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OverLord2011 [107]
3 years ago
12

When adding two numbers, the number of significant figures in the sum is equal to the number of significant figures in the least

accurate of the numbers being added. Group of answer choices True False
Mathematics
1 answer:
inessss [21]3 years ago
7 0

<u>Answer:</u> The given statement is true.

<u>Step-by-step explanation:</u>

Significant figures are defined as the figures that are present in a number. It expresses the magnitude of a quantity to a specific degree of accuracy.

There are some rules to detect the significant figures in a number:

  • All digits ranging from 1 to 9 are always considered significant.
  • Every non-zero number is always considered significant. For example, 274, 2.74, and 27.4 all have three significant figures.
  • All zero’s that are present between the integers is always considered significant. For example, 5007, 5.007, and 50.07 all have four significant figures.
  • All zero’s preceding the first integer is never considered significant. For example, 0.0089 has two significant figures.
  • All zeros that are present after the decimal point are always significant. For example, 4.800, 48.00, and 480.0 all have four significant figures.

<u>Rule applied when numbers are added or subtracted:</u>

The number having less number of significant figures after the decimal point will determine the number of significant figures in the final answer.

Hence, the given statement is true.

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1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x
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1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is (2x+10)^\circ, so the measure of arc DF is

m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ

The inscribed angle theorem tells us that the central angle subtended by arc DF, \angle DOF, has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

m\angle DOF=2m\angle OEF=64^\circ

so the measure of arc DF is also 64 degrees. So we have

170-2x=64\implies106=2x\implies\boxed{x=53}

###

2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}

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