Which property justifies the following statement?
1 answer:
In the above question 13m=156 we are dividing both sides by 13 so that m=12 .As
According to Division property of Equality: If you divide one side of an equation by a number, you also must divide the other side by the same number so that your equation stays the same.
The property Division Property of Equality is justified .
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<h3>Domain: (-5, 3]</h3><h3>Range: [-4, 5)</h3>
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Explanation:
The domain is the set of allowed x values. In terms of a graph, we look at the left most point to see that x = -5 is the smallest x value possible. However, there's an open hole at this endpoint, so -5 itself is actually not part of the domain. So x must be larger than -5. At the same time, x can be as large as x = 3. Look at the very right tip of the graph to find this x value.
So x spans from -5 to 3, excluding -5 but including 3. We would write which converts to the interval notation (-5, 3]. Note the mix of curved parenthesis and square bracket. The curved parenthesis means to exclude the endpoint, while the square bracket means include the endpoint.
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The range is the set of possible y outputs. Find out the lowest point of the graph. That is when y = -4 and this value is included due to the filled in circle at the endpoint. But we do not include the largest y value y = 5 as there's an open hole at this endpoint.
So the range is the set of y values such that which in interval notation would be written as [-4, 5)
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So in short, you're looking for the min and max of x and y to get the domain and range respectively. Be sure to exclude any values where there are open holes as those do not count as part of the graph.
The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.
<h3>How to calculate the scale factor?</h3>Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
Thus, scale factor is the ratio of the new measurement to the old measurement.
For this case, we're specified that:
Dimensions of the original pool = 24 feet wide by 36 feet long
The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).
So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:
Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:
Scaled length = s times original length
Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.
Learn more about scale factors here :