If (9x − 4)(9x + 4) = ax^2 − b, what is the value of a?

If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system

olya-2409 [2.1K]

Answer:

b) If the graphs of the linear equations in a system are parallel, there is no solution to the given system of equation.

Step-by-step explanation:

Parallel Lines:

Two straight lines l and m are said to be parallel if they do not intersect at any point, if infinitely extended in either direction.

Now, if the graphs of the linear equations in a system are parallel

⇒ By the definition, both the graphs have NO INTERSECTING POINT.

⇒There is not even one common point available to the given system of

equation.

Hence, There is no solution to the given system of equation.

7 0

3 years ago

Could the value of x below be 4, 6, 9, or 10

lions [1.4K]

Answer:

the answer is 6 i think

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Gabriela has an apartment that costs 30% of her monthly budget, which is $3,575. What is the amount of money she has left over f

irina [24]

Answer:

$3003

Step-by-step explanation:

30/100×$3,575=3000/$3,575=0.84%

0.84%/100×$3,575

84/100×3,575=$300,300/100

$3003

4 0

2 years ago

kyle took at total of 8 quizzes in the first 4 weeks of school. How many weeks of school will he have to attend before he will h

Elden [556K]

Answer:

6 weeks

Step-by-step explanation:

8 quizzes = 4 weeks

So 2 quizzes/week

It will take her 12/2 weeks (6) to finish 12 quizzes

-Chetan K

6 0

2 years ago

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