Answer:
0.4375
Step-by-step explanation:
3/7= 0.42857143
rounded to the neared thousandth, it is 0.429
To solve this system by substitution, we must substitute in the value we are given for x in terms of y (the first equation) into the second equation. This is modeled below:
x = -8y - 15
2x + 5y = -8
2 (-8y - 15) + 5y = -8
Now, we should solve this new equation for y. To begin, we should use the distributive property to get rid of the parentheses on the left side of the equation and begin the simplification process.
-16y - 30 + 5y = -8
Next, we can combine like terms on the left side of the equation by adding together the two terms that both contain the variable y.
-11y - 30 = -8
Next, we should add 30 to both sides in order to move all of the constant (number) terms to the left side of the equation.
-11y = 22
After that, we should divide both sides of the equation by -11 in order to get the variable y alone.
y = -2
Now, we can substitute our value for y back into one of our original equations (it doesn't matter which one you choose; they will yield the same answer).
x = -8y - 15
x = -8(-2) - 15
To simplify, we should following the order of operations outlined by PEMDAS and compute the multiplication and then the subtraction.
x = 16 - 15
x = 1
Therefore, the answer to the system is x = 1 and y = -2, or (1,-2) when written as an ordered pair.
Hope this helps!
<h3>
Answer: 5 - 4i (choice A)</h3>
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Work Shown:
x = the other number
(5+4i)*x = 41
x = 41/(5+4i)
x = 41*(5-4i)/( (5+4i)*(5-4i) ) ..... see note below
x = 41*(5-4i)/( 41 )
x = (41/41)*(5-4i)
x = 5 - 4i
As a way to check, (5+4i)*(5-4i) = 5^2+4^2 = 25+16 = 41
The rule used is (a-bi)(a+bi) = a^2 + b^2
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Note: I multiplied top and bottom by (5-4i) to get rid of the imaginary term in the denominator.
