Answer:
The three zeros of the original function f(x) are {-1/2, -3, -5}.
Step-by-step explanation:
"Synthetic division" is the perfect tool for approaching this problem. Long div. would also "work."
Use -5 as the first divisor in synthetic division:
------------------------
-5 2 17 38 15
-10 -35 -15
--------------------------
2 7 3 0
Note that there's no remainder here. That tells us that -5 is indeed a zero of the given function. We can apply synthetic div. again to the remaining three coefficients, as follows:
-------------
-3 2 7 3
-6 -3
-----------------
2 1 0
Note that the '3' in 2 7 3 tells me that -3, 3, -1 or 1 may be an additional zero. As luck would have it, using -3 as a divisor (see above) results in no remainder, confirming that -3 is the second zero of the original function.
That leaves the coefficients 2 1. This corresponds to 2x + 1 = 0, which is easily solved for x:
If 2x + 1 = 0, then 2x = -1, and x = -1/2.
Thus, the three zeros of the original function f(x) are {-1/2, -3, -5}.
Answer:
They both have 1/2
Step-by-step explanation:
For the first one there are 6 numbers and 3 of them are odd. That makes it 1/2.
For the second one it is self explanatory.
Answer:
<h2>
Letter C</h2>
Step-by-step explanation:
If we look on the number line we see that there is a point on -3, another point on -1, 2, and 7.
These points tell us our answer, but the question states it doesn't have to be in any order.
As we look at answer A we see -3, 1, 2, and -7. That's incorrect since there is no positive 1 nor an -7.
As we look at answer B we see -3, 7, 1, and -2. That's incorrect since there is no positive 1, and not a -2.
As we look at answer D we see -2, 3, 1, and 7. That's incorrect since there is no positive 2, no positive 3, and no negative 1.
C has to be the correct answer since it's the only answer left and has the 4 numbers that are on the number line.
Therefore, the correct answer is C.
Best of Luck to you.
If you have any questions, feel free to comment below.
(please open my photo for reference as you read, I am a visual learner/explainer so it will make the most sense that way)
So the first thing you want to do is look at the exterior angle 130°. A straight line is 180°, and every Triangle's angular sum is 180°. How I think of it is that every straight line has a mini protractor on either side. It makes it a bit easier to understand.
180 - 130 = 50
You now know that two of the angles are 50°.
You now have two of the measurements for the triangle farthest to the left.
75° and 50°
75 + 50 = 125
180 - 125 = 55
a = 55°
Now that you have all the measurements for the first triangle, let's move onto the next one.
With two measurements for the second triangle, all you need to do is find their sum and subtract that from 180 and you will have the third measurement!
50 + 60 = 110
180 - 110 = 70
b = 70°
Finally, for the last triangle, you already have two of the measurements 60° and 85°.
85 + 60 = 145
180 - 145 = 35
c = 35°
Sorry if this explanation is a bit messy, it's hard to describe certain things without a letter or some kind of name to differentiate between them verbally.
I hope this helps! <3
