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3 years ago

Find a formula for the nth term of the arithmetic sequence a1=-17 a2=-12 a3=-7 a4=-2

Mathematics

1 answer:

MAVERICK [17]3 years ago

3 0

Answer:

Step-by-step explanation:

Recursive formula

a1 = -17

a^n = a^n-1 + 5

Explicit formula:

a^n = -17 + (n-1) * 5

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Please help!!!!!!!! Determine the function which corresponds to the given graph.

zzz [600]

The rational function shown in the graph is:

$y = \frac{x - 6}{x - 5}$

<h3>How to determine the function?</h3>

First, we can see that we have an asymptote at x = 5, so the denominator becomes equal to zero when x = 5.

Then the rational function is something like:

$y = \frac{g(x)}{x - 5}$

We also can see that when x = 6, the function intercepts the x-axis, then we must have that:

g(6) = 0

So we can define:

g(x) = x - 6

So the rational function is:

$y = \frac{x - 6}{x - 5}$

If you want to learn more about rational functions, you can read:

brainly.com/question/1851758

5 0

2 years ago

What is the value to this solution

saw5 [17]

-1/8 because it would be -1/16 which is closer to 0 then -1/8. We want something that will return a value where the denominator is large for a negative value.

4 0

2 years ago

Read 2 more answers

Opal walked from school to home, which

lianna [129]

Answer:

Slope = -4

x intercept = 3

Step-by-step explanation:

See attachment for graph

Required

a. Determine the slope

b. Find the x intercept and explain what it represents

a. The slope

To calculate the slope, we start by selecting any two corresponding values of x and y from the graph.

$(x_1,y_1) = (3,0)$

$(x_2,y_2) = (0,12)$

Next, we calculate the slope (m)

$m = \frac{y_1 - y_2}{x_1 - x_2}$

$m = \frac{0 - 12}{3 - 0}$

$m = \frac{- 12}{3}$

$m = -4$

b. The x intercept

This is the point where $y = 0.$

From the graph.

$x = 3$ when $y = 0$

This implies that:

After 3 hours, the distance left to cover is 0miles.

In other words, she arrived home in 3 hours

8 0

3 years ago

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?

AysviL [449]

Answer:

$\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}$ .

Step-by-step explanation:

According to the Rational Root Theorem, the potential roots of a polynomial are

$x=\pm\dfrac{p}{q}$

where, p is a factor of constant and q is a factor of leading term.

The given polynomial is

$f(x)=9x^8+9x^6-12x+7$

Here, 9 is the leading term and 7 is constant.

Factors of 9 are ±1, ±3, ±9.

Factors of 7 are ±1, ±7.

Using rational root theorem, the rational or potential roots are

$x=\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}$

Therefore, the potential root of f(x) are $\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}$ .

4 0

4 years ago

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After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temper

Fiesta28 [93]

Newton's Law of Cooling:

$T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}$

$T(t) =$ Temperature given at a time

$t =$ Time

$T_{s} =$ Surrounding temperature

$T_{o}=$ Initial temperature

$e =$ Constant (Euler's number) ≈ 2.72

$k =$ Constant

Using this information, find the value of $k$ , to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.

First, plug in the given values in the equation and solve for $k$ :

$T(t) =$ 197°, $t =$ 1.5 minutes, $T_{s} =$ 70° and $T_{o}=$ 210°

$T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k$