A. Which reduction should she use so the picture fills as much of the frame as possible, without being too large?
Find the scale factor to get rom 7 1/3 inches to 5 1/3 inches:
5 1/3 / 7 1/3 = 0.7272
Now rewrite the fraction as decimals:
2/3 = 0.667
¾ = 0.75
5/9 = 0.555
The closest scale that would still fit the frame would be 2/3 because it is under 0.727.
B. How much extra space is there in the frame when she uses the reduction from Part A?
Multiply the original size by the scale factor to use:
7 1/3 x 2/3 = 4 8/9
Now subtract the scaled size from the original size:
7 1/3 – 4 8/9 = 2 4/9 inches extra
C. If she had a machine that could reduce by any amount, so that she could make the reduced picture fit in the frame exactly, what fraction would the reduction be?
Convert the scale from part A to a fraction:
0.72 = 72/99 which reduces to 8/11
You are asked to find the missing value in
... 40 + ? = 70
given that it is also the solution to
... ? + 5 = 35
Either way, you subtract the constant that is on the same side of the equation as the unknown.
... 40 + ? - 40 = 70 - 40
... ? = 30 . . . . the missing value
_____
You can check to see if this also satisfies the equation
... 30 + 5 = 35 . . . . . . . true
Answer:
Step-by-step explain
Find the horizontal asymptote for f(x)=(3x^2-1)/(2x-1) :
A rational function will have a horizontal asymptote of y=0 if the degree of the numerator is less than the degree of the denominator. It will have a horizontal asymptote of y=a_n/b_n if the degree of the numerator is the same as the degree of the denominator (where a_n,b_n are the leading coefficients of the numerator and denominator respectively when both are in standard form.)
If a rational function has a numerator of greater degree than the denominator, there will be no horizontal asymptote. However, if the degrees are 1 apart, there will be an oblique (slant) asymptote.
For the given function, there is no horizontal asymptote.
We can find the slant asymptote by using long division:
(3x^2-1)/(2x-1)=(2x-1)(3/2x+3/4-(1/4)/(2x-1))
The slant asymptote is y=3/2x+3/4
Answer:
L=21.6in and w=13.6
Step-by-step explanation:
If the length is 8 inches longer than its width, we can write the width as "w" and the length as the width w+ 8
Area is (width)(Length) = (width)(width+8)
W
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| |
| |
| | L = w+8
| |
| |
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A = (w+8)(w)
A = w2 + 8w = 295.
(Problem states that area is 295 sq in)
Need to solve this quadratic equation
w2 +8y - 295 = 0
Factor:
(w - 13.64) (w + 21.64) = 0
So
w - 13.64 = 0. or. w + 21.64= 0
Solve these and get
w = 13.64. or. w = -21.64
Only one that makes sense in real life is the poitive one.
So the dimensions are
Width = 13.64 inches
Length = 21.64 inches
