i) The given function is
The domain is all real values except the ones that will make the denominator zero.
The domain is all real values except, x=2.5.
ii) To find the vertical asymptote, we equate the denominator to zero and solve for x.
iii) If we equate the numerator to zero, we get;
This implies that;
iv) To find the y-intercept, we put x=0 into the given function to get;
.
.
.
v)
The degrees of both numerator and the denominator are the same.
The ratio of the coefficient of the degree of the numerator to that of the denominator will give us the asymptote.
The horizontal asymptote is 
.
vi) The function has no common factors that are at least linear.
The function has no holes in it.
vii) This rational function has no oblique asymptotes because it is a proper rational function.
The base of its triangular face of the triangular prism is found as 17.7 cm.
<h3>What is defined as the triangular prism?</h3>
- A polyhedron with two triangular bases as well as three rectangular sides is known as a triangular prism.
- It is a three-dimensional shape with three side faces but also two base faces that are connected by the edges.
The formula for the volume of triangular prism is;
Volume = base area x length
The base area of the triangular base.
The area of the triangle = 1/2 base×height
The given values are-
- volume = 2,354. 1 cubic centimeters.
- length = 19 cm
- height = 14 cm.
Thus, volume = base area x length
volume = 1/2 base × height × length
base = 2v/(height × length)
Put the values;
base = 2×2,354.1/(14 × 19)
base = 4708.2/(14 × 19)
base = 17.7 cm
Thus, the base of the triangular prism is found as 17.7 cm.
To know more about the triangular prism, here
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Answer is in the attached figure.
Work backwards.
Start with z = 4.
Now deal with the middle equation
y + 3z = 11 Substitute z = 4 and solve for y
y + 3(4) = 11 Subtract 12 from both sides
y + 12 = 11
y + 12 - 12 = 11 -12 Combine terms on the left and right
y = - 1 Now use the top equation for x
z = 4 z still = 4
2x + 4(-1) +3(4) = 14
2x - 4 + 12 = 14 Solve 3z
2x + 8 = 14 Subtract 8
2x + 8 - 8 = 14 - 8 Combine
2x = 6 Divide by 2
x = 6/2
x = 3
Answer
x = 3
y = - 1
z = 4
