We have points (-3, 4), (-1, 2), (4, -3) and (6,-5)
Let's verify it's a line by calculating the slopes between successive points.
Slope is change in y over change in x.
(2 - 4)/(-1 - -3) = -2/2 = -1
(-3 - 2)/(4 - -1) = -5/5 = -1
(-5 - -3)/(6 - 4) = -2/2 =-1
Yup. We have a line of slope -1 through point (-1, 2)
y - 2 = -1(x - -1)
y = -x - 1 + 2
y = -x + 1
That's the linear equation for the table.
Answer: Linear equation: y = -x + 1 slope = -1
The simplified expression for the given function is 2x + 4 - ( 1 / x-1). The correct option is A.
<h3>What is an expression?</h3>
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the functions are f(x) = x + 2 and h(x) = 1 / x-1. The value of the function 2f(x) – h(x) will be calculated as,
E = 2f(x) – h(x)
E = 2( x + 2 ) - ( 1 / x-1)
E = 2x + 4 - (1/x-1)
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(2x+1)+(3x-5)=5x-4 you just have to try some of them out and see which ones work
The airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent the rate of the airplane with no wind. and b the rate of the wind, hence:
(a - b)3.2 = 640
a - b = 200 (1)
Also:
(a + b)2 = 640
a + b = 320 (2)
The solution to equation 1 and 2 is:
a = 260, b = 60
The airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.
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