5. Graph the given system of linear inequalities on the coordinate plane below. (2 points)sy <-3x - 4< 21-15NA11 2 3 4 5 6
7-7 -6 -5 4-3-2-11-2-34-567.6. Give two ordered pairs that are solutions and two that are not solutions to the system of linear inequalitiesyou graphed above. (2 points)
1 answer:
ANSWERS
(5) Graph:
(6) Solutions: (-1, -5) and (-2, -7)
Not solutions: (1, 1) and (-4, -3)
EXPLANATION
(5) To graph this system, first, we have to graph each of the inequalities. Both are linear, so we have to graph each line with a dashed line - this is because they are "less than" the line, so the line is not included, and shade the area below each of them.
The first inequality is y < -3x-4,
The second inequality is y < 2x - 1,
The graph of the system is the area shared by both graphs,
(6) Any point that is inside the shaded area is a solution of the system. For example, points (-1, -5) and (-2,-7) are solutions to the system.
On the other hand, any point outside that area, or on the dashed lines is not a solution. For example, points (1, 1) and (-4, -3) are not solutions
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Answer:
a. 2^(x-2) = g^(-1)(x)
b. A, B, D
Step-by-step explanation:
the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)
1. replace g(x) with y and solve for x
y = log₂(x) + 2
subtract 2 from both sides to isolate the x and its log
y - 2 = log₂(x)
this text is replaced by the second image -- it was marked as inappropriate
thus, 2^(y-2) = x
replace x with g^(-1)(x) and y with x
2^(x-2) = g^(-1)(x)
2. plug this in to points A, B, C, D, E, and F
A: (2,1)
plug 2 in for x
2^(2-2) = 2⁰ = 1 so this works
B: (4, 4)
2^(4-2) = 2²= 4 so this works
C: (9, 3)
2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work
(5, 8)
2^(5-2) = 2³ = 8 so this works
E: (3, 5)
2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work
F: (8, 5)
2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work
Answers:
Row one: 1 and 1
Row two: 1, 2, and 1
Row three: 1, 3, 3, and 1
Row four: 1, 4, 6, 4, and 1
=========================================
Explanation:
Each value can be found in Pascal's triangle. You can also use the nCr combination formula to get each value. The nCr formula is
The value of n represents the row number. The r value is the column number, so to speak, for each row.
<h2>Answer:</h2>
Our functions are:
To solve this, we must use the expression g(-10) - f(3).
The value of the expression g(-10) - f(3) is <em>15</em>.