Answer:
The length and width of the rectangle are 20 feet and 31.25 feet, respectively.
Step-by-step explanation:
Let the scale be 
and the dimensions of the rectangle being 4 inches and 5 inches, respectively. The scale (
), measured in inches per feet, is equivalent to the following rational number:
We can convert each length by dividing it by scale factor. That is:
Length
Width
The length and width of the rectangle are 20 feet and 31.25 feet, respectively.
Answer:
A. 
B. 
Step-by-step explanation:
Consider the equation
A. This equation has no solutions when the coefficients at x are the same and the free coefficients are not the same.
First, use distributive property:
So, the equation is
This equation has no solutions when
B. The equation has infinitely many solutions when the coefficients at x are the same and the free coefficients are the same too.
So, the equation
has infinitely many solutions when
In other cases, the equation has a unique solution
RS is perpendicular to MN and PQ.
We can use the slopes of these lines to determine the answer.
Slope is given by the formula
m=.
Using the coordinates for M and N, we have:
m=.
Since PQ is parallel to MN, its slope will be as well, since parallel lines have the same slope.
Using the coordinates for points T and V in the slope formula, we have
m=.
This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.
Using the coordinates for R and S in the slope formula, we have
m=. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.
Answer:
10×4 = 40
10^4 = 10,000
Step-by-step explanation:
10^4 is another way to write 10⁴ = 10·10·10·10 = 10,000.
Essentially, the exponent tells you how many places to the right of the leading digit the decimal point lies (here, the number of zeros in the number).
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<em>Comment on the answer choice</em>
The appropriate answer depends on what you mean by your problem statement. Some microscopes magnify 40 times; others magnify 10,000 times, so we cannot tell the appropriate answer using our knowledge of microscopes.
2 1/4 * 1 3/8 = 3 3/32 or 99/32
