If a linear system has four equations and seven variables, then it must have infinitely many solutions. True or False
1 answer:
Answer:
The statement is False.
Step-by-step explanation:
Consider the provided information.
If a linear system has four equations and seven variables, then it must have infinitely many solutions.
We need to determine the above statement is true or false.
The above statement is false, it could be inconsistent, and therefore have no solutions,
For example:
Hence, there is no solution.
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Complete question is;
A park has a 3 meter tall tether ball pole and a 6.8 m tall flagpole. The lengths of their shadows are proportional to their heights.
Which of the following could be the lengths of the shadows?
Choose 2 answers from the options attached.
Answer:
Options B & D
Step-by-step explanation:
From the question, the proportional relationship between the height and shadow length is a direct proportionality. This means that an increase in the height, leads to an increase in the length of shadow and vice versa. Thus, the height to shadow length ratio is a constant.
Now, if we use x and y to denote length of shadow of tether ball pole and length of flagpole receptively, we will have;
3/x = 6.8/y
Let's make y the subject.
y = 6.8x/3
Looking at the options;
Option A: When x = 1.35 m, we have;
y = (6.8 × 1.35)/3 = 3.06 m
For Option B:
When x = 1.8 m,
y= (6.8 × 1.8)/3 = 4.08 m
For Option C:
When x= 3.75 m,
y = (6.8 × 3.75)/3 = 8.5 m
For option D:
When x = 0.6
y = (6.8 × 0.6)/3 = 1.36 m
For option E;
When x = 2,
y = (6.8 × 2)/3 = 4.533 m
From our calculations, the only values of y that correspond with the given value of y in the options are Options B & D
Answer:
See explanation
Step-by-step explanation:
You forgot to give the coordinates of C.
Note that, the mapping for 90° clockwise rotation around the origin is given by:
Assuming the coordinates of C were (-6,6), then the coordinates of C after a 90° clockwise rotation
around the origin is (-6,-6)