3 copies of of 1/3 what is the answer

MissTica

Answer:

$2x\left(x-2\right)\left(x+3\right)\left(x+2\right)$

Step-by-step explanation:

Lets go ahead and take a step by step approach to solving your problem.

First we must start by factoring $x^2+x-6$ .

To do this, we must break the expression into groups! Although I will also provide a definition to help you understand! For $ax^2+bx+c$ we need to find u, v > $u\cdot \:v=a\cdot \:c$ and $u+v=b$ which we will group into $\left(ax^2+ux\right)+\left(vx+c\right)$ .

The values we have are... $a=1,\:b=1,\:c=-6$ and $u\cdot v=-6,\:u+v=1$ .

Now we need the factors of 6 which are 1, 2, 3 and 6. We also need the negative factors which you get simply by multiplying the positives by -1 or just reversing them.

Now we need to check for every two factors if u + v = 1.

$\mathrm{Check}\:u=1,\:v=-6: \:u\cdot v=-6,\:u+v=-5 \Rightarrow \mathrm{False}$

$\mathrm{Check}\:u=2,\:v=-3: \:u\cdot v=-6,\:u+v=-1 \Rightarrow \mathrm{False}$

$\mathrm{Check}\:u=3,\:v=-2: \:u\cdot v=-6,\:u+v=1 \Rightarrow \mathrm{True}$

$\mathrm{Check}\:u=6,\:v=-1: \:u\cdot v=-6,\:u+v=5 \Rightarrow \mathrm{False}$

Therefore $u=3,\:v=-2$ .

Now we want to $\mathrm{Group\:into\:}\left(ax^2+ux\right)+\left(vx+c\right)$ . Which is $\left(x^2-2x\right)+\left(3x-6\right)$ .

Now we must factor x from $x^2-2x$ .

Lets apply the exponent rule of $a^{b+c}=a^ba^c$ which means $x^2=xx$ .

Therefore we now have xx - 2x. Lets factor out the common term of x to get x(x - 2).

Now factor 3 out of $3x-6$ .

Rewrite 6 as 3 * 2. $3x-3\cdot \:2$ .

Now factor out the common term of 3 > $3\left(x-2\right)$ .

$x\left(x-2\right)+3\left(x-2\right)$ > Factor out the common term of x - 2 > $\left(x-2\right)\left(x+3\right)$ .

Now lets factor $2x^2+4x$ .

Apply the previous exponent rule of $a^{b+c}=a^ba^c$ > $x^2=xx$ > $2xx+4x$ .

Now rewrite 4 as 2 * 2 > $2xx+2\cdot \:2x$ .

Now factor out the common term of 2x to get 2x(x + 2).

Combine it all and we get $2x\left(x-2\right)\left(x+3\right)\left(x+2\right)$ .

Hope this helps!

7 0

3 years ago

Jimmy is planning his birthday party! He spent $35 on balloons and chocolate cake. He bought balloons that cost $0.25 each and a

emmainna [20.7K]

In the equation, x represents the number of balloons. We say that 25 cents per balloon becomes 0.25x.

Jimmy also purchased a chocolate cake. This is the PLUS sign in the equation.

The total for everything purchased is $35.

Balloons x at 25 cents each = 0.25x plus a chocolate cake for $10 together equals $35.

5 0

3 years ago

The weather forecast states that the temperature will be lower than -5*F tonight. Let t represent the temperature in degrees Fah

nikdorinn [45]

SO IT IS POSITIVE. THAT IS CONFUSING lol!

5 0

4 years ago

Alisa hair grows at a rate of 1/2 inch per month. How many months will it take for her hair to grow 8 inches

Alekssandra [29.7K]

It takes Alisa 16 months to grow her hair 8 inches.

3 0

4 years ago

Stephen Curry's Free Throws As we see in Exercise P.37, during the 2015-16 NBA season, Stephen Curry of the Golden State Warrior

Reil [10]

Answer:

A) $P(X=x) = \binom{2}{x}.(0.908)^x.(0.092)^{2-x}$

B) Mean = 1.816

Step-by-step explanation:

We are given the following information:

We treat Stephen Curry making any given free throw as a success.

P(Stephen Curry makes any given free throw) = 0.908

Since the probability for the free throw is equal for each trial and free throws are independent.

Then the number of free shots follows a binomial distribution.

A) Probability distribution

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Here n = 2, p = 0.908

$P(X=x) = \binom{2}{x}.(0.908)^x.(1-0.908)^{2-x}\\\\P(X=x) = \binom{2}{x}.(0.908)^x.(0.092)^{2-x}$

Now x can take values 0, 1 , 2

Putting values, we get,

$P(x = 0) = 0.008464\\P(x = 1) = 0.167072\\P(x = 2) = 0.82446$

B) Mean of X

$\mu = np = 2(0.908) =1.816$

Thus, the mean number of free shots made by Stephen Curry is 1.816

4 0

3 years ago