<h2>1.</h2><h3>1)</h3>
Put the given values of p and q in the factored form equation.
... f(x) = (x -(-1))(x -(-2)) . . . . p and q values put in
... f(x) = (x +1)(x +2) . . . . . . .simplified
<h3>2)</h3>
Multiplying the factors, we have
... f(x) = x(x +2) + 1(x +2) = x² +2x +1x +2
... f(x) = x² +3x +2
<h2>2.</h2>
We want to factor x³ -x² -6x. We notice first of all that x is a factor of all terms. Thus we have
... = x(x² -x -6)
Now, we're looking for factors of -6 that add up to -1. Those are -3 and 2. Thus the factorization is ...
... = x(x -3)(x +2)
<h2>3.</h2>
We want a description of the structure and an equivalent expression for
... 64x⁹ -216
We note that 64, 216, and x⁹ are all cubes, so this expression is ...
... the difference of cubes.
It can be rewritten to
... = 8((2x³)³ -3³)
and so can be factored as
... = 8(2x³ -3)(4x⁶ +6x³ +9)
2(4.25 + 2.25) = 2(6.50) = 13...this is the cost without the tax
13 + 0.05(13) = 13 + 0.65 = 13.65 <=== total with the sales tax added
For each vertex just take the x and y coordinate and apply the translation. so for the point (-3,-2) make them (-3+2, -2+3)=(-1,1) and do the same for the other two points (0,2) and (-7,3)
Answer:
Step-by-step explanation:
Notice that angles <1 and <3 are opposed by the vertex, which makes them of equal measure, therefore, <1 = 47 degrees.
Notice as well that angles <1 and <2 combine into a straight line, therefore, they are supplementary angles whose addition gives 180 degrees then we can find the value of angle <2 via:
And finally, angle <4 is opposite through the vertex to angle <2, and therefore they must have the same measure. So, <4 = 133 degrees.
