A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
2 answers:
Answer:
Step-by-step explanation:
We know that this line passes through the point where "a" is the unknown x-coordinate of that point and 1 is the y-coordinate.
We also know that this line passes through the points (-1, -5) and (4, 5).
Then, in order to find the value of "a", we can plot the known points and draw the line (Observe the image attached).
You can observe in the image attached that the point whose y-coordinate is 1 is the point (2,1). Therefore, the value of "a" is:
Answer:
a = 2
Step-by-step explanation:
Let's find the equation of the line using the 2 points given.
Let's call -1 as x_1 and -5 as y_1
also, 4 as x_2 and 5 as y_2
The equation of line is :
<em>Let's plug the points and get the equation of the line:</em>
Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:
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We need to find an inequality that represents the possible landing or take of conditions of an aircraft, the required graph and one case where the inequality will be tested.
The required inequality is .
The graph represents the allowable temperature range in which the aircraft can takeoff or land.
The pilot could not have taken off on June 1990, the temperature in Phoenix, Arizona.
Let the temperature be denoted by
The temperature cannot be at or below , so
The temperature cannot be at or above , so
The inequality will be .
In the graph it can be seen that all points between -40 and 118 falls in the shaded region but it will exclude the points -40 and 118.
The graph represents the allowable temperature range in which the aircraft can takeoff or land.
The temperature in June 1990 in Phoenix, Arizona was which is more than
.
Hence, the pilot could not have taken off on this day.
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To factor both numerator and denominator in this rational expression we are going to substitute 
with 
; so 
and 
. This way we can rewrite the expression as follows:
Now we have two much easier to factor expressions of the form
. For the numerator we need to find two numbers whose product is 
(30) and its sum 
(-11); those numbers are -5 and -6. 
and 
.
Similarly, for the denominator those numbers are -2 and -5.
and 
. Now we can factor both numerator and denominator:
Notice that we have
in both numerator and denominator, so we can cancel those out:
But remember than
, so lets replace that to get back to our original variable:
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is
Now we have two much easier to factor expressions of the form
Similarly, for the denominator those numbers are -2 and -5.
Notice that we have
But remember than
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is