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3 years ago

Factor by grouping : xy + 6y - 2x - 12 (if you don't know the answer don't comment)

Mathematics

1 answer:

alexira [117]3 years ago

6 0

<h3> Hey There today we will solve your problem</h3>

First we will factor out $y$ from $xy+6y$ which gives us $y(x+6)$

Next we will factor out $-2$ from $-2x-12$ which gives us $-2(x+6)$

This gives us the equation

$y(x+6)-2(x+6)$

then factor out the common term $x+6$ <em> and we get</em>

<em /> $\left(x+6\right)\left(y-2\right)$

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What are the solutions to the quadratic equation below x^2+20x+100=7

aleksandrvk [35]

First you must have the quadratic equal to zero. In order to do this you must subtract 7 to both sides

x^2 + 20x + (100 - 7) = 7 - 7

x^2 + 20x + 93 = 0

Now you must find two numbers who's sum equals 20 and their multiplication equal 93

Are there any? NO!

This means that you have to use the formula:

$\frac{-b±\sqrt{b^{2} - 4ac} }{2a}$

In this case:

a = 1

b = 20

c = 93

$\frac{-(20) plus/minus\sqrt{20^{2} - 4(1)(93)} }{2*1}$

$\frac{-20 plus/minus\sqrt{400 - 372} }{2}$

$\frac{-20 plus/minus\sqrt{28} }{2}$

^^^We must simplify √28

√28 = 2√7

so...

$\frac{-20 plus/minus 2\sqrt{7} }{2}$

simplify further:

$-10 plus/minus\sqrt{7$

-10 + √7

-10 - √7

***plus/minus = ±

Hope this helped!

~Just a girl in love with Shawn Mendes

7 0

3 years ago

To be able to do the problem 5(10 + 4) mentally, Zack does 50 + 20 instead of 5(14).

Eddi Din [679]

Answer:

1. Distributive

Step-by-step explanation:

This is because you multiply the number outside the parentheses into the numbers inside the parentheses.

Hope it helped.

8 0

3 years ago

Read 2 more answers

In how many ways can a quality-control engineer select a sample of3 transistors for testing frm a batch of 100 transistors?

Advocard [28]

Answer:

161700 ways.

Step-by-step explanation:

The order in which the transistors are chosen is not important. This means that we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

3 transistors from a set of 100. So

$C_{100,3} = \frac{100!}{3!(100-3)!} = 161700$

So 161700 ways.

6 0

3 years ago

Sarah went to an electronics store, purchased 3 CDs and 5 DVDs, and spent $137. Michelle went to the same store, bought 2 CDs an

vesna_86 [32]

C. thats the only one that will give you the same price for the DVDS as well. they charge $14 for CDS and $19 for DVDS

5 0

4 years ago

Read 2 more answers

interpret r(t) as the position of a moving object at time t. Find the curvature of the path and determine thetangential and norm

Igoryamba

Answer:

The curvature is $\kappa=1$

The tangential component of acceleration is $a_{\boldsymbol{T}}=0$

The normal component of acceleration is $a_{\boldsymbol{N}}=1 (2)^2=4$

Step-by-step explanation:

To find the curvature of the path we are going to use this formula:

$\kappa=\frac{||d\boldsymbol{T}/dt||}{ds/dt}$

where

$\boldsymbol{T}}$ is the unit tangent vector.

$\frac{ds}{dt}=|| \boldsymbol{r}'(t)}||$ is the speed of the object

We need to find $\boldsymbol{r}'(t)$ , we know that $\boldsymbol{r}(t)=cos \:2t \:\boldsymbol{i}+sin \:2t \:\boldsymbol{j}+ \:\boldsymbol{k}$ so

$\boldsymbol{r}'(t)=\frac{d}{dt}\left(cos\left(2t\right)\right)\:\boldsymbol{i}+\frac{d}{dt}\left(sin\left(2t\right)\right)\:\boldsymbol{j}+\frac{d}{dt}\left(1)\right\:\boldsymbol{k}\\\boldsymbol{r}'(t)=-2\sin \left(2t\right)\boldsymbol{i}+2\cos \left(2t\right)\boldsymbol{j}$

Next , we find the magnitude of derivative of the position vector

$|| \boldsymbol{r}'(t)}||=\sqrt{(-2\sin \left(2t\right))^2+(2\cos \left(2t\right))^2} \\|| \boldsymbol{r}'(t)}||=\sqrt{2^2\sin ^2\left(2t\right)+2^2\cos ^2\left(2t\right)}\\|| \boldsymbol{r}'(t)}||=\sqrt{4\left(\sin ^2\left(2t\right)+\cos ^2\left(2t\right)\right)}\\|| \boldsymbol{r}'(t)}||=\sqrt{4}\sqrt{\sin ^2\left(2t\right)+\cos ^2\left(2t\right)}\\\\\mathrm{Use\:the\:following\:identity}:\quad \cos ^2\left(x\right)+\sin ^2\left(x\right)=1\\\\|| \boldsymbol{r}'(t)}||=2\sqrt{1}=2$

The unit tangent vector is defined by

$\boldsymbol{T}}=\frac{\boldsymbol{r}'(t)}{||\boldsymbol{r}'(t)||}$

$\boldsymbol{T}}=\frac{-2\sin \left(2t\right)\boldsymbol{i}+2\cos \left(2t\right)\boldsymbol{j}}{2} =\sin \left(2t\right)+\cos \left(2t\right)$

We need to find the derivative of unit tangent vector

$\boldsymbol{T}'=\frac{d}{dt}(\sin \left(2t\right)\boldsymbol{i}+\cos \left(2t\right)\boldsymbol{j}) \\\boldsymbol{T}'=-2\cdot(\sin \left(2t\right)\boldsymbol{i}+\cos \left(2t\right)\boldsymbol{j})$