MATHEMATICS HIGH SCHOOL

Solve x2 − 3x = −8.x equals quantity of 3 plus or minus I square root of 29 all over 2

x equals quantity of 3 plus or minus I square root of 23 all over 2

x equals quantity of negative 3 plus or minus I square root of 29 all over 2

x equals quantity of negative 3 plus or minus I square root of 23 all over 2

Answers

Answer 1

Answer:

we have

$x^(2) -3x=-8$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^(2) -3x+1.5^(2)=-8+1.5^(2)$

$x^(2) -3x+1.5^(2)=-5.75$

Rewrite as perfect squares

$(x-1.5)^(2)=-5.75$

Square Root both sides

$x-1.5=(+/-)√(-5.75)$

Remember that

$√(-1)=i$

$√(5.75)= \sqrt{(23)/(4)}=(√(23))/(2)$

Substitute

$x-1.5=(+/-)i(√(23))/(2)$

$x=1.5(+/-)i(√(23))/(2)$

$x=(3/2)(+/-)i(√(23))/(2)$

$x=(3/2)+i(√(23))/(2)=(3+i√(23))/(2)$

$x=(3/2)-i(√(23))/(2)=(3-i√(23))/(2)$

therefore

the answer is

x equals quantity of 3 plus or minus I square root of 23 all over 2

Answer 2

Answer:

Answer:

x equals 3 plus or minus i square root of 23 all over 2

Step-by-step explanation:

I got it right on the test.

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Six people share 34pound of peanuts equally. What fraction of a pound of peanuts does each person receive? Enter your answer in simplest form.

Find five rational numbers between - 1⁄3 and 1⁄3 (both are fractions : negative one third and positive one third)

Answers

1/4,1/5,1/10,1/20,1/40

Write 850 as the product of its prime factor

Answers

2*5*5*17=850

Is this what you were asking for?

20,612,439 scientific notation

Answers

The scientific notation of the population is $2.0*10^(7)$ .

It is required to find the solution.

What is Scientific notation?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. Scientific Notation is the expression of a number n in the form a∗10b. where a is an integer such that 1≤|a|<10. and b is an integer too.

Given :

The given number is

20,612,439

in scientific notation is

$2.0*10^(7)$

Move the decimal point so that there is seven non-zero digit to the left.

Hence, the scientific notation of the population is $2.0*10^(7)$ .

Learn more about scientific notation here:

brainly.com/question/18073768

#SPJ2

Answer:

2.0612439 x 10 to the 7th power

Step-by-step explanation:

Which regular polygon has a minimum rotation of 45 degrees to carry the polygon onto itself?A. octagon
B. decagon
C. Hexagon
D. Pentagon

Answers

Answer:

Hence, a regular polygon that has a minimum rotation of 45 degrees to carry the polygon onto itself is:

A. octagon.

Step-by-step explanation:

We know that the for a regular polygon with 'n' sides the minimum rotation that can carry the polygon onto itself is:

$(360\degree)/(n)$

Here we are given the minimum angle of rotation such that polygon is transformed to itself as 45 degree.

i.e. we have:

$(360)/(n)=45\n\nn=(360)/(45)\n\nn=8$

Hence, the number of sides of a polygon are 8.

Hence, the polygon is:

A. octagon.

( Since a polygon with 8 sides is called a octagon)

octagon, because 360/8 = 45

Is 7 divided by 8 equal to, greater then, or less then 3 divided by 4

Answers

7 divided my 8 is greater than 3 divided by 4

a stuntman uses a 30 foot rope to swing 136 degrees between two platforms of equal height, grazing the ground in the middle of the swing. If the rope stays taut throughout the swing, how far above the ground was the stuntman at the beginning and the end of the swing?

Answers

By geometry and trigonometry the stuntman is 18.762 feet above the ground at the beginning and the end of the swing.

How to determine the initial and final height of the stuntman

After a careful reading of the statement, we prepared a geometricdiagram of the trajectory done by the stuntman between the two platforms. We must use trigonometricexpressions related to righttriangles to determine the initial/finalheight of the stuntman by means of this formula:

h = L · (1 - cos 0.5θ) (1)

Where:

L - Length of the rope, in feet.
θ - Swing angle, in degrees.
h - Initial/final height of the stuntman, in feet.

If we know that L = 30 ft and θ = 136°, then the initial/final height of the stuntman is:

h = (30 ft) · (1 - cos 68°)

h ≈ 18.762 ft

By geometry and trigonometry the stuntman is 18.762 feet above the ground at the beginning and the end of the swing. $\blacksquare$

To learn more on angles, we kindly invite to check this verified question: brainly.com/question/13954458

Alright, let's start with what we know in this equation. If the two platforms are of equal height, and the stuntman swings 136 degrees on his rope to reach them, we should be able to split up his swing into two equal triangles which both have the angle on top equal to 68 degrees.

Another thing we can learn from the question is the measurements of the other two angles in both of the triangles. If the 30 feet of rope is taut throughout their swing, we know that two of the triangle's sides are 30 ft, and if a triangle has two equal sides, the anlgles opposite of those sides should have the same measurements. To find those measurements, what we need to do is take the sum of the leftover angles, which is 180-68, or 112 degrees, and then divide that by two. So, the other angles in both triangles should both be 56 degrees.

Our next step should be to use the Law of Sines to find the measurement of the third side of the triangles. The law of Sines is the idea that sin(a)/A = sin(b)/B = sin(c)/C where the lowercase letters represent an angle and the uppercase letters represent the side opposing the angle of the same letter. Using this, we can take the top angle and the side we don't know and set it equal to one of the other sides. So our equation should look something like sin(68)/x = sin(56)/30. Next we need to cross multiply, giving us sin(68)*30 = sin(56)*x. Simplifying this should give us 27.815 = sin(56)*x, and when we divide both sides by sin(56) we should end up with a measurement of about 33.551 for the third side of our triangle.

Once we have that information, we need to set up another triangle that connects the ground to one of the platforms, with the hypotenuse being the last measurement of 33.551. This triangle should make a right angle of 90 degrees between the ground and the platform, meaning we only have to find two more angles. To do this, we can look at the angle where the ground connected with the rope in the first part. We found that this angle is 56 degrees, and this angle is complementary to the one that we are trying to find in our new triangle, which gives a good place to start. Complementary angles add up to 90 degrees, so to find the new angle's measurement, all we have to do is subtract 56 from 90, which gives us 44 degrees as the measurement of our new angle.

Next, we just have to find the last angle's measurement, which should be pretty easy once we know the other two angles. Because all the angles in a triangle add up to 180 degrees, we just have to subtract the two angles we know from 180! 180-44-90= 46, which should be our last angle's measurement. Now that we have the measurement of one side and all the angles, we can use the Law of Sines again to find out the height from the ground to one of the platforms. To do this, we need to set up a proportion again, and this time it should look something like this: sin(90)/33.551 = sin(46)/x. Cross multiplying will give us sin(90)*x = sin(46)*33.551, and before we simplify, it's good to remember that sin(90) is the same thing as 1, so that makes this last step a little easier. After remembering that, simplifying gives us x = 30.255, which should be the height from the ground to either one of the platforms.

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