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marta [7]
3 years ago
10

How many solutions exist for the given equation? 0.75(x+40)=3(4x+1)-2

Mathematics
2 answers:
AveGali [126]3 years ago
6 0
The given equation is
0.75(x + 40) = 3(4x + 1) - 2

Expand the equation.
0.75x + 30 = 12x + 3 - 2
0.75 - 12x = 3 - 2 - 30
-11.25x = -29
x = -29/-11.25 = 2.5778

Answer: There is 1 solution, which is 2.5778.

maw [93]3 years ago
4 0
Let's eliminate the fractional multiplier 0.75.  To do this, mult the entire equation by 4/3:

x+40 = (4/3)(3)(4x+1) - 2(4/3)

(4/3)(3) simplifies to just 4, so now we have:

x+40 = 4(4x+1) - 8/3

Mult. all 3 terms by 3 to eliminate the fraction:

3x + 120 = 12(4x+1) - 8

Perform the multiplication:

3x + 120  = 48x + 12 - 8,            or            116 = 45x

Solving for x,    x = 2.578, or     x = 7/90 (answer)


We could also simplify the original equation,  <span>0.75(x+40)=3(4x+1)-2, by multiplying all 3 terms by 100:

75x + 3000 = 1200x + 300 - 200

Then 3000 - 300 + 200 = 1125x, and x = 7/90 (same as before)</span>
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An equation is an expression that shows the relationship between two or more numbers and variables.

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Step-by-step explanation:

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The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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P(X > 25) = 0.69

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