What is the value of x?
1 answer:
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Answer:
y = -1/2x + 5/2
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 2x + 3. Its slope is 2. A line perpendicular to this one will have a slope of -1/2.
Plug this value (-1/2) into your standard point-slope equation of y = mx + b.
y = -1/2x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (1, 2). Plug in the x and y values into the x and y of the standard equation.
2 = -1/2(1) + b
To find b, multiply the slope and the input of x (1)
2 = -1/2 + b
Now, add 1/2 to both sides to isolate b.
5/2 = b
Plug this into your standard equation.
y = -1/2x + 5/2
This equation is perpendicular to your given equation (y = 2x + 3) and contains point (1, 2)
Hope this helps!
now, notice, we use the decimal format for the percent, namely 17% is 17/100 or 0.17 and so on
so.... we know, whatever "x" and "y" is, they must add up to 100 grams
thus x + y = 100
and whatever the concentrated amount is, it must add up to 17 grams for the composition
thus 0.1x + 0.2y = 17
solve for "x", to see how much is needed of the 10% alloy
what about "y"? well, y = 100 - x
Since this is a right triangle, you can use the pythagorean theorem:
(a^2+b^2=c^2)
your formula will be:
your hypotenuse will take the place of c. (8) and 6 will take the place of a.
simplify the squares:
subtract 36 from each side:
un-square the b by square rooting 28.
this will come out as a large # that's equal to:
(a^2+b^2=c^2)
your formula will be:
your hypotenuse will take the place of c. (8) and 6 will take the place of a.
simplify the squares:
subtract 36 from each side:
un-square the b by square rooting 28.
this will come out as a large # that's equal to: