Show why 5/6 is not proportional to 10/15.

<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%2013x%3D%20-6" id="TexFormula1" title="x^{2} + 13x= -6" alt="x^{2} + 13x= -6

HACTEHA [7]

Answer:

Is that a magic spell??

Step-by-step explanation:

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6 0

2 years ago

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

The cost of the tank and filter system is $280. The base of the tank is a square with a perimeter of 60 inches what is the side

Kaylis [27]

Answer:

The side length of of the base of the tank is 15 inches.

Step-by-step explanation:

We are given the following in the question:

Cost of the tank and filter system = $280

Perimeter of tank base = 60 inches

The perimeter of tank is in the shape of square.

We have to find the side length of the base of the tank.

Perimeter of tank base = Perimeter of square =

$P = 4a\\\text{where a is the side of square}\\60 = 4a\\\Rightarrow a = 15\text{ inches}$

Thus, the side length of of the base of the tank is 15 inches.

4 0

3 years ago

(50 POINTS) A group of workers is harvesting berries at a constant rate. An equation that represents the number of baskets of be

goldenfox [79]

Hi There!

Follow y = mx + b

m = slope

b = y intercept

(a) What are the slope and the y-intercept for the equation that represents the number of baskets of berries the workers picked over a period of time?

Slope = 5

Y intercept = 10

(b) What are the rate of change and the initial amount? Explain the meaning of the rate of change and the initial amount for the situation.

The rate of change is how much it takes for the amoun to change. The initial amount should be going up with a slope of 5 each time.

(c) Use graph paper to draw a graph representing the situation. Label the axes appropriately.

Start at the origin than continue with a slope of 5 and make sure the y intercept is correctly graphed.

4 0

3 years ago

Read 2 more answers

Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p dollars, the revenue R in dollars i

cestrela7 [59]

Answer: The maximum revenue is $1,000,000.

The function that is given is a quadratic equation and the graph would be an upside down parabola.

Therefore, the maximum revenue would be at the vertex of the parabola.

To find the vertex, we can use the expression -b/2a to find the x-value.

It would be -4000/2(-4) = 500

Now, input 500 for p and you will get a revenue of 1,000,000.

5 0

2 years ago

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