(x²+4x+3)/2(x²-10x+25)
the horizontal asymptote when the numerator and the denominator have the same degree (in this case, both of a degree of 2) is ration of the coefficients of the numerator and denominator. In this case, the coefficient for numerator x² is 1, and the coefficient for the denominator 2x² is 2, so the horizontal asymptote is y=1/2=0.5
the vertical asymptote is the x value. the denominator cannot be zero, if x²-10x+25=0, x would be 5, so the vertical asymptote is x=5
this is just one example. There can be others:
(2x²+5x+2)/[(4x-7)(x-5)] for another example, but this example has a second vertical asymptote 4x-7=0 =>x=7/4
ANSWER
EXPLANATION
A) From the diagram, we see that the base of the triangular face is 4 cm long and the height of the triangular face is 3 cm.
B) From the diagram, we see that the length of two of the rectangular face is 15 cm and the width of the rectangular face is 5 cm.
The third rectangular face has a length of 15 cm and a width of 4 cm.
C) The surface area of the prism is the sum of the areas of the faces of the prism.
The area of a triangle is given as:
where b = base, h = height
The area of a rectangle is given as:
where l = length, w = width
Therefore, the surface area of the prism is:
Answer:
32
Step-by-step explanation:
We can write an algebraic equation to solve this situation: 
, where x = first integer (small number) and x + 1 = the following integer.
Step 1: Combine like terms.
Step 2: Subtract 1 from both sides.
Step 3: Divide both sides by 2.
Therefore, the smaller number is 32 while the larger number is 33.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
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This is an exercise you should actually do with real physical objects. The objects don't have to be wood and they don't have to be square for you to be able to arrange them into a rectangular shape. You can cut squares from paper, or use Scrabble™ tiles, poker chips, pennies, M&M™ candies, bottle caps, Legos™, Cheez-It™ crackers, pebbles, or any other objects of similar size and shape.
What you will find is that there are 8 possibilities, corresponding to the number of divisors of 24:
1×24, 2×12, 3×8, 4×6, 6×4, 8×3, 12×2, 24×1
_____
If you make rectangles from numbers of pieces other than 24, you will find that only two rectangles are possible for prime numbers, like 23: 1×23 or 23×1. Even numbers of tiles will all have rectangles of 1×_ and 2×_ (as well as _×1 and _×2).
Doing this sort of playing with physical objects helps you develop number sense that can serve you well later. Don't discount it.
