The <em><u>correct answers</u></em> are:
A-theorem
; B-corollary
; C-Postulate
; and E-Definition.
Explanation:
In a proof, we are tasked with proving one statement using other information that has already been proven.
Theorems are statements that have already been proven, and are used to prove other statements.
A postulate is a statement that is assumed to be true, and is used to prove other statements.
A corollary is a direct consequence of a proven fact, and as such, are used to prove other statements.
A definition is an absolute truth, so it can also be used to prove another statement.
The correct answer is: [D]: " y = - 4x − 13 " .
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Explanation:
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All the answer choices given are written in "point-slope format" (also known as "slope-intercept format" — that is: " y = mx + b" .
All of the answer choices given have a slope of "-4" ; that is: "m = -4" .
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The only answer choice with the equation that passes through point
"(-3, 1)" — that is, when "x = -3, y = 1" — is:
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Answer choice: [D]: " y = - 4x − 13 " .
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In the equation: " y = - 4x − 13 " ; when "x = - 3, y = 1" .
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Given: " y = - 4x − 13 " ;
↔ - 4x − 13 = y ;
Plug in "(-3)" for "x" ; and see that "y = 1" ;
-4(-3) − 13 = y ;
12 − 13 = y = -1 ;
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So, when x = -3, y = 1 .
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The correct answer is: [D]: " y = - 4x − 13 " .
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Consider choice: [A]: " y = - 4x + 13 " ;
Substitute "(-3)" for "x" and see if "y = -1" ;
-4(-3) + 13 = y ; 12 + 13 = 25 ; NOT "-3" .
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Consider choice: [B]: " y = - 4x + 7 " ;
Substitute "(-3)" for "x" and see if "y = -1" ;
-4(-3) + 7 = y ; 12 + 7 = 19 ; NOT "-3" .
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Consider choice: [C]: " y = - 4x − 7 " ;
Substitute "(-3)" for "x" and see if "y = -1" ;
-4(-3) − 7 = y ; 12 − 7 = 9 ; NOT "-3" .
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This leaves us with "Answer choice: [D]: " y = - 4x − 13 " ; the only remaining answer choice; which we have already confirmed is correct; so we do not need to check.
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Hope this helps!
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I’m working on the same thing in school! For number 2, what i would do is start by setting up the scatter plot by using the X and Y table and create origins to place on the graph. ( ex. (1,30) for your first one ). Also, remember to write in the laps completed and calories burned. Next, estimate a line that meets as many points as possible. ( I would use the completed scatter plot in number 3 for an example for how to draw the line ). And that’s all I can help you with :( I forgot how to do the equation part because I just started with this on Monday. Hope this helps!
-Taylor
