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frosja888 [35]
3 years ago
11

If the graph f(x)= 9x^2+36x+41/3x+5 has an oblique asymptote at y=3x+k what is the value of k

Mathematics
2 answers:
Galina-37 [17]3 years ago
7 0

Answer:

7

Step-by-step explanation:

Gelneren [198K]3 years ago
5 0

Answer:

  • <u><em>The value of k is 7.</em></u>

Explanation:

To find the<em> oblique asymptote</em> of a rational function you divide the numerator by the denominator and take the quotient (not the remainder).

Such quotient (without the remainder) is the equation of the line that is the oblique asymptote of the rational function.

The rational function is:

             \frac{9x^2+36x+41}{3x+5}

You can see the long division in the picture attached. The quotient is 3x + 7.

Hence, by comparison with y = 3x + k, k = 7.

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Solve the equation for the y-value and choose whether it is a direct variation or inverse variation.
muminat

Answer:

B

Step-by-step explanation:

the equation representing direct variation is

y = kx ← k is the constant of variation

The equation representing inverse variation is

y = \frac{k}{x} ← k is the constant of variation

Given

3y = x ( divide both sides by 3 )

y = \frac{1}{3} x ← equation representing direct variation

with k = \frac{1}{3}

5 0
3 years ago
Find the function h(x) = f(x) + g(x) if f(x) = 4^x + 2 and g(x) = x - 4.
Rzqust [24]

Answer:

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

Step-by-step explanation:

h(x)=f(x)+g(x)=4^x+2+x-4=<u>4^x+x-2</u>

4 0
3 years ago
Solve: 2/x + 3/2x - 1/2 = 2/3
polet [3.4K]

Answer:

Step-by-step explanation:

\frac{2}{x}+\frac{3}{2x}-\frac{1}{2}=\frac{2}{3}\\multiply ~by~6x\\12+9-3x=4x\\21=4x+3x\\7x=21\\x=21/7=3

6 0
3 years ago
BRAINLIEST PLS HELP ASAP!!!
andrew11 [14]

Answer:

fourth option

Step-by-step explanation:

let t be tennis balls and g be golf balls, then

5t + 3g = 70 → (1)

2t + 5g = 85 → (2)

Multiplying (1) by 5 and (2) by - 3 will eliminate g

25t + 15g = 350 → (3)

- 6t - 15g = - 255 → (4)

Add (3) and (4) term by term to eliminate g

19t = 95 ( divide both sides by 19 )

t = 5

Substitute t = 5 into either of the 2 equations and solve for g

Substituting into (1)

5(5) + 3g = 70

25 + 3g = 70 ( subtract 25 from both sides )

3g = 45 ( divide both sides by 3 )

g = 15

Thus

$5 for tennis balls and $15 for golf balls

7 0
3 years ago
Smith's age is 8 and his mother is 42.in how many years will the mother be three times as his son​
frozen [14]
Let’s make an equation
Let’s say x = amount of years after
Smith = 8, mother = 42
3(8 + x) = 42 + x
24 + 3x = 42 + x
2x = 18, x = 9
Solution: after 9 years
3 0
3 years ago
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