Solve the equation by completing the square. If necessary, round to the nearest hundredth.

2 answers:

8 0

Ax^2+bx=c
REMEMBER THIS

ok
first, make sure that a is 1
done

now take 1/2 of b and square it

-18/2=-9, (-9)^2=81
add that to both sides

x²-18x+81=19+81
x²-18x+81=99
factor perfect square
(x-9)²=100
square root both sides
don't forget positive and negative root
x-9=10
x-9=-10
ad 9 to both sides

x=19
x=-1

answer is -1; 19

2nd choice is answer

Kobotan [32]4 years ago

5 0

Answer:

Option B. x = -1, 19

Step-by-step explanation:

The given equation is x² - 18x = 19

We can get the value of x by factorizing the expression or by quadratic formula.

We will try to factorize the equation first. If we find no factors then we will apply quadratic formula to get the value of x.

x² - 18x - 19 = 0

x² - 19x + x - 19 = 0

x(x - 19) + 1(x - 19) = 0

(x - 19)(x + 1) = 0

x = 19, -1 will be the solutions.

So there is no need to apply quadratic formula.

Option B. x = -1, 19 is the answer.

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Suppose theta(????) measures the minimum angle between a clock’s minute and hour hands in radians. What is theta′(????) at 4 o’c

makvit [3.9K]

Answer:

$\frac{\pi }{30}$ radians per minute.

Step-by-step explanation:

In order to solve the problem you can use the fact that the angle in radians of a circumference is 2π rad.

The clock can be seen as a circumference divided in 12 equal pieces (because of the hour divisions). Each portion is $\frac{1}{12}$

So, you have to calculate the angle between each consecutive hour (Let ∅ represent it). It can be calculated dividing the angle of the entire circumference by 12.

∅= $\frac{2\pi }{12} = \frac{\pi }{6} rad$

Now, you have to find how many pieces of the circumference are between 12 and 4 to calculate the angle (Because 4 o'clock is when the minute hand is in 12 and the hour hand is in 4)

There are 4 portions from 12 to 4, so the angle (Let α represent it) is:

α= $(4)\frac{\pi }{6} = \frac{2\pi }{3}$