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dmitriy555 [2]
3 years ago
7

Use the table below to fill in missing values.

Mathematics
1 answer:
aliina [53]3 years ago
4 0

Step-by-step explanation:

We can observe from the table that the value of independent variable and then the values of function on that variable are given.

So,

<u>f(5) = 6</u>

As the value of function at x=5 is 6

<u>If f(x) = 4 then x = 7</u>

The value of function is 4 only on x=7 so the answer is x = 7

When the inverse is taken, the inputs become output and the outputs become inputs

f^{-1}(6) = 5

The value of inverse will be 5 because in original function 5 is input and 6 is output when this will be reversed for inverse, the output will be 5 for 6

Now,

Lastly

if\ f^{-1}(x) = 7,\ then \x = 4

The reverse rule of input and output will be used. The reverse function will generate 7 at input 4.

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What is the solution to the system of equations below?
Andre45 [30]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equations

y=-6x-10

y=-3x-21

solving the system of the equations

Arrange the equation variables for elimination

\begin{bmatrix}y+6x=-10\\ y+3x=-21\end{bmatrix}

y+3x=-21

-

\underline{y+6x=-10}

-3x=-11

\begin{bmatrix}y+6x=-10\\ -3x=-11\end{bmatrix}

solve

-3x=-11

Divide both sides by -3

\frac{-3x}{-3}=\frac{-11}{-3}

x=\frac{11}{3}

\mathrm{For\:}y+6x=-10\mathrm{\:plug\:in\:}x=\frac{11}{3}

y+6\cdot \frac{11}{3}=-10

y+6\cdot \frac{11}{3}=-10

y=-32

Therefore, the solutions to the system of the equations are:

y=-32,\:x=\frac{11}{3}

But, it seems none of the options is true.

8 0
3 years ago
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Let f be defined by the function f(x) = 1/(x^2+9)
riadik2000 [5.3K]

(a)

\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt

=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}

(b) The series

\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}

converges by comparison to the convergent <em>p</em>-series,

\displaystyle\sum_{n=3}^\infty\frac1{n^2}

(c) The series

\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}

converges absolutely, since

\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

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3 years ago
Latoya earns $25.05 for 3 hours of tutoring. How much money does latoya earn each hour?
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Answer:

$8.35 per hour

Step-by-step explanation:

Take the dollars and divide by the hours to determine the dollars per hour

25.05/3

$8.35 per hour

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Answer by Mimiwhatsup:

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faltersainse [42]

Answer:The pictures not that clear

Step-by-step explanation:

5 0
2 years ago
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