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Lana71 [14]
3 years ago
14

Need some help! Graph the equations y=3x-5 and x+3y=6 on the same xy-plane. What is significant about these two lines? (Explain

your answer)
Thanks!

Mathematics
1 answer:
adell [148]3 years ago
6 0
To solve this, we must first put both lines in Slope Intercept Form (y=mx+b where m is the slope and b is the y-intercept).

y=3x-5 is already in SIF, so we only need to work on the other one.

 x+3y=6
-x       -x
 3y=-x+6
 /3      /3
 y=-1/3x+2

Now we have both equations in slope intercept form, so we can start graphing from the y-intercepts and just follow the slopes.

When we do this, we will see that the lines meet at an exactly 90° angle. When a pair of lines does this, it means they are perpendicular.

Below I have attached an image that has both lines graphed so that you may visualize it. The green dots show the slopes, while the highlighted areas show the y-intercepts. Note that the lines intersect at a 90° angle, making them perpendicular.

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Find a compound proposition involving the propositional variables p, q, and r that is true when exactly two of p, q, and r are t
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Consider the proposition C=(p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)

Step-by-step explanation:

This compound proposition C uses the outer disjunction (∨) then the proposition is true if and only if one of the three propositions (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.

First, it is impossible that two or three of these propositions are simultaneously true. For example, if (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjuntion) and r is true (from the second one), a contradiction. All the other possibilities can be discarded reasoning in the same way.

Since these propositions are mutually excluyent, C is true if and only if exactly one of the three propositions is true (and false otherwise). This can only happen if exactly two of p,q, and r are true and the other one is false. For example, (p∧q∧¬r) is true when p and q are true, and r is false.

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Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberrie
agasfer [191]

Answer:

170

Step-by-step explanation:

Ann, Ben, and Cindy were eating strawberries.

The ratio of the numbers of berries they ate is 5:5:7.

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