Answer:
(3x^2 - 2x + 5)
Step-by-step explanation:
3x^2 - 2x + 5
- <u>(6x^3 + 3x^2)</u>
-4x^2 +8x +5
- <u>(-4x^2 - 2x)</u>
10x + 5
-(<u>10x + 5)</u>
00
(2x+1) (3x^2 - 2x + 5) = 6x^3 - x^2 + 8x + 5
Therefore the other factor of the polynomial is (3x^2 - 2x + 5)
Answer: positive: 1; negative: -1, -2, -3
Step-by-step explanation: 1 is greater than -2 and less than 2
-1, -2, and -3 are all greater than it equal to -3 and less than 2
Answer:
2.5% and 2.5 · 10^-3, 0.25, 2/5, √5
Step-by-step explanation:
0.25, 2/5, 2.5 · 10^-3, 2.5%, √5
Now let's list them all in the same form, why not decimals.
0.25 = 0.25
2/5 = 4/10 = 40/100 = 0.4
2.5 · 10^-3 = 2.5 · 0.01 = 0.025
2.5% = 0.025
√5 ≅ 2.236
Here i how I would do it:<span>f(x)=−<span>x2</span>+8x+15</span>
set f(x) = 0 to find the points at which the graph crosses the x-axis. So<span>−<span>x2</span>+8x+15=0</span>
multiply through by -1<span><span>x2</span>−8x−15=0</span>
<span>(x−4<span>)2</span>−31=0</span>
<span>x=4±<span>31<span>−−</span>√</span></span>
So these are the points at which the graph crosses the x-axis. To find the point where it crosses the y-axis, set x=0 in your original equation to get 15. Now because of the negative on the x^2, your graph will be an upside down parabola, going through<span>(0,15),(4−<span>31<span>−−</span>√</span>,0)and(4+<span>31<span>−−</span>√</span>,0)</span>
To find the coordinates of the maximum (it is maximum) of the graph, you take a look at the completed square method above. Since we multiplied through by -1, we need to multiply through by it again to get:<span>f(x)=31−(x−4<span>)2</span></span><span>
Now this is maximal when x=4, because x=4 causes -(x-4)^2 to vanish. So the coordinates of the maximum are (4,y). To find the y, simply substitute x=4 into the equation f(x) to give y = 31. So it agrees with the mighty Satellite: (4,31) is the vertex.</span>
Answer:
B
Step-by-step explanation:
<DCE = BCA (vertical angles are congruent)
DC corresponds to CB,
DC/CB = 15/5 = 3
EC corresponds to CA,
EC/CA = 12/4 = 3
Thus, two sides in ∆ABC are proportional to two corresponding sides in ∆EDC, and also, the included angle in ∆ABC and ∆EDC are congruent to each other. Therefore, based on the SAS Similarity Theorem, ∆ABC and ∆EDC are similar.
