Solve this quadratic equation using factorization 8xsquared-14x-4=0
2 answers:
Answer:
x = - , x = 2
Step-by-step explanation:
Given
8x² - 14x - 4 = 0 ( divide through by 2 to simplify )
4x² - 7x - 2 = 0
To factorise the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 2 = - 8 and sum = - 7
The factors are - 8 and + 1
Use these factors to split the x- term
4x² - 8x + x - 2 = 0 ( factor the first/second and third/fourth terms )
4x(x - 2) + 1(x - 2) = 0 ← factor out (x - 2) from each term
(x - 2)(4x + 1) = 0
Equate each factor to zero and solve for x
4x + 1 = 0 ⇒ 4x = - 1 ⇒ x = -
x - 2 = 0 ⇒ x = 2
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Answer:
Option A is correct
The only figure after composition of to figure R is Figure H
Step-by-step explanation:
From the given figure in R;
The coordinates in Figure R ;
(1 , -1) , (2, -2) ,(4, -2) ( 0, -4)
Composite function defined as when one function is substituted into another function.
To Apply the composition to figure R;
First apply the Reflection in Figure R;
The rule of reflection is given by:
By applying the rule of reflection in Figure R ,
then, the coordinates becomes;
(1 , -1) (1, 1)
(2 , -2) (2, 2)
(4 , -2) (2, 4)
(0, -4) (4, 0)
Now, apply the translation
Translation : It is a type of transformation that moves each point in a figure the same distance in the same direction.
then,
the rule of translation is:
Apply the rule of translation on coordinates (1,1) , (2,2), (2,4) and (4,0)
then
(1 , 1) (1+0 1+3) =(1,4)
(2, 2) (2+0 2+3) =(2, 5)
(2, 4) (2+0 4+3) =(2 ,7) and
(4, 0) (4+0 0+3) =(4 ,3)
Then, the only figure after composition of to figure R is Figure H