All categories

3 years ago

Factor each expression completely.

Mathematics

1 answer:

netineya [11]3 years ago

5 0

$Use:\\a^2-b^2=(a-b)(a+b)\\(a\pm b)^2=(a^2\pm2ab+b^2\\==============================\\27.\\18z^2-8=2(9z^2-4)=2\left[(3z)^2-2^2\right]=2(3z-2)(3z+2)\\\\29.\\2a^2-16a+32=2(a^2-8a+16)=2(a^2-2a\cdot4+4^2)=2(a-4)^2\\=2(a-4)(a-4)\\\\31.\\12x^2+36x+27=3(4x^2+12x+9)=3[(2x)^2+2\cdot2x\cdot3+3^2]\\=3(2x+3)^2=3(2x+3)(2x+3)$

$33.\\3x^2-24x-27=3(x^2-8x-9)=3(x^2+x-9x-9)\\=3[x(x+1)-9(x+1)]=3(x+1)(x-9)\\\\35.\\-x^2+5x-4=-(x^2-5x+4)=-(x^2-x-4x+4)\\=-[x(x-1)-4(x-1)]=-(x-1)(x-4)\\\\37.\\x^2-y^2=(x-y)(x+y)\\\\39.\\-6z^2-600=-6(z^2+100)$

You might be interested in

Can anyone help with expanding this?

Readme [11.4K]

Answer:

is this collage mathz

Step-by-step explanation:

7 0

3 years ago

Using both the rotation matrices earlier in this lesson and your matrix calculator, find each determinant.

Trava [24]

Answer:

both are one

8 0

3 years ago

Read 2 more answers

Find the indefinite integral. (Use C for the constant of integration.) <br> e2x 25 e4x dx.

Sladkaya [172]

Answer:

The solution is $\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C$

Step-by-step explanation:

From the question

The function given is $f(x) = \frac{e^{2x}}{ 25 + e^{4x}} dx$

The indefinite integral is mathematically represented as

$\int\limits {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx$

Now let $e^{2x} = u$

=> $\frac{du}{dx} 2e^{2x}$

=> $2 e^{2x}dx = du$

$\int\limits {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx = \int\limits {\frac{1}{ 2(25 + u^2)} } \, du$

$= \frac{1}{2} \int\limits {\frac{1}{ 25 + u^2)} } \, du$

$= \frac{1}{2} \int\limits {\frac{1}{ 5^2 + u^2)} } \, du$

$= \frac{1}{2} \frac{tan^{-1} [\frac{u}{5} ]}{5} + C$

Now substituting for u

$\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C$

3 0

3 years ago

Help please help please

xxTIMURxx [149]

Answer:

Combine like terms

Step-by-step explanation:

The first step in such equations is to simplify the equation which is done most often by combining like terms, and by combining like terms i mean for example:

1 + 5 + 3x = 4y + z

You will combine the like terms (those that can be added or subtracted):

6 + 3x = 4y + z

In our example, combining terms would be adding 2x/3 and 1x/3 to give

3x/3 + 2 = 5

The equation is now simple and easy to solve as you simplify 3x/3 to 1x and then proceed to rearrange the equation to yield the value of x

Hope this helps!

6 0

3 years ago

Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.

Rainbow [258]

The solution of the given exponential equation is 0.688.

Given that Mike is working on solving the exponential equation 37ˣ = 12.

An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.

firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:

aˣ = y

logₐy = x

Now, we will apply this transformation to our equation and we get

log₃₇12=x

Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:

x=log12/log37

So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:

x≈1.079/1.568

x=0.688

Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.

Learn more about exponential equation from here brainly.com/question/24162621

#SPJ4

4 0

2 years ago