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anastassius [24]
3 years ago
15

5x+21+178/(x-7) How do I solve for domain and range on this equation?

Mathematics
1 answer:
Luda [366]3 years ago
3 0
The domain is easiest. You simply need to find the fractions, and exclude any X that makes the denominator zero. So in this case, your domain is everything except X=7.

For range, you are trying to find out what are the possible answers. Usually the best way to do this is to try x=infinity, and x=negative infinity, which here gives you answers of infinity and negative infinity. Since the function is almost continuous, I think your range is any real number.
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At 107°F, a certain insect chirps at a rate of 92 times per minute, and at 113°F, they chirp 116 times per minute. Write an equa
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Answer:

The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.

Step-by-step explanation:

A linear equation can be expressed in the form y=m*x + b. In this equation, x and y are coordinates of a point, m is the slope and b is the y coordinate of the y-intercept. Since this equation describes a line in terms of its slope and its y-intercept, this equation is said to be in its slope-intercept form.

When there are two points of a line (x1, y1) and (x2, y2), the slope is determined by the quotient between the difference of the ordinate of these two points and the difference of the abscissa of the same points. This is:

m=\frac{y2-y1}{x2-x1}

Having a point on the line, you can substitute the values ​​of m, x and y in the equation y = mx + b and thus find b.

In this case:

  • (x1, y1): (92, 107)
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So:

m=\frac{113-107}{116-92}

m= 0.25

substituting the values ​​of m, x1 and y1 in the equation y = mx + b you have:

107= 0.25*92 + b

107 - 0.25*92= b

84=b

<u><em>The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.</em></u>

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