All categories

3 years ago

Simplify quantity x squared plus 5 x plus 6 end quantity over quantity x plus 2 x2 + 1 x2 − 1 x + 3 x − 3

Mathematics

1 answer:

Marina CMI [18]3 years ago

7 0

Answer:

$\frac{x^2+5x+6}{x+2}$

⇒ $x+3$

Step-by-step explanation:

To simplify:

$\frac{x^2+5x+6}{x+2}$

To simplify the given expression we need to factor the numerator.

We have

$x^2+5x+6$

Using split the middle term method by splitting $5x$ into two terms $ax$ and $bx$ such that $ax+bx=5x$ and $ax(bx)=6x^2$

We see that [ $ax=2x$ and $bx=3x$ ]

Thus we can write

⇒ $x^2+2x+3x+6$

Factoring in pairs by taking the GCF of terms in pairs.

⇒ $x(x+2)+3(x+2)$

Factoring the whole expression as $(x+2)$ is a common factor.

⇒ $(x+2)(x+3)$

Now, the expression can be rewritten as:

$\frac{(x+2)(x+3)}{x+2}$

Canceling out the common expressions, we have.

⇒ $x+3$

You might be interested in

What is equivalent to 4 2/3

Svet_ta [14]

8
46
is equivalent to 4
23
because 4 x 2 = 8 and 23 x 2 = 46
12
69
is equivalent to 4
23
because 4 x 3 = 12 and 23 x 3 = 69
16
92
is equivalent to 4
23
because 4 x 4 = 16 and 23 x 4 = 92

4 0

3 years ago

and 2008 Classic Car Wash estimated its business would increase by 20% each year. if they washed 19,300 in 2008, how many cars c

professor190 [17]

Well, from 2008 to 2010 is just 2 years, so let's say the initial amount is the 19300 from 2008, how many will it be in 2010?

$\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &19300\\
r=rate\to 20\%\to \frac{20}{100}\to &0.20\\
t=\textit{elapsed time}\to &2\\
\end{cases}
\\\\\\
A=19300(1+0.2)^2$

6 0

3 years ago

In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled a

Art [367]

Answer:

The answer is " $\bold{T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5}$ "

Step-by-step explanation:

Given value:

Temp-maximum= $18^{\circ}$

Temp. minimum = $3^{\circ}$

It is halfway between 10 am and 10 pm to 4 am.

The sinus and cosine roles could be used throughout the year to predict fluctuations in climate models. Its type of formula that can be used to model such information is:

$T = A \cos B(t-C) + D,$ where parameters are A, B , C, D, T is the ° C temperature and t is the time (1-24)

$A = amplitude = \frac{(T_{max} - T_{min})}{2}\\\\$

$= \frac{(3 - 18)}{2}\\\\= - \frac{15}{2}\\\\ = -7.5$

$B = \frac{2 \pi}{24}\\\\$

$= \frac{\pi}{12}$

$C = \text{ units translated to the right}= 4$

$D = y_{min} + amplitude = units \ translated \ up\\\\$

D = 7.5 + 3 = 10.5

Its trigonometric function equation that model temperature T hours after midnight in Johannesburg t.

$T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5$

6 0

4 years ago

Please help! <br> Express 35 marks out of 40 as a percentage.

Blizzard [7]

Answer:

$\huge\boxed{\sf 87.5 \ \%}$

Step-by-step explanation:

35 marks out of 40<u> as a fraction:</u>

35 / 40

<u>As a percentage:</u>

<u></u> $\sf \frac{35}{40} * 100 \ \%\\\\0.875 * 100 \ \%\\\\87.5 \ \%\\\\\rule[225]{225}{2}$

Hope this helped!

7 0

3 years ago

How many different 4 digit even numbers can be written using 0,5,6,3,8,7?<br><br> help asap please!!

fiasKO [112]

Step-by-step explanation:

I guess that means the digits can not be repeated in such a number.

let's start with how many numbers in general can be created :

we have 6 basic digits, and we are pulling 4 of them for a number.

if the sequence of the pulled digits would not matter, it would be combinations C (6, 4).

but we are creating different numbers, so the sequence of the digits does matter. so, it is permutations P (6, 4).

P(6, 4) = 6!/(6-4)! = 6!/2! = 6×5×4×3 = 360

so. bauxite, we can create 360 different 4 digit numbers out of these 6 digits.

but not all of them are wanted.

for example, I assume we don't want the numbers that start with a 0, because they would normally count as 3-digit numbers.

if that assumption is correct, we need to find how many would start with a 0, and subtract those from the total number.

since we are handling all 6 digits in the same way, an equal number must start with 0, with 5, with 6, with 3, with 8 and with 7.

so, 1/6 of the total number start with 0 : 360×1/6 = 60.

that means the total number of 4-digit numbers out of these 6 digits that do not start with 0 is 360-60 = 300.

but we are still not finished : we only want even numbers. that means they end with 0, 6 or 8.

in the same way we considered the first position, we consider also the last position. we have an equal amount of numbers that end with the different digits.

and so, we have 1/6 of 300 for each ending digit.

we want the specified 3 digits as end digits, so we get

3×1/6 of the 300 = 1/2 × 300 = 150

so, we can write 150 different 4-digit even numbers out of these 6 digits.

3 0

2 years ago