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What are the roots of x in -10x2 + 12x − 9 = 0?

hoa [83]

Answer:

$x_1=\frac{3(2+i\sqrt{6})}{10}$

$x_2=\frac{3(2-i\sqrt{6})}{10}$

Step-by-step explanation:

Use the Quadratic formula:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

You can identify that, in this case:

$a=-10\\b=12\\c=-9$

Now you need to substitute these values into the formula:

$x=\frac{-12\±\sqrt{12^2-4(-10)(-9)}}{2(-10)}$

$x=\frac{-12\±\sqrt{-216}}{-20}$

Remember that:

$i=\sqrt{-1}$

Therefore,rewriting and simplifying, you get:

$x=\frac{-12\±6i\sqrt{6}}{-20}$

$x=\frac{-6(2\±i\sqrt{6})}{-2(10)}$

$x=\frac{3(2\±i\sqrt{6})}{10}$

Then, you get the following roots:

$x_1=\frac{3(2+i\sqrt{6})}{10}$

$x_2=\frac{3(2-i\sqrt{6})}{10}$

6 0

2 years ago

Read 2 more answers

PLEASE HELP THANK YOU!!!

Paul [167]

Answer:

Only C is a function

Step-by-step explanation:

To test whether a graph is a function you use the vertical line test.

If you can place a vertical line anywhere on the plane (in the domain of the "function" to be tested) and it intersects the curve at more than one point, the curve is not a function.

We see with A, wherever we put the vertical line it intersects twice.

With B, it intersects infinitely many times.

C is a function because wherever we put the vertical line, it only intersects once.

D is a function because it intersects twice providing we do not put it on the "tip" of the parabola.

The mathematical reasoning behind this is that a function must be well-defined, that is it must send every x-value to one specific y-value. There can be no confusion about where the function's input is going. If you look at graph B and I ask you what is f(3)? Is it 1? 2? 3? ... Who knows, it's not well-defined and so it's not a function. However if I ask you about C, whichever input value for x I give you, you can tell me to which y-value it gets mapped/sent to.

7 0

3 years ago

In jims class, 5 times has many students take the bus as those who walk. A total of 24 students walk or take the bus. How many m

lubasha [3.4K]

Take bus=5 times walk
b=5w
b+w=24
sub 5w for b
5w+w=24
6w=24
divide both sides by 6
w=4

sub back
b=5w
b=5(4)
b=20

bus-walk=20-4=16

answer is 16 more take the bus than walk

7 0

2 years ago

How do I get the answer y= 2x^2+9x-5

guapka [62]

Answer:

Quadratic Formula

so

x = -5

and

x = 0.5

Step-by-step explanation:

Whenever you see a problem in this form, which you will see a lot of, you can try to factor it or use the "least squares" method or what have you, but those won't always work, unfortunately.

Fortunately, the quadratic formula will never fail you with quadratic expressions.

This is the Quadratic Formula

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

a is the the number on the variable with the exponent ^2

b is the number on the variable with no exponent

c is the third number

a and b cannot be equal to 0; c can be

Since we're looking for a number with an equation that has a square root in it, we're going to get two answers. These two answers come from the radical being separately added AND subtracted from the radical. It's basically two problems.

Plugging in our numbers to this equation gives us x values of -5 and 0.5. This will always work with polynomials with factors of ^2 in them.

If you have a TI-84 calculator or newer, there's a tool on it that will factor polynomials like this one for you just by giving it the numbers.

7 0

2 years ago

4÷25times4÷100times4÷4

notsponge [240]

Answer:

0.0064 is your answer

Step-by-step explanation:

because 4÷25 = 0.16 and 4÷100=0.04 and of course 4÷4=1

When the 0.16 and 0.04 that gets 0.0064

3 0

2 years ago