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Dvinal [7]
2 years ago
9

How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) a

t x, rather than a vertical asymptote? Give an example​
Mathematics
1 answer:
Eva8 [605]2 years ago
5 0

Consider that,

x^2+4x+4 = (x+2)(x+2)

x^2+7x+10 = (x+2)(x+5)

Dividing those expressions leads to

(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)

The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.

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H(x) = x2 + 3x – 2; 12 - h(7)10​
nikitadnepr [17]

Answer:

2x + -10 = 10 + -3x

Reorder the terms:

-10 + 2x = 10 + -3x

Move all terms containing x to the left, all other terms to the right.

Add '3x' to each side of the equation.

-10 + 2x + 3x = 10 + -3x + 3x

Combine like terms: 2x + 3x = 5x

-10 + 5x = 10 + -3x + 3x

Combine like terms: -3x + 3x = 0

-10 + 5x = 10 + 0

-10 + 5x = 10

Add '10' to each side of the equation.

-10 + 10 + 5x = 10 + 10

Combine like terms: -10 + 10 = 0

0 + 5x = 10 + 10

5x = 10 + 10

Combine like terms: 10 + 10 = 20

5x = 20

Divide each side by '5'.

x = 4

hope dis helps <3

8 0
2 years ago
A scale drawing of a movie screen is 21 inches long and 9 inches tall. The actual screen is 30 feet tall. What is the scale of t
MatroZZZ [7]
<span>A scale factor is the ratio of two similar geometric figures of their corresponding sides. The scale factor is calculated by locating the corresponding sides on each figure. We calculate as follows:

scale factor = 9/30 = 0.3

Hope this answers the question. Have a nice day. </span>
8 0
3 years ago
Use the given conditions to write an equation for the line in​ point-slope form and general form. Passing through (8 comma negat
miskamm [114]

Answer:

The answer to your question is   y = -5x + 32          point-slope form

                                                      5x + y - 32 = 0      general form

Step-by-step explanation:

Data

(8, -8)

⊥ x - 5y - 6 = 0

Process

1.- Get the slope of the line given

   x - 5y - 6 = 0

   -5y = -x + 6

      y = -x/-5 + 6/-5

      y = x/5 - 6/5

slope = 1/5

slope of the new line -5, because the lines are perpendicular

2.- Get the equation of the new line

          y - y1 = m(x - x1)

          y + 8 = -5(x - 8)

          y + 8 = -5x + 40

          y = -5x + 40 - 8

         y = -5x + 32          point-slope form

Equal to zero to find the general form

         5x + y - 32 = 0      general form

5 0
2 years ago
A group of teachers and students will take a bus trip to a museum, and each teacher will lead a group of no more than 4 students
ValentinkaMS [17]

Answer:

A maximum of 43 students and 11 teachers can go to the trip.

Step-by-step explanation:

Since a group of teachers and students will take a bus trip to a museum, and each teacher will lead a group of no more than 4 students, and the bus can hold a maximum of 54 teachers and students, to determine the possible numbers of teachers and students who can go on the trip, the following calculation must be performed:

4 + 1 = 5

54/5 = X

10.8 = X

10 x 4 = 40

10 x 1 = 10

4 - 1 = 3

Therefore, a maximum of 43 students and 11 teachers can go to the trip.

8 0
2 years ago
Given that ƒ(x) = x² + 4x, evaluate ƒ(-2)
Amiraneli [1.4K]
F(-2)=(-2)2+4(-2)
4-8
-4
3 0
3 years ago
Read 2 more answers
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