Which number can each term of the equation be multiplied by to eliminate the decimals before solving? –m + 0.02 + 2.1m = –1.45 – 4.81m a)0.01 b)0.1 c)10 d)100

The decimals place in a number can be shifted right or left by multiplying or dividing by powers of 10 respectively

The option which gives the number that will multiply each term of the equation -m + 0.02 + 2.1·m = -1.45 - 4.81·m to eliminate the decimals before solving, is option D)

D) 100

Reason:

The given expression is presented as follows;

-m + 0.02 + 2.1·m = -1.45 - 4.81·m

The number that can multiply the terms to eliminate the decimals before solving

Solution;

The number of decimal places to which the coefficient and constant values are given = 2 decimal places

Therefore, to eliminate the decimal places, the decimal point of each term has to be moved two places to the right

To move decimal points to the right x number of places is given by multiplying the number by 10ˣ

Therefore, to move the decimal point two places to the right so as to eliminate the decimal point, by multiplicative property of equality, we have;

10² × (-m + 0.02 + 2.1·m) = 10² × (-1.45 - 4.81·m)

10² = 100, therefore, we have;

100 × (-m + 0.02 + 2.1·m) = 100 × (-1.45 - 4.81·m)

-100·m + 2 + 2,100·m = -145 - 481·m

Therefore, the number the equation, -m + 0.02 + 2.1·m = -1.45 - 4.81·m, is to be multiplied by is 100

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since the 2 in 0.02 is in the hundredths place, you need to multiply that by 100 to eliminate the decimal, then you would need to multiply the other numbers by 100 as well

 Answer is D) 100

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4