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nlexa [21]
3 years ago
8

Which system of equations does the graph represent?

Mathematics
1 answer:
zubka84 [21]3 years ago
8 0
Your answer should be the last one. All you do is put your x&y intercept into the equation. It’s pretty simple and easy
You might be interested in
Find the integral using substitution or a formula.
Nadusha1986 [10]
\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx

Derivative of the denominator:
\rm (x^2+2x+5)'=2x+2

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx

and then split the fraction,

\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx

Based on our previous test, we know that a simple substitution will work for the first integral: \rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx

So the first integral changes,

\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx

integrating to a log,

\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2

So we have this going on,

\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx

Bringing all that stuff together as a single square,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx

Making the substitution: \rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx

giving us,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du

simplying a lil bit,

\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du

and hopefully from this point you recognize your arctangent integral,

\rm ln|x^2+2x+5|+\frac52arctan(u)

undo your substitution as a final step,
and include a constant of integration,

\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c

Hope that helps!
Lemme know if any steps were too confusing.

8 0
3 years ago
He sum of two numbers, x and y, is 12. the difference of x and two times y is 6. what are the values of x and y? x = 8, y = 4 x
Sveta_85 [38]
The last choice is correct
8 0
2 years ago
If 35% of 300 children had zero cavities, how many children was that???
igomit [66]

Answer:

105 children

Step-by-step explanation:

35/100×300

105

6 0
2 years ago
PLEASE HELP ME I REALLY NEED HELP ON THIS QUESTION!!!!\
Vinil7 [7]

Answer:

total \: earning \: in \: a \: week \:  \\  = 14 \times  \frac{77}{2}  \\  = 7 \times 77 \\  = 539 \\ now \: pay \: for \: her \: friend \\ 539 \times  \frac{1}{5}  = 107.8

5 0
3 years ago
Rearrange your equation to isolate a:(a+b/c)(d-e)=f
sukhopar [10]
To rearrange the equation given, we need to take note the rules in adding, subtracting, multiplying and dividing terms. We rearrange the equation as follows:

<span>((a+b/c)(d-e)=f) 1/(d-e)

</span>(a+b/c = f/(d-e))c

a+b = fc/(d-e)

a = [fc/(d-e)] - b

Hope this answers the question.

8 0
3 years ago
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