How to factorise 15x-10x^3

(x-3)^2=5 ? confused

Vanyuwa [196]

$(x-3)^2=5\implies \sqrt{(x-3)^2}=\sqrt{5}\implies (x-3)=\sqrt{5}\implies x = \sqrt{5}+3$

5 0

2 years ago

Prove that an = 4^n + 2(-1)^nis the solution to

olga nikolaevna [1]

Answer:

See proof below

Step-by-step explanation:

We have to verify that if we substitute $a_n=4^n+2(-1)^n$ in the equation $a_n=3a_{n-1}+4a_{n-2}$ the equality is true.

Let's substitute first in the right hand side:

$3a_{n-1}+4a_{n-2}=3(4^{n-1}+2(-1)^{n-1})+4(4^{n-2}+2(-1)^{n-2})$

Now we use the distributive laws. Also, note that $(-1)^{n-1}=\frac{1}{-1}(-1)^n=(-1)(-1)^{n}$ (this also works when the power is n-2).

$=3(4^{n-1})+6(-1)^{n-1}+4(4^{n-2})+8(-1)^{n-2}$

$=3(4^{n-1})+(-1)(6)(-1)^{n}+4^{n-1}+(-1)^2(8)(-1)^{n}$

$=4(4^{n-1})-6(-1)^{n}+8(-1)^{n}=4^n+2(-1)^n=a_n$

then the sequence solves the recurrence relation.

4 0

3 years ago

Justin did push-ups for the past 5 days. The following data points are the number of push-ups he did each day.

irga5000 [103]

Answer:

2.67

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

For a random sample of children from a school district in South Carolina, a regression analysis is conducted of yequalsamount s

AveGali [126]

Answer:

Option B. Standard error of predicted amount.

Step-by-step explanation:

A standard error predicted amount will work best in this scenario. The data, when extracted from the standard mean, provides the most accurate presentation of the statistical data on question. By using the standard error, the variation from the central point can be determined.

3 0

3 years ago

A.) The median player salary for the New York Yankees was $1.5 million in 2007 and $1.7 million in 2013. Write a linear equation

egoroff_w [7]

A general linear equation is given by:

$y = a*x + b$

Where a is the slope and b is the y-intercept.

Here we will find that the linear equation that represents the situation is

$y = 0.033*x + 1.269$

And we can expect that the median salary in 2048 is $2.853 million

If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

Here we know that:

in 2007 (x = 7) the median player salary was y = $1.5 million

in 2013 (x = 13) the median player salary was y = $1.7 million.

Then we have two points that we can write as:

(7, 1.5)

(13, 1.7)

Note that the y-value is in millions.

Then the slope of the linear equation will be:

$a = \frac{1.7 - 1.5}{13 - 7} = 0.033$

So the linear equation is something like:

$y = 0.033*x + b$

To find the value of b, remember the point (7, 1.5), this means that when we have x = 7, we also have y = 1.5, then we can replace these in the above equation:

$1.5 = 0.033*7 + b\\\\1.5 - 0.033*7 = b = 1.269$

Then the linear equation is:

$y = 0.033*x + 1.269$

b) Now we want to predict the median salary in 2048. For 2048 the x-value is x = 48

So we just need to evaluate this in the linear equation:

$y = 0.033*48 + 1.269 = 2.853$

Then the median salary in 2048 will be $2.853 million

If you want to learn more, you can read:

brainly.com/question/1189779

5 0

2 years ago