Please help me on both?!?

labwork [276]

The values of x for which the rational expression is undefined are -6 and -8.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a rational function:

$\rm f(x) = \dfrac{3x+20}{x^2+14x+48}$

As we know in the rational function denominator cannot be zero:

The values of x for which the rational expression is undefined.

x² + 14x + 48 = 0

$\rm x_{1,\:2}=\dfrac{-14\pm \sqrt{14^2-4\cdot \:1\cdot \:48}}{2\cdot \:1}$

$\rm x_1=\dfrac{-14+2}{2\cdot \:1},\:x_2=\dfrac{-14-2}{2\cdot \:1}$

x = -6, -8

Thus, the values of x for which the rational expression is undefined are -6 and -8.

Learn more about the function here:

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6 0

1 year ago

Seema covered 3 4/13(three four by thirteen)km by bus,2 5/13(Two five by thirteen)km by metro and 1 2/13(One two by thirteen)km

Ad libitum [116K]

Answer: 89/13 km

Step-by-step explanation:

3 4/13 + 2 5/13 + 1 2/13

= 43/13 + 31/13 + 15/13

= 89/13 km

6 0

2 years ago

How many solutions does a triangle with side lengths a = 4, A = 112º and b = 9 have?

Ainat [17]

Answer:

This case has NO solutions.

Step-by-step explanation:

Notice that you are in a case of an obtuse triangle (one of its angles is larger than 90 degrees), the side opposite to the obtuse triangle is shorter than the side adjacent to the angle, so no actual triangle can be formed.

This can be found by simply trying to apply the Law of Sines to solve for the value of angle "B" opposite to side "b":

$\frac{sin(A)}{a} =\frac{sin(B)}{b}\\sin(B)=\frac{b\,sin(A)}{a}\\sin(B)=\frac{9\,sin(112^o)}{4}\\\\sin(B)=2.086$

As shown above, we get an impossible mathematical condition (also call an absurd), since the sine of an angle cannot give a value larger than 1 (one).

Therefore, there is no angle we can find to build a triangle with the given data.

7 0

3 years ago

. Which ordered pairs in the form (x, y) are solutions to the equation 7x – 5y = 28?

Brut [27]

we know that

If a ordered pair (x,y) is a solution of the equation, then the ordered pair must satisfy the equation

we have the equation

$7x-5y=28$

Let's verify all the cases to determine the solution to the problem.

case A) point $(-6,-14)$

Substitute the values of x and y in the equation

$x=-6\\y=-14$

$7(-6)-5(-14)=28$

$-42+70=28$

$28=28$ -------> is true

therefore

The point $(-6,-14)$ is a solution of the equation

case B) point $(-1,-7)$

Substitute the values of x and y in the equation

$x=-1\\y=-7$

$7(-1)-5(-7)=28$

$-7+35=28$

$28=28$ -------> is true

therefore

The point $(-1,-7)$ is a solution of the equation

case C) point $(4,10)$

Substitute the values of x and y in the equation

$x=4\\y=10$

$7(4)-5(10)=28$

$28-50=28$

$-22=28$ -------> is not true

therefore

The point $(4,10)$ is not a solution of the equation

case D) point $(7,9)$

Substitute the values of x and y in the equation

$x=7\\y=9$

$7(7)-5(9)=28$

$49-45=28$

$4=28$ -------> is not true

therefore

The point $(7,9)$ is not a solution of the equation

therefore

the answer is

$(-6,-14)$

$(-1,-7)$

8 0

3 years ago

Read 2 more answers

A convex parabola is shown in a coordinate plane. The parabola connects the points left-parenthesis negative 4.5 comma 12 right-

spayn [35]

Since the parabola is connecting the points, it means that the points given are on the parabola or that the points are solutions of the parabola. Thus, when we substitute the points into the function, we should end up with the correct y-value.

To find the correct choice, let's test a point. An easy point to test I believe would be (-3, 0) because we should be getting 0 as a y-value. Let's test:

$A. (- 3 - 3)(3 + 4) = -42$

$B. (-3 + 3)(-3 - 4) = 0$

$C. (-3 + 2)(-3 - 4) = 7$

$D. (-3)(-3 + 12) = -27$

We can see that Choice B is the correct function, because it produces 0 when we substitute $x = - 3$ . Thus, Choice B, or (x + 3)(x - 4) is the answer.

8 0

2 years ago