Answer:
the new area is 1% smaller.
Step-by-step explanation:
the area of a rectangle is length times breadth.
let's call them a and b
Area = a × b
now, a is increased by 10%. that means it is multiplied by 11/10.
because 100% means the whole thing, 1% means a 1/100th part of the whole. and 10% then means 10 times the 1/100th part of 10 × 1/100 = 10/100 = 1/10
if then simmering increases by 10% it means that it is the original 100% plus 10%.
so, it is 100/100 + 10/100 = 10/10 + 1/10 = 11/10
therefore the new length is
a(new) = a(old)×11/10
in exactly the same way, when the breadth is reduced by 10% we get then
breadth(new) = breadth(old)×9/10
so, Area(new) = a(new)×b(new) = a(old)×11/10 × b(old)×9/10
remember, Area(old) = a(old)×b(old)
so, Area(new) = a(old)×b(old) × 11/10 × 9/10 =
= Area(old) × 11/10 × 9/10 =
= Area(old) × 99/100
that means the new area has lost compared to the old area 1/100th of its size. 1/100th = 1%
Expand
6 - 3x + 15 = 5x - 11
Simplify 6 - 3x + 15 to -3x + 21
-3x + 21 = 5x - 11
Add 3x to both sides
21 = 5x - 11 + 3x
Simplify 5x - 11 + 3x to 8x - 11
21 = 8x - 11
Add 11 to both sides
21 + 11 = 8x
Simplify 21 + 11 to 32
32 = 8x
Divide both sides by 8
32/8 = x
Simplify 32/8 to 4
4 = x
Switch sides
<u>x = 4</u>
Step-by-step explanation:
x³ - 23x² + 142x - 120
x³ - x² - 22x² + 22x + 120x - 120
x²(x - 1) - 22x(x - 1) + 120(x - 1)
(x - 1)(x² - 22x + 120)
(x - 1)(x² - 10x - 12x + 120)
(x - 1)[x(x - 10) - 12(x - 10)]
(x - 1) (x - 10) (x - 12)
Let x=gallons of 80% solution to be mixed
x+80=gallons go final 70% mixture
..
80%*x+30%*80=70%*(x+80)
.8x+24=.7x+56
.1x=32
x=320
gallons of 80% solution to be mixed=320
