The inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
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The nth term of the sequence is 2n - 8
<h3>Equation of a function</h3>
The nth term of an arithmetic progression is expressed as;
Tn = a + (n - 1)d
where
a is the first term
d is the common difference
n is the number of terms
Given the following parameters
a = f(1)=−6
f(2) = −4
Determine the common difference
d = f(2) - f(1)
d = -4 - (-6)
d = -4 + 6
d = 2
Determine the nth term of the sequence
Tn = -6 + (n -1)(2)
Tn = -6+2n-2
Tn = 2n - 8
Hence the nth term of the sequence is 2n - 8
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Answer:
The hypotenuse of a right triangle is 4m longer than the shorter leg and 2m longer than the longer leg. What are the lengths of the sides?
Just for variety, consider the hypotenuse = h, the short leg h-4 and the long leg h-2.
c^2 = a^2 + b^2; so h^2 = (h-4)^2 + (h-2)^2; h^2 = h^2 - 8h + 16 +h^2 -4h +4;
h^2 -12h +20 = 0 factors to (h - 10)(h - 2) = 0 so h = 2 or h = 10
Since (h - 2) = (2 - 2) = 0 and a triangle cannot have a side of zero length, 10 is the length of the hypotenuse.
h^2 = (h-4)^2 + (h-2); 10^2 = (10-4)^2 + (10-2); (10)^2 = (6)^2 + (8)
The hypotenuse is 10 cm, short leg 6 cm and long leg 8 cm.
Answer:
1) (a/3) - (b/2)
2) (m/3) + (5n/12)
3) (-5m/3) + (4x/3)
4) (4x/9) + (8y/9) - (z/3)
5) (-5a/8) + (-3b/8) + (-3c/2)
Step-by-step explanation:
1) 2a-3b divided by 6
(2a-3b)/6 = (2a/6) - (3b)/6 = (a/3) - (b/2)
2) 4m+5n divided by 12
(4m+5n)/12 = (4m/12) + (5n/12) = (m/3) + (5n/12)
3) 5m-4x divided by -3
(5m-4x)/(-3) = (-5m/3) + (4x/3)
4) 4x+8y-3z divided by 9
(4x+8y-3z)/9 = (4x/9) + (8y/9) - (3z/9) = (4x/9) + (8y/9) - (z/3)
5) 5a+3b+12c divided by -8
(5a+3b+12c)/(-8) = (-5a/8) + (-3b/8) + (-12c/8) = (-5a/8) + (-3b/8) + (-3c/2)
