A discounted amusement park ticket costs $12.95 less than the original price P write and solve an equation to find the original
1 answer:
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EF = 50 in.
In similar figures, corresponding sides are proportional. We use the similarity statement ABCD~EFGH to write a proportion:
Cross multiply the proportion:
45*x = 75*30
45x = 2250
Divide both sides by 45:
45x/45 = 2250/45
x = 50
In similar figures, corresponding sides are proportional. We use the similarity statement ABCD~EFGH to write a proportion:
Cross multiply the proportion:
45*x = 75*30
45x = 2250
Divide both sides by 45:
45x/45 = 2250/45
x = 50
Answer with step-by-step explanation:
The way the question is worded, this actually shouldn't be correct. The correct answer should be .
Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.
Why?
By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.
Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are and
.
The ratio of is
.
The reason why it ideally should be and not
is because the question states
, which mentions
first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.
The function is 
.
To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:
f(1)=1-11+36-36, not 0
f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).
Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).
We can also try some other factors of 36. Indeed we can check that
f(3)=27-99+108-36=135-135=0,
and
f(6)=216-396+216-36=0.
Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.
This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).
Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6.
The y-intercept is f(0), which is -36.
Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly,
we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.
Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity,
and it goes to minus infinity as x goes to - infinity.
To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:
f(1)=1-11+36-36, not 0
f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).
Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).
We can also try some other factors of 36. Indeed we can check that
f(3)=27-99+108-36=135-135=0,
and
f(6)=216-396+216-36=0.
Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.
This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).
Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6.
The y-intercept is f(0), which is -36.
Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly,
we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.
Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity,
and it goes to minus infinity as x goes to - infinity.