What is the oblique asymptote of the function f(x) = the quantity x squared minus 5x plus 6 over the quantity x minus 4?
1 answer:
Answer:
x - 1
Step-by-step explanation:
We know that, a slant or oblique asymptote of a rational function is the asymptote that helps in determining the direction of the function.
It occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.
Now, we divide the numerator by denominator using long division method and the first two terms in the quotient ( forming a linear function ) is the equation of the oblique asymptote.
We are given the rational function, .
After dividing we get that, the quotient is x - 1.
Hence, the equation of the oblique asymptote is x-1.
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Answer:
1/16
Step-by-step explanation:
This question involves two distinct genes; one coding for seed shape and the other for cotyledon color. The alleles for round seeds (R) and yellow cotyledons (Y) are dominant over the alleles for wrinkled seed (r) and green cotyledon (y) respectively.
In a cross between a truebreeding (i.e. same alleles for both genes) pea having round seeds and yellow cotyledon (RRYY) and a truebreeding pea having wrinkled seeds and green cotyledon (rryy), the F1 offsprings will all possess a heterozygous round seed and yellow cotyledon (RrYy).
The F1 offsprings (RrYy) will produce the following gametes: RY, Ry, rY, and ry. Using these gametes in a punnet square (see attached image), 16 possible offsprings will be produced in a ratio 9:3:3:1.
According to the question, 3/16 of the F2 offsprings will possess round seeds and green cotyledons, however, only 1 of them will be truebreeding i.e. RRyy. Hence, 1/16 of the F2 offsprings will be truebreeding for round seeds and green cotyledons.
Answer : Distance of plane from a given point =0.408
Explanation:
Since the equation of plane is x-y+2z-2=0
and the given point is (1,2,1)
And we know the formula of distance of plane from a point
i.e.
D=
where A,B,C are the coefficient of x, y, z respectively ,
and are the given points .
So,
=
=
=
Now by using calculator we can find the value of √6 i.e. 2.449 upto three decimal places.
∴ Distance = 0.408
The common features of f(x) = 2x² + 7x + 6 and g(x) = 2^x + 5 are
- Same y-intercept at y = 6
- Same end behavior as x approaches positive infinity, both functions approach positive infinity
The functions are given as:
f(x) = 2x² + 7x + 6
g(x) = 2^x + 5
See attachment for the graphs of both functions.
From the attached graph, we have the following common features
- Same y-intercept at y = 6
- Same end behavior as x approaches positive infinity, both functions approach positive infinity
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