Step-by-step explanation:
xy + 10 = 0. => y = -10/x.
2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.
When -10/x = -2/3 x + 7/3,
-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.
=> 2x² - 7x - 30 = 0
=> (2x + 5)(x - 6) = 0
=> x = -2.5 or x = 6.
dy/dx = d/dx [-10/x] = 10/x².
When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.
When x = 6, dy/dx = 10 / (6)² = 5/18.
Hence the gradients at the points are 1.6 and 5/18.
The simplified expression of the function 
is
. f(x) is increasing for all x > –4.The correct answer is option C.
<h3>What is a function?</h3>
A function is defined as a relation between the set of inputs having exactly one output each.
The function expression is given as:
Expand the denominator
Factorize the denominator
Factor out x + 9
The simplified expression of the function is
. f(x) is increasing for all x > –4
Read more about functions at:
brainly.com/question/1851758
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Answer:
-1/2.
Step-by-step explanation:
Slope = rise / run
= (1 - -7) / (-1 -3)
= 8/-4
= -1/2.
Whenever a number is followed by percent, you can turn it into a fraction by simply moving the decimal places two places to the left:
90.0 % becomes .90
As a fraction, this is 90 over 100. To reduce it to its simplest form, divide by 10:
9/10
