Answer:
x = 6
Step-by-step explanation:
3x + 4 = 5x - 8
==> add 8 to both sides
in doing so we get 3x + 4 + 8 = 5x - 8 + 8
the -8 and the +8 cancels out and 4 + 8 = 12
we are left with 3x + 12 = 5x
==> subtract 3x from both sides
in doing so we get 3x - 3x + 12 = 5x - 3x
the 3x and -3x cancel out and 5x - 3x = 2x
we are left with 12 = 2x
==> divide both sides by 2
in doing so we get 12/2 which equals 6 and 2x/2x which leaves us with
6 = x
9514 1404 393
Answer:
(b) x +2y = 8
Step-by-step explanation:
The only offered line that includes the given point is ...
x +2y = 8
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We can check the other choices:
x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)
2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice
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<em>Getting there from scratch</em>
The standard form equation for a line can be written from ...
(y2 -y1)x -(x2 -x1)y = constant
(-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)
-4x -8y = constant
For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.
x +2y = constant
The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...
x +2y = (2) +2(3) = constant = 8
The desired line has the equation ...
x +2y = 8
The answer would be 78 because 10% of 60 is 6. 6 x 3 = 18 60+18=78
Start with 180.
<span>Is 180 divisible by 2? Yes, so write "2" as one of the prime factors, and then work with the quotient, 90. </span>
<span>Is 90 divisible by 2? Yes, so write "2" (again) as another prime factor, then work with the quotient, 45. </span>
<span>Is 45 divisible by 2? No, so try a bigger divisor. </span>
<span>Is 45 divisible by 3? Yes, so write "3" as a prime factor, then work with the quotient, 15 </span>
<span>Is 15 divisible by 3? [Note: no need to revert to "2", because we've already divided out all the 2's] Yes, so write "3" (again) as a prime factor, then work with the quotient, 5. </span>
<span>Is 5 divisible by 3? No, so try a bigger divisor. </span>
Is 5 divisible by 4? No, so try a bigger divisor (actually, we know it can't be divisible by 4 becase it's not divisible by 2)
<span>Is 5 divisible by 5? Yes, so write "5" as a prime factor, then work with the quotient, 1 </span>
<span>Once you end up with a quotient of "1" you're done. </span>
<span>In this case, you should have written down, "2 * 2 * 3 * 3 * 5"</span>
