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3 years ago

Six plus x minus two x equals five

Mathematics

1 answer:

AleksandrR [38]3 years ago

4 0

The "plus x minus two x" part basically means "minus x".

So, "six minux x equals five".

This means that six minus five is x. So, x is one!

Now, let's check this in the problem: replace x with 1. Six plus one minus two ones equals five? Yes, it does!

The answer is x=1.

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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

2 years ago

Which statement is true about Angle B P D? Line A B intersect line C D at point P. It is adjacent to Angle A P C. It is compleme

mel-nik [20]

Answer:

It is congruent to Angle A P C

Step-by-step explanation:

we know that

<u><em>Vertical angles</em></u> are the angles opposite each other when two lines cross. They are always congruent.

In this problem we have that

$m\angle APC=m\angle BPC$ -----> by vertical angles

see the attached figure to better understand the problem

therefore

It is congruent to Angle A P C

7 0

3 years ago

Read 2 more answers

Jenny is throwing a surprise birthday party for her best friend Katie. She has decided to make Katie’s favorite dish, meat loaf.

miskamm [114]

Answer:

The answer is below

Step-by-step explanation:

a) The recipe for the meat loaf used by Jenny can serve a total of 8 people. Since there are 40 people in total to serve, the number of each ingredient needed is:

Number of each ingredient = total number of people / number of people served by one recipe

Number of each ingredient = 40 / 8 = 5

b) Since each recipe contains 1 1/2 lb (1.5 lbs) of ground beef, the total amount of ground beef needed to feed everyone is:

Total amount of ground beef = 1.5 lbs * 5 = 7.5 lbs

c) Since one serving would require 8 oz of milk. To serve everyone, the amount of milk needed is:

Amount of milk = 40 people * 8 oz = 320 oz

128 oz = 1 gallon

Amount of milk = 320 oz * 1 gallon / 128 oz = 2.5 gallon

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2 years ago

(36.97*100-x)*100 = ???

inna [77]

The answer to X is = 369700

7 0

2 years ago

Solve equation 1/2(4d - 2) = d + 5

kogti [31]

The answer is d=6 i can show my work in the comments if you need it

7 0

2 years ago

Read 2 more answers