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3 years ago

Which of the following describes the correct process for solving the equation 2x + 6 =22 and arrives at the correct solution

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

3 0

Answer:

Step-by-step explanation:

Starting with 2x+6=22

You subtract 6 from each side of the equation:

2x=16

You want to isolate the "x" so you divide each side by 2.

x = 8

check your answer: 2x + 6 = 22

2(8) + 6 = 22

16 + 6 = 22

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Solve 2x^2 - 3x = 12 using the quadratic formula.

makkiz [27]

Answer:

$x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4} \\$

Step-by-step explanation:

2x² - 3x - 12 = 0

Using the quadratic formula which is

$x = \frac{ - b \pm\sqrt{ {b}^{2} - 4ac} }{2a} \\$

From the question

a = 2 , b = - 3 , c = - 12

So we have

$x = \frac{ - - 3\pm \sqrt{ ({ - 3})^{2} - 4(2)( - 12)} }{2(2)} \\ = \frac{3\pm \sqrt{9 + 96} }{4} \\ = \frac{3\pm \sqrt{105} }{4} \: \: \: \: \: \:$

Separate the solutions

We have the final answer as

$x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4} \\$

Hope this helps you

6 0

3 years ago

Is 1/2 x 3/5 larger or smaller than 1/2? Why?

Shalnov [3]

1/2 is smaller than 3/5. if you to give them common denominators 1/2 would be 5/10 but 3/5 would be 6/10

6 0

3 years ago

An airplane has its auto pilot set to fly in a direction of 40 degrees at a speed of 320 mph. The wind is blowing the airplane t

Effectus [21]

Answer:

distance: 320.624 miles

direction: 43.576°

Step-by-step explanation:

The speed and direction can be found by adding the given vectors.

... 320∠40° + 20∠130°

... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))

... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)

The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.

... = √(232.278² +221.013²)∠arctan(221.013/232.278)

... = 320.624∠43.576°

_____

A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.

_____

<em>Comment on coordinate systems</em>

Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.

Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.

_____

Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.

8 0

3 years ago

What is the solution of the equation when solved over the complex numbers?

kumpel [21]

Answer:

$x=+i\sqrt{20}\approx+4.472i$

$x=-i\sqrt{20}\approx-4.472i$

Step-by-step explanation:

Starting from $x^2+20=0$ , we do $x^2=-20$ , which means $x=\pm\sqrt{-20}$ , which can be written as $x=\pm\sqrt{(-1)(20)}$ , which gives us $x=\pm\sqrt{(-1)}\sqrt{(20)}$ , which we know is $x=\pm i \sqrt{(20)}$ , so our solutions are: