Which expression has the greater value justify your answer A. -8+4 B. -8×3

1 answer:

8 0

Answer:
A has the greater value

Explanation:
-8 is a negative number, so if you multiply it by any positive number greater than 1 it will only go further left on the number line (become “more” negative). However, if you add a positive number to a negative number, it will go further right on the number line.

Proof:
B: -8*3=-24
A:-8+4=-4

-4>-24

I hope this helps!

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Estimate square root of 12 to the nearest tenth. A 4.5 B 3.9 C 4.1 D 3.5

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Answer:

3.5

Step-by-step explanation:

As a first approximation of the square root, you can look at the integers relating the given number to the next lower square number. The next lower square number is 3^2 = 9.

12 = n^2 +r = 3^2 +3 . . . . . n = 3, r = 3

The approximate square root is ...

n +r/(2n+1) = 3 +3/7 ≈ 3.429

This value tends to be a little low. Alternatively, the root can be estimated as ...

n +r/(2n) = 3 +3/6 = 3.5

This value tends to be a little high.

A reasonable estimate of √12 is 3.5.

Of course, your calculator can tell you instantly that the root is about 3.464102, close to 3.5.

_____

Additional comment

The relation we used above simplifies the work of linear interpolation between the points (9, 3) and (16, 4) on the square root curve. For some n between 9 and 16, the interpolated root value r would be found from ...

(n -9)/(16 -9) = (r -3)/(4 -3)

(n -9)/7 = (r -3)/1

r = 3 +(n -9)/7 = 3 +(12 -9)/7 = 3 +3/7 . . . . as above

Note that "r" is used for "root" in this discussion. In the above answer, "r" is used for "remainder."

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