1/2. Half a gallon...........
<h3>
Answer:</h3>
no
<h3>
Step-by-step explanation:</h3>
The triangles are only similar if B lies on AD and C lies on AE.
There is nothing in the given information indicating B lies on AD, or that C lies on AE. AB and BD are identified as separate segments, so don't necessarily lie on the same line. C is not identified as being anywhere in particular. "The figure shown" cannot be assumed to have any characteristics not specifically identified.
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<em>Comment on the problem</em>
The answer depends somewhat on the context of the problem. If this comes from course material in which you are routinely asked to make assumptions about figures, then the correct answer here is probably "yes." If this comes from course material that expects you to exercise critical thinking and to make no assumptions about geometrical figures, then the answer here is definitely "no."
In my opinion, one of the main purposes of studying math is to learn critical thinking—to pay attention to given facts and any assumptions you need to make.
Answer:
Negative
Step-by-step explanation:
(-2)^4 will be positive because the exponent is even.
(-3)^7 will be negative because the exponent is odd.
An positive number times a negative number is negative, so we know the result will be negative.
Look at the attached image for further clarification.
Answer:
No solution
Step-by-step explanation:
There are no values of x that make the equation true.
When you replace the comparison symbol (<) with an equal sign (=), you get the equation of a line in slope-intercept form:
... y = mx + b
where <em>m</em> is the slope, and <em>b</em> is the y-intercept.
Your equation has m = -1/4 and b = -1. To graph this line, find the point (0, -1) on the y-axis. To find another point on the line, you can use the slope value (rise/run = -1/4), which tells you the line "rises" -1 for each "run" of +4. That is, another point on the line will be 4 units to the right and 1 unit down, at (4, -2). Working in the other direction (to the left, instead of to the right), the -1/4 slope tells you the point 4 units left and 1 unit up (-4, 0) will also be on the line. <em>Draw a dashed line through these points,</em>
The dashed line you just drew is the boundary of the solution region. It is dashed because the line itself is not part of the solution. (Those points do not meet the requirement for "less than.")
Appropriate values of y are ones that are <em>less than</em> those on the line, so the solution region is indicated as being the half-plane <em>below</em> the line. You indicate this by shading the solution region. (See the attachment for an example of the way this can be graphed.)
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If the comparison is ≤ instead of <, then the line is solid (not dashed), indicating it is part of the solution region. If the comparison is > or ≥, then the shaded region is <em>above</em> the line, where y-values are greater than those on the line.