We try to represent each number inside the square root as a product of a square and another number.
a) 7√32 - 5√2 + √8
√32 = √(16 *2) = √16 * √2 = 4* √2 = 4√2
√8 = √(4 *2) = √4 * √2 = 2* √2 = 2√2
7√32 - 5√2 + √8 = 7*(4√2) - 5√2 + 2√2 =
= 28√2 - 5√2 + 2√2 Factorize out √2
= (28 - 5 + 2)√2
= 25√2
b) 2√150 - 4√54 + 6√24
√150 = √(25 * 6) = √25 * √6 = 5*√6 = 5√6
√54 = √(9 * 6) = √9 * √6 = 3*√6 = 3√6
√24 = √(4 * 6) = √4 * √6 = 2*√6 = 2√6
2√150 - 4√54 + 6√24 = 2*(5√6) - 4*(3√6) + 6*(2√6)
= 2*5√6 - 4*3√6 + 6*2√6
= 10√6 - 12√6 + 12√6 Factorize √6
= (10 - 12 + 12)√6
= 10√6
We need to solve x+2y=11 for x
Let's start by adding -2y to both sides
x+2y -2y = 11-2y
x= -2y+11
Now substitute -2y+11 for x in x-2y =-1
x-2y=-1
-2y+11-2y=-1
-4y+11=-1
Add -11 to both sides
-4y+11-11=-1-11
-4y=-12
Divide both sides by -4
-4y/-4 = -12/-4
y= 3
Substitute 3 for y in x=-2y+11
x= -2y+11
x = (-2)(3)+11
x=-6+11
x=5
The answer is x=5 and y=3
(5,3)
I hope that's help:)
Multiply 100 times 5 in your head to get 500,
100 * 5 = 500
90 * 5 = 450
8 * 5 = 40
Put those 3 together into one equation, \/
(100 * 5) + (90 * 5) + (8 * 5) = 990 OR (100 * 5) + (98 * 5) = 990
depends on how distributed the teacher wants it to be.
That would first be a conversion factor is a number used to change one set of units to another, by multiplying or dividing. when a conversion is necessasry
