Solve the following systems of 3-variable linear equations.50 points
1 answer:
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Step-by-step explanation:
Given inequality is .
To graph that inequality, first we need to graph the line . Then shade it for the inequality symbol <.
Graphing line can be done using two points.
plug x=0 into , we get:
Hence first point is (0,2)
Similarly plug any random number for x say x=4, we get:
Hence first point is (4,5).
Now we just need to graph both points and join them by a dotted line. because we have < not <=.
Next part is to test for shading.
Which can be done using any test point which is not on the given line. Say (0,0)
plug x=0,y=0 into .
0<2
which is true, hence shading will be in direction of test point (0,0).
Hence final answer will be the choice which looks like the graph attached below;
Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.