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Svetlanka [38]
3 years ago
13

Use substitution to solve the system of equations.

Mathematics
2 answers:
adelina 88 [10]3 years ago
5 0

Answer:

(2, -5)

Step-by-step explanation:

x is defined by the first equation as x = -3y – 13.  Substitute  -3y – 13 for x in the second equation:

2( -3y – 13) + 2y = -6.

Performing the indicated multiplication, we get:

-6y - 26 + 2y = -6

Combining like terms results in:

-4y = 20, so that y = -5

Using the first equation, we find x for y = -5:

x = -3(-5) - 13 = 2

The solution is thus (2, -5) (Answer C)

omeli [17]3 years ago
5 0

Answer:

x=2 & y=-5, so the answer is C

Step-by-step explanation:

x = -3y-13 ------(1)

2x + 2y = -6 ---------(2)

sub(1)into(2)

(2)=> 2(-3y-13) + 2y = -6

-6y - 26 + 2y = -6

-4y = 20

y = -5

sub y=-5 into(1)

(1)=> x = -3(-5) - 13

= 15 - 13

= 2

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Solution :

Give that a shark can chase prey about 30 miles per hour.

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4 years ago
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
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neonofarm [45]

Answer:

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Step-by-step explanation:

Because the coefficient is not greater than 1, you can simply solve the problem without the quadratic formula.

By using the "x" method, you must figure out what multiplies to give you -10, and adds to give you 3

So, you find your values as 5 and -2. You then set these values equal to zero in terms of Y. As so---- (y+5)=0 and (y-2)=0

Then, you solve out to get your answer! Y is equal to -5 and 2

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