Answer:
Solution. The domain of g(x) consists of all real numbers except x = 32, since that input value would cause us to divide by 0. Likewise, the domain of f consists of all real numbers except 1. So we need to exclude from the domain of g(x) that value of x for which g(x) = 1.
Step-by-step explanation:
Answer:
PART A: Inequality (a)
Solve for y
The graph of y ≥ ⅓(8-x) is represented by the upper red line and all points in the shaded area below it. The line is solid because points on the line satisfy the conditions.
Inequality (b)
Solve for y
The graph of y ≥ 2 - x is represented by the lower blue line and all points in the shaded area above it. The line is solid because points on the line satisfy the conditions. The solution lies in the purple area. It consists of all combinations of x and y that make y ≥ ⅓(8 - x) and y ≥ 2 - x. A practical but not a mathematical condition is that all values of x and y must be zero or positive numbers (for example, you can't have -2 servings of food), so I have plotted only the numbers in the first quadrant.
PART B: If a point is a solution of the system, then the point must satisfy both inequalities of the system.
For x=8, y=2. Verify inequality A is not true. So the point does not satisfy inequality A. Therefore, the point is not included in the solution area for the system.
PART C: I choose the point (3,1) which is included in the solution area for the system.
That means Michelle buys 3 serves of dry food and 1 serving of wet food.
Step-by-step explanation:
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Let the number of orders Eric served be x
Eric = x
Mai = x+ 8 [Mai served 8 more than Eric]
Dean = 3x [Dean served 3 times as many as Eric]
Given that the total is 103
x + x + 8 + 3x = 103
5x + 8 = 103
5x = 103 - 8
5x = 95
x = 19
x = 19
x + 8 = 19 + 8 = 27
3x = 19 x 3 = 57
Eric served 19
Mai served 27
Dean served 57
Answer:
The height of the model is 138 cm.
Step-by-step explanation:
Simply multiply the height by the scale factor.
230*0.006
= 1.38 m
We need to convert this measure to centimeters. Centimeters are 1/100 of a meter. Therefore, we can multiply 1.38 meters by 100 to find how many centimeters it is equal to.
1.38*100 = 138
The height of the model is 138 cm.
Answer:
a.
b.
Step-by-step explanation:
Solving (a):
Required
Determine her savings.
Solving (a):
Required
Determine the price before tax
First, we need to determine her savings
The price before tax is calculated as follows: