choose... 3x and 4(x + 1) – x – 4 Choose... 5.5 + 2.1x + 3.8x – 4.1 and 1.4 + 5.9x Choose...
Mathematics
1 answer:
natima [27]2 years ago
4 0

Answer:

B. 2 + 6x and 2(3x + 1) Choose

D. 3x and 4(x + 1) – x – 4 Choose...

E. 5.5 + 2.1x + 3.8x – 4.1 and 1.4 + 5.9x Choose...

Step-by-step explanation:

A. 3x + 14 – x + 112 and 4x + 134 Choose...

3x + 14 - x + 112

= 2x + 126

And

4x + 134

Not equivalent

B. 2 + 6x and 2(3x + 1) Choose...

2 + 6x

And

2(3x + 1)

= 6x + 2

Yes, equivalent

C. 3(x + 1) – (1 + x) and 2x + 3 Choose...

3(x + 1) - (1 + x)

3x + 3 - 1 - x

2x + 2

And

2x + 3

No, not equivalent

D. 3x and 4(x + 1) – x – 4 Choose...

3x

And

4(x + 1) - x - 4

= 4x + 4 - x - 4

= 3x

Yes, equivalent

E. 5.5 + 2.1x + 3.8x – 4.1 and 1.4 + 5.9x Choose...

5.5 + 2.1x + 3.8x - 4.1

1.4 + 5.9x

And

1.4 + 5.9x

Yes, equivalent

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Answer

a) C

b) B

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Step-by-step explanation

a) A linear equation can be written as y=mx+c where m is the slope and c is the intercept on the y-axis. The slope describes how y changes when x changes. A negative value means the it is a decreasing change. In our case, y is A and x is t. Thus, the slope of the equation is m=-0.062. This means that the area of glacier is decreasing by 0.062 \text{km}{}^2 = 62000 \text{m}{}^2 every year since 2000.

b) The A-intercept (= 16.2 \text{km}{}^2) represents the area covered when t=0. But t=0 starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 \text{km}{}^2.

c) A=f(t) means the area covered after year 2000. Setting it to 12 means the area covered after t years is 12 \text{km}{}^2). t is therefore the number of years since 2000 that the total area covered will be 12 \text{km}{}^2).

d) f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2 to 1 decimal place.

e) The term involving t represents the disappearing area. In 12 years, the disappeared area is 0.062\times12=0.744 =0.7 \text{km}{}^2 to 1 decimal place.

f) f(t)=16.2−0.062t =12

0.062t = 16.2-12 = 4.2

t = \dfrac{4.2}{0.062}=67.7419\ldots =67.7 years to 1 decimal place.

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