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Answer:
-2
Step-by-step explanation:
 
        
             
        
        
        
The <em>speed</em> intervals such that the mileage of the vehicle described is 20 miles per gallon or less are: v ∈ [10 mi/h, 20 mi/h] ∪ [50 mi/h, 75 mi/h]
<h3>How to determine the range of speed associate to desired gas mileages</h3>
In this question we have a <em>quadratic</em> function of the <em>gas</em> mileage (g), in miles per gallon, in terms of the <em>vehicle</em> speed (v), in miles per hour. Based on the information given in the statement we must solve for v the following <em>quadratic</em> function:
g = 10 + 0.7 · v - 0.01 · v²      (1)
An effective approach consists in using a <em>graphing</em> tool, in which a <em>horizontal</em> line (g = 20) is applied on the <em>maximum desired</em> mileage such that we can determine the <em>speed</em> intervals. The <em>speed</em> intervals such that the mileage of the vehicle is 20 miles per gallon or less are: v ∈ [10 mi/h, 20 mi/h] ∪ [50 mi/h, 75 mi/h].
To learn more on quadratic functions: brainly.com/question/5975436
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A good place to start is to set  to y. That would mean we are looking for
 to y. That would mean we are looking for  to be an integer. Clearly,
 to be an integer. Clearly,  , because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since  is a radical, it only outputs values from
 is a radical, it only outputs values from ![[0,\infty]](https://tex.z-dn.net/?f=%20%5B0%2C%5Cinfty%5D%20) , which means y is on the closed interval:
, which means y is on the closed interval: ![[0,120]](https://tex.z-dn.net/?f=%20%5B0%2C120%5D%20) .
.
With that, we don't really have to consider y anymore, since we know the interval that  is on.
 is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval ![[0,120]](https://tex.z-dn.net/?f=%20%5B0%2C120%5D%20) , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
, which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:

Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.