Standard form is ax+by=c
normally a is positive and a and b are integres
y=mx+b
m=slope
b=yint
y=1/2x+3
minus 1/2 x both sides
-1/2x+y=3
times -2
x-2y=-6
Answer:
1. 8y - 9y = -1y
( 8 - 9 = -1)
3. <u>8a</u> - 6 <u>+a</u> - 1
( i have showed the like terms here)
8a - 1a= 7a
-6 - 1 = -7
7a - 7
5. -x - 2 + 15x
( i have showed the like terms here)
-x + 15x = 14x
(x = 1)
14x + 2
7.<u> 8d</u> - 4 <u>- d</u> - 2
( i have showed the like terms here)
8d - d = 7d
-4 -2 = -6
7d - 6
8. 9a <u>+ 8</u> - 2a<u> - 3</u> - 5a
( i have showed the like terms here)
9a - 2a - 5a = 2a
8 - 3= 5
2a + 5
Step-by-step explanation:
= (1 + 5z)(-4)
= (1 + 5z) × (-4)
= 1.(-4) + 5z. (-4)
= -4 - 20z
I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
Decimal Form:
4.59375<span>
</span>
Exact Form:
<span>147/32</span><span>
</span>Mixed Number Form: <span>4 19/32</span>
