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3 years ago

Solve for x X^2+6x+9=20

Mathematics

2 answers:

natta225 [31]3 years ago

8 0

Answer:

x=1.472 or x=-7.472

Step-by-step explanation:

Lets begin by rearranging the equation into the format ax²+bx+c=0

The equation will be:

x²+6x+9-20=0

x²+6x-11=0

We shall use the quadratic formula to solve the equation.

x=[-b±√(b²-4ac)]/2a

=[-6±√(6²-4×1×-11)]/2

=[-6±√80]/2

=[-6±8.944]2

x= Either (-6+8.944)/2 or x= (-6-8.944)/2

Solving for x in each case gives:

x=1.472 or x=-7.472

Masja [62]3 years ago

4 0

Answer:

x = 1.47 or x = -7.47

Step-by-step explanation:

x²+6x+9=20

This is a quadratic equation

x²+6x+9-20=0

x²+6x-11=0

Step 1 : Write the quadratic formula

x = <u>-b±√b²-4(a)(c)</u>

Step 2 : Substitute values in the formula

a = 1

b = 6

c = -11

x = <u>-6±√6²-4(1)(-11)</u>

2(1)

x = <u>-6±√80</u>

x = -3 + 2√5 or x = -3 - 2√5

x = 1.47 or x = -7.47

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Linda throws a dart that hits the square shown below: A square is drawn. A circle of radius 9 units touches the sides of the squ

nataly862011 [7]

Probability helps us to know the chances of an event occurring. The probability of Linda's dart hitting the circle is 0.7857.

<h3>What is Probability?</h3>

The probability helps us to know the chances of an event occurring.

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

As it is given that the circle touches the sides of the square. therefore, the length of the side of the square is the diameter of the circle.

Now, in order to calculate the probability that the dart hits a point in the circle we need to calculate the area of the circle and the area of the square.

Area of the circle with a given radius of 9 units,

$\text{Area of the circle} = \pi r^2$

$\rm = \pi \times (9^2)\\\\= 81\pi\ units^2$

Area of the square with sides equal to the diameter of the circle,

$\rm \text{Area of square} = side^2$

$\rm = Diameter ^2\\\\= (2 \times radius)^2\\\\= (2 \times 9)^2\\\\= 18^2\\\\= 324\ units^2$

Now, the probability that the dart hits a point in the circle can be written as,

$\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\\\Probability=\dfrac{\text{Area of the circle}}{\text{Area of square}}\\\\\\Probability=\dfrac{81 \pi}{324} = 0.7857$