ALGEBRA I:
QUESTION: 18
Find the ratios . a = 4b
Solution:
a = 4b
so, b = ¼ a
The ratio of a:b is 4:1
ALGEBRA
QUESTION:19
Find the ratio of a and b. 4a + 2b = 0.
Solution:
We can solve the equation,
4a + 2b = 0
4a = -2b
Divide both sides by -2
-2a = b
The ratio of a: b is equal to -1/2 : 1 or -1 : 2
ALGEBRA
QUESTION:20
Factor trinomial 28x^2 - 33x - 28
Solution:
28x^2 - 33x - 28. Procedure for splitting middle term
To factor this trinomial, Product of coefficient of x^2 and constant = -784
Split the middle term, sum of the factors of -784 = -33
Using this method we couldn't factor the given trinomial
exactly with whole numbers. So, use quadratic formula
to find the factors.
Use quadratic formula here,
-b +/- root (b^2 - 4ac)
x = -----------------------------
2a
Here, a = 28, b= -33 and c - -28
Plug in the values of a , b and c in the formula,
-(-33) +/- (1089) + 3136
x = ----------------------------------
2(28)
33+/- 4225
x = ----------------
56
x = (33+/- 65)/ 56
x = 98/56 or x = -32/56
x = 1.75 or x = -0.57
The factors are (x- 1.75) (x+0.57)
ALGEBRA
QUESTION:21
Find the solution using completing square method.
x^2 + 10x -9 = 0
Solution:
x^2 + 10x - 9 = 0
x^2 + 2.x.5 -9 =0
Here, to complete the square, just add 5^2 and subtract 5^2 in the left side of the equation.
x^2 + 10x +5^2 - 5^2 -9 = 0
Using the identity (a+b)^2 = a^2 +2ab + b^2
We can write x^2 + 10x + 5^2 as (x+5)^2
For the given equation,
(x+5)^2 - 25-9 = 0
(x+5)^2 -34 = 0
(x+5)^2 = 34
To solve for x
(x+5)(x+5) = 34
x+5 = 34 or x+5 = -34
x = 34 -5 = 29 or x = -34-5 = -39.
x = 29 or x = -39
ALGEBRA
QUESTION: 22
Find the solution using completing square method.
x^2- 6x + 9 = 1
Solution:
x^2 - 6x +9 = 1
x^2 - 2.x.3 + 3^2 =1
The left side of the equation is already in complete squared form, here,
We no need to add or subtract anything.
We can write x^2-6x +9 = (x-3)^2
For the given equation,
(x - 3)^2 = 1
To solve for x
(x-3)(x-3) = 1
x -3 = 1 or x-3 = -1
x = 1+3 or x = -1+3
x = 4 or x = 2.
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