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sleet_krkn [62]
2 years ago
11

Anyone good with algebra 2??

Mathematics
1 answer:
sweet [91]2 years ago
6 0
A discontinuity is a point that cannot exist because the x-coordinate would cause a problem in the equation. If you have a polynomial in the denominator, you must find which values of x would cause the polynomial in the denominator to evaluate to zero. Since division by zero is undefined, that would cause a discontinuity.

Let's look at your function.

f(x) = \dfrac{x^2 - 16}{6x - 24}

x^2 - 16  is in the numerator. It is defined for every value of x. There is no problem there.

6x - 24  is in the denominator. This is a function defined for every value of x, but since it is in the denominator, we must exclude the x-value that would cause this polynomial to evaluate to zero.

We set it equal to zero and solve the equation for x.

6x - 24 = 0

6x = 24

x = 4

For x = 0, the denominator has a value of zero, so at this point there is a discontinuity in function f(x).

The answer is:

x \ne 4

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Solving inequalities for word problems:
zepelin [54]

For this case we have to:

x: Let the variable representing the unknown number

We algebraically rewrite the given expression:

Twice a number plus 10, is represented as:2x + 10

Three times that number less 4. is represented as:

3x-4

Thus, the complete expression is:

2x + 10> 3x-4

Subtracting 3x from both sides of the inequality:

2x-3x + 10> -4\\-x + 10> -4

Subtracting 10 from both sides of the inequality:

-x> -4-10

Equal signs are added and the same sign is placed:

-x> -14

We multiply by -1 on both sides, taking into account that the sense of inequality changes:

x

The solution is given by all values of "x" less than 14.

Answer:

x

5 0
2 years ago
Geometry boy yo please help
densk [106]

Answer:

x=12

Step-by-step explanation:

ab=dc so 15=x+3 you subtract 3 from both sides... x=12

4 0
2 years ago
the height of a triangle is 9m less than its base. the area of the triangle is 56 m^2 find the length of the base (SHOW STEPS)
Veronika [31]
Hey there :)

We know the area formula of a triangle
\frac{1}{2} (base)(height)

We are given:
The area = 56 m²
The base = let p represent this
The height = 9 m less than the base = p - 9

Apply the formula
56 = \frac{1}{2} × ( p ) × ( p - 9 )
56 = \frac{1}{2} × ( p² - 9p )

Divide \frac{1}{2} on both sides
56 ÷ \frac{1}{2} = p² - 9p
112 = p² - 9p

Bring 112 to the other side and equate equation to 0
p² - 9p - 112

Factorise { Sum = -9 , Product = - 112 , therefore suitable factors = - 16 × 7 )
( p - 16 )( p + 7 ) = 0
     ↓          ↓
 p = 16    p = - 7  ←  Reject p = - 7 since length cannot be negative

So, the length  of the base is 16 m

Check:
56 m² = \frac{1}{2} × 16 × ( 16 - 9 )
56 m² = 8 × 7
56 m² = 56 m²
7 0
3 years ago
Find the slope of the line through points
gayaneshka [121]

Answer:

The answer is

\huge  \frac{1}{9}  \\

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

m =  \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\

From the question we have

m =  \frac{3  - 2}{1 -  - 8}  =  \frac{1}{1 + 8}  =  \frac{1}{9}  \\

We have the final answer as

\frac{1}{9}  \\

Hope this helps you

8 0
3 years ago
MARK AS BRAINLIEST....<br><br><br> -4-(-2)=?<br> 9-(-5)?
Flauer [41]

-2

Answer:

14

Step-by-step explanation:

- 4 - ( - 2) =  - 4 + 2 =  - 2 \\  \\ 9 - ( - 5) = 9 + 5 = 14

5 0
3 years ago
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