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3 years ago

9

Simplify the expression. (5x2 - x - 7) + (2x2 + 3x + 4)

1 answer:

kifflom [539]3 years ago

5 0

Answer:

$7x^2-2x-3$

Step-by-step explanation:

First get rid of the parenthesis

$5x^2-x-7+2x^2+3x+4$

Next simplify the variables

$7x^2-x-7+3x+4$

$7x^2-2x-7+4$

$7x^2-2x-3$

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A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

3 years ago

HOWDY YALL 333 111 222 444 POOP

Savatey [412]

Answer:

333 111 poop to you to

Step-by-step explanation:

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3 years ago

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10. A video rental store charges a $20 membership fee and $2.50 for each video

Pavel [41]

Y= 2.50(x) + $20 is the linear equation

If 15 videos are rented
Y=2.50(15) + $20
Y= $57.50

67.50 = 2.50(x) + 20
19= x
19 videos were rented in 3 months

8 0

3 years ago

In 2006, 5,200 highway accidents were recorded in a city. The number of highway accidents increases by 5% every year. Let y repr

borishaifa [10]

Answer:

C. The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

Step-by-step explanation:

The initial number of accidents = 5200 = Po

It increases 5% every year.

So r = 5% = 0.05

y = Po(1 + r)^x

y = 5200(1 + 0.05)^x

y = 5200(1.05)^x

This sequence is an exponential. Which is a geometric sequence.

Answer: C. The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

Thank you.

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3 years ago

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charlene takes the bus to work in the morning,then walks home for lunch,walks back to work, and finally walks home in the evenin

kolezko [41]

So she walks at least 3 times.The distance is 600 meters So 600·3=1800 meters= 1 kilometers and 800 meters-she going in the single day.

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3 years ago

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