Find the nth term of 2, 8, 18, 32, 50

Answers

Answer 1

Answer: From the series, 2, 8, 18, 32, 50,...

By observation and by trial and error.

The first term, n = 1    = 2*1*1 = 2

Second term, n =2,     = 2*2*2 = 8

Third, n =3,    = 2*3*3 = 18

Third term, n = 4, = 2*4*4 = 32

Fourth term, n =5, 2 * 5* 5 = 50

For nth term, 2 *n *n = 2n²

Therefore nth term = 2n²

I hope this helps.

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after a 30% reduction, you purchase a dictionary for $30.80 what was the dictionary price before the reduction

Answers

The dictionary price before the reduction is $44

How to determine the dictionary price before the reduction

From the question, we have the following parameters that can be used in our computation:

Reduction = 30%

Price after = $30.80

Using the above as a guide, we have the following:

Price after = Price before * (1 - Reduction)

substitute the known values in the above equation, so, we have the following representation

Price before * (1 - 30%) = 30.80

Evaluate

Price before = 44

Hence, the dictionary price before the reduction is $44

Answers

Answer with explanation:

3.9= 3 ones + 9 Tenths

1 ones =10 Tenths

3 ones =3 × 10 Tenths=30 Tenths

3.9=30 Tenths +9 Tenths

=39 Tenths

So, 39 Tenth

$=(39)/(10)\n\n=3.9$

10 is in 3, so that's 30. There's another 9.

30 + 9 = 39.

39 tenths.

Paula used synthetic division to divide the polynomial f(x) by x + 1, as shown: -1|-2 -5 4 2 3 ___________ -2-3 7 What is the value of f(-1)? 7 -2 -1 1I think it's 7 but not sure about my answer

Answers

yes it is 7 for sure

Answer:

The correct option is A. The value of f(-1) is 7.

Step-by-step explanation:

It is given that Paula used synthetic division to divide the polynomial f(x) by x + 1, as shown in the attached figure.

According to the remainder theorem, If a function f(x) is divided by (x-c), then

$f(c)=remainder$

From the given division it is clear that if the polynomial f(x)is divide by x + 1, then the remainder is 7.

Using remainder theorem, we get

$f(-1)=7$

The value of f(-1)=7, therefore the correct option is A.

Find the equation of all tangent lines having slope of -1 that are tangent to the curve y=(9)/(x+1)

Answers

Answer: y = -x + 5 and y = -x - 7 (see attached graph)

Step-by-step explanation:

y = $(9)/(x + 1)$

= 9(x + 1)⁻¹

Use the product rule to find the derivative

a = 9 a' = 0

b = (x + 1)⁻¹ b' = -(x + 1)⁻²

ab' + a'b

= 9[-(x + 1)⁻²] + 0[(x + 1)⁻¹ ]

= $(-9)/((x + 1)^(2))$

Set the derivative equal to the desired slope of -1 to solve for x

-1 = $(-9)/((x + 1)^(2))$

-(x + 1)² = -9

(x + 1)² = 9

√(x + 1)² = √9

x + 1 = +/- 3

x + 1 = 3 x + 1 = -3

x = 2 x = -4

Plug those values into the original equation to solve for y:

y = $(9)/(x + 1)$

= $(9)/(2 + 1)$

= 3

(2, 3)

y = $(9)/(x + 1)$

= $(9)/(-4 + 1)$

= -3

(-4, -3)

Next, plug in the given slope (-1) and the coordinates above into the Point-Slope formula y - y₁ = m(x - x₁) to find the equations:

m = -1, (x₁ y₁) = (2, 3) m = -1, (x₁ y₁) = (-4, -3)

y - 3 = -1(x - 2) y + 3 = -1(x + 4)

y - 3 = -x + 2 y + 3 = -x - 4

y = -x + 5 y = -x - 7

Answer:

$f(x)=\frac9{x+1}\n f'(x)=-\frac9{(x+1)^2}\n f'(x)=-1\ \iff\ -\frac9{(x+1)^2}=-1\ \to \ \frac9{(x+1)^2}=1\ \to \ (x+1)^2=9\n |x+1|=3\ \to \ x+1=3\ \vee\ x+1=-3\n x_1=2\ \vee\ x_2=-4\n f(x_1)=f(2)=\frac9{2+1}=3\n f(x_2)=f(-4)=\frac9{-4+1}=-3$