To solve the quadratic by complete square method we proceed as follows:
x²-6x+7=0
this can be written as:
x²-6x=-7
but
c=(-b/2a)^2
c=(-(-6)/2)^2=9
next we add 9 on both sides of our expression to get:
x²-6x+9=-7+9
x²-6x+9=2
factoring out the LHS we get:
(x-3)(x-3)=2
(x-3)²=2
getting the square root of both sides we obtain:
x-3=+/-√2
hence:
x=3+/-√2
The absolute value equation for the scores within one standard deviation of the mean is:
|x - 20.9| = 5.3.
The minimum score that is within one standard deviation of the mean is of 15.6.
<h3>What is the absolute value function?</h3>
The absolute value function is defined by:
It measures the distance of a point x to the origin of x = 0.
One standard deviation is of 5.3, while the mean is of 20.9, hence the absolute value equation for the scores within one standard deviation of the mean is:
|x - 20.9| = 5.3.
Which means that the minimum score is:
x - 20.9 = -5.3
x = 15.6.
More can be learned about the absolute value function at brainly.com/question/24734454
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Answer:
C.
Multiply each term inside the parentheses by 3.
Step-by-step explanation:
Answer:
Option :" Use distance formula to prove that the lengths of the diagonals are equal" is correct
Step-by-step explanation:
Option : Use distance formula to prove that the lengths of the diagonals are equal" is correct.
Because " By using the coordinate geometry to prove that the diagonals of the rectangle are congruent, first we have to find the lengths of the top and bottom of the rectangle and then solve it for the lengths of the diagonals by using the distance formula".
Answer:
x = 12
m(QS) = 52°
m(PD) = 152°
Step-by-step explanation:
Recall: Angle formed by two secants outside a circle = ½(the difference of the intercepted arcs)
Thus:
m<R = ½[m(PD) - m(QS)]
50° = ½[(12x + 8) - (4x + 4)] => substitution
Solve for x
Multiply both sides by 2
2*50 = (12x + 8) - (4x + 4)
100 = (12x + 8) - (4x + 4)
100 = 12x + 8 - 4x - 4 (distributive property)
Add like terms
100 = 8x + 4
100 - 4 = 8x
96 = 8x
96/8 = x
12 = x
x = 12
✔️m(QS) = 4x + 4 = 4(12) + 4 = 52°
✔️m(PD) = 12x + 8 = 12(12) + 8 = 152°
