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Oliga [24]
3 years ago
15

Factor the following equation to find its zeros.

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
6 0

Answer:

  A|  12, 3

Step-by-step explanation:

The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...

  y = (x -12)(x -3)

A quick check shows this product is ...

  y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required

The factors are zero when x is either 12 or 3.

The zeros of the equation are 12 and 3.

____

Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).

Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.

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2×3=6. And 1/2(2×2)=2. 2+6=8. 8 square units.
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2 years ago
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2. At 1 pm, you leave Ellensburg at a constant speed of 75 miles per hour. At 2:30 pm, your
MA_775_DIABLO [31]

Here, we are required to determine how many hours your friend will drive in order to catch you.

(a)<em> Your friend will have to drive 7 and a half hours inorder to catch </em><em>you.</em>

<em>(</em><em>b)</em><em> </em><em>You </em><em>both </em><em>will </em><em>be </em><em>6</em><em>7</em><em>5</em><em> </em><em>miles</em> <em>away </em><em>from </em><em>Ellensburg</em><em> </em><em>at </em><em>that </em><em>time.</em>

If you leave at 1 pm; At 2:30pm;

  • That is; 1 and a half hours after leaving; you must have covered a distance, d = 75 × 1.5
  • d = 112.5miles.

Therefore, your position; S after 2:30pm is given by;

S(a) = 75t + 112.5 miles from Ellensburg.

For your friend; travelling at 90miles/hr;

  • His position is given as; S(b) = 90 × t

(a) For your friend to catch you, you both must be in the same position;

  • i.e S(a) = S(b)

75t + 112.5 = 90t

90t -75t = 112.5

t = 112.5/15

t = 7.5hours

(b) To determine how far you both are from Ellensburg; we can either evaluate:

S(b) = 90t or S(a) = 75t + 112.5

Therefore, By evaluating S(b) = 90t.

S(b) = 90 × 7.5

S(b) = 675miles from Ellensburg.

Read more:

brainly.com/question/24234606

6 0
1 year ago
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7. A road construction crew was working under lights at night to pave a major state highway between
pashok25 [27]

Answer:

11.45 miles

Step-by-step explanation:

you add

5 0
3 years ago
I need help :) ( 12 points)
Agata [3.3K]

Answer:

B

Step-by-step explanation:

The graph starts at 15, so that's the y intercept and the Gallons of gasoline is going down so the slope is  negative

3 0
3 years ago
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre
lilavasa [31]

Answer:

(5a−3)^2

Step-by-step explanation:

25a^2 - 30a + 9

Factor the expression by grouping. First, the expression needs to be rewritten as 25a^2+pa+qa+9. To find p and q, set up a system to be solved.

p+q=−30

pq=25×9=225

Since pq is positive, p and q have the same sign. Since p+q is negative, p and q are both negative. List all such integer pairs that give product 225.

−1,−225

−3,−75

−5,−45

−9,−25

−15,−15

Calculate the sum for each pair.

−1−225=−226

−3−75=−78

−5−45=−50

−9−25=−34

−15−15=−30

The solution is the pair that gives sum −30.

p=−15

q=−15

Rewrite 25a^2 - 30a + 9 as (25a^2−15a)+(−15a+9).

(25a^2−15a)+(−15a+9)

Factor out 5a in the first and −3 in the second group.

5a(5a−3)−3(5a−3)

Factor out common term 5a−3 by using distributive property.

(5a−3)(5a−3)

Rewrite as a binomial square.

(5a−3)^2

3 0
3 years ago
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