Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers?
Subtract 5 from both sides of the equation
Add 3 to both sides of the equation
Add 5 to both sides of the equation
Subtract 3 from both sides of the equation
The given quadratic equation can be represented in the form
by adding 3 to both sides of the equation.
The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by
where .
The given quadratic equation is
Case 1: Subtract 5 from both sides of the equation
i.e.
⇒
The LHS of the above equation can not be expressed in form. Hence, it is not the correct step.
Case 2: Add 3 to both sides of the equation.
i.e.
⇒
⇒
⇒
The above equation is expressed in form where p = 4 and q = 3.
Case 3: Add 5 to both sides of the equation
i.e.
⇒
The LHS of the above equation can not be expressed in the . Hence, it is not the correct step.
Case 4: Subtract 3 from both sides of the equation
i.e.
⇒
The LHS of the above equation can not be expressed in the . Hence, it is not the correct step.
Hence, "Add 3 to both sides of the equation" is the correct step.
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a. True
b. False
The measure of each angle will be 10° and 170°.
A supplementary angle refers to an angle that has the sum to be equal to 180°.
Let the small angle be represented by x
Therefore, the big angle will be: = 17 × x = 17x
Therefore, the value of both angles will be:
x + 17x = 180
18x = 180
Divide both side by 18
18x/18 = 180/18
x = 10
Therefore, the bigger angle will be:
17x = 17 × 10 = 170
Therefore, the angles are 10° and 170°
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