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3 years ago

What are the solution of the equation 2|×+7|-3=5

Mathematics

2 answers:

goblinko [34]3 years ago

5 0

Answer:

Solution of the equation 2|x +7|-3=5 is :

<u>x1 = - 11 </u>and<u> x2 = - 3</u>

AURORKA [14]3 years ago

3 0

Answer:

x = -3 and x = -11

Step-by-step explanation:

Find the "bare" absolute value function, then solve the two resulting equations.

2|x+7| -3 = 5

2|x +7| = 8 . . . . . add 3

|x +7| = 4 . . . . . . divide by 2

This resolves to two equations:

x +7 = 4

x = -3 . . . . . subtract 7

and

x +7 = -4

x = -11 . . . . . subtract 7

The two solutions are ...

x = -3 and x = -11

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2 years ago

For the differential equations dydx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to thi

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Answer:

1. (-4,6) there is no a solution to the equation through this point

2. (2,−6) there is no a solution to the equation through this point

3. (−5,39) there is a solution to the equation through this point

4. (−1,45) there is a solution to the equation through this point

Step-by-step explanation:

Using the existence and uniqueness theorem:

Let:

$F(x,y)=\sqrt{y^2-36} \\\\and\\\\\frac{\partial F}{\partial y} =\frac{y}{\sqrt{y^2-36} }$

Now, let's find the domain of $F(x,y)$ , due to the square root:

$y^2-36 \geq 0\\\\y^2\geq 36\\\\y \geq 6\hspace{12}or\hspace{12}y\leq-6$

So the domain of the function is:

$y \in R\hspace{12}y\geq6\hspace{12}or\hspace{12}y\leq-6$

Now, due to the fraction $\frac{\partial F}{\partial y}$ the denominator must be also different from 0, so:

$y^2-36\neq0\\\\y \neq \pm6$

So, the theorem tells us that for each $y_0\in R:\hspace{12}y_0>6\hspace{12}or\hspace{12}y_0$ there exists a unique solution defined in an open interval around $x_0$ .

1. (-4,6) there is no a solution to the equation through this point because $y_0=6$

2. (2,−6) there is no a solution to the equation through this point because

$y_0=-6$

3. (−5,39) there is a solution to the equation through this point because

$y_0>6$

4. (−1,45) there is a solution to the equation through this point because

$y_0>6$

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Lenny has a remaining balance on his credit card of $800. His credit card has an APR of 22 percent. How much will he pay in inte

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2 years ago

What are the solution of the equation 2|×+7|-3=5​

What are the solution of the equation 2|×+7|-3=5