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3 years ago

Given g(x) = x squared - x, find g (2/3)

Mathematics

2 answers:

lesantik [10]3 years ago

8 0

Answer:

$\large\boxed{g\left(\dfrac{2}{3}\right)=-\dfrac{2}{9}}$

Step-by-step explanation:

$g(x)=x^2-x=x(x-1)\\\\g\left(\dfrac{2}{3}\right)\to\text{put }\ x=\dfrac{2}{3}\ \text{to the eqation of the function:}\\\\g\left(\dfrac{2}{3}\right)=\left(\dfrac{2}{3}\right)\left(\dfrac{2}{3}-1\right)=\left(\dfrac{2}{3}\right)\left(\dfrac{2}{3}-\dfrac{3}{3}\right)=\left(\dfrac{2}{3}\right)\left(-\dfrac{1}{3}\right)=-\dfrac{(2)(1)}{(3)(3)}=-\dfrac{2}{9}$

Elza [17]3 years ago

5 0

Answer:

-2/9

Step-by-step explanation:

g(x) = x^2 -x

Let x = 2/3

g(2/3) = (2/3) ^2 - 2/3

= 4/9 - 2/3

We need a common denominator of 9

4/9 - 2/3*3/3

4/9 - 6/9

-2/9

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write the equation of a line that is parallel to y = - 3/2 x -1 and that passes through the point (4,6)

maria [59]

Answer:

Step-by-step explanation:Given Equation of line has slope m=-3/2

So the line passing through (4,6) has the same slope because both are parallel

From slope intercept form we have

y-y1=m(x-x1)

y-6=-3/2(x-4)

y-6=-3/2x +3/2(4)

y=-3/2x+12

2y=-3x+24

3 0

3 years ago

What is Permutations and Combinations?

marissa [1.9K]

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

$\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }$

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

$\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}$

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

$\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }$

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

$\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}$

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

5 0

2 years ago

I need the answer please

eduard

Answer:

bujvunvyjctn

Step-by-step explanation:

v uh yhfnx zhjd dd djsi dh

Sorry i dont know but if you want points you could spam things like this and get points

8 0

2 years ago

What is the x-intercept for the following linear equation:

Alexandra [31]

The "x-intercept" occurs when y=0, because it is at this point that the equation touches the x axis. So if you plug in y=0 into the equation you can solve for the x coordinate.

4x-2(0)-8=0

4x-8=0

4x=8

x=2

So the x-intercept is the point (2,0)

3 0

3 years ago

Parallelogram R S T U is shown. Diagonals are drawn from point R to point T and from point U to point S and intersect at point V

stiv31 [10]

Answer:

Option C.

Step-by-step explanation:

Given information: RSTU is a parallelogram, Digonals RT and SU intersect each other at point V, UV=(x-3) and VS=(3x-13).

According to the properties of a parallelogram, the diagonals of a parallelogram bisect each other.

Using the properties of parallelogram we can say that point V divides the diagonal SU in two equal parts, UV and VS.

$VS=UV$