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Lerok [7]
3 years ago
12

Factor completely: What ways can I factor this out to make it less complicated

Mathematics
1 answer:
Mkey [24]3 years ago
3 0
6x² - x -12. This is a quadratic equation. Find its roots (Zeros):

x' = [-b+√(b²-4.a.c)]/2a  and x" = [-b-√(b²-4.a.c)]/2a 

x' = 3/2 and x" = - 4/3

remember : ax²+bx + c = a(x-x')(x-x')

Then 6x² -x - 12 = 6(x-3/2)(x+4/3) (Reduce to the same denominator and simplify after  reduction):
(2x-3)(3x+4)

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A herd of horses split and went to three areas. One fourth of the herd of horses was seen in the forest. Twice the square root o
melamori03 [73]

Answer:the total number of horses in the herd is 36

Step-by-step explanation:

Let x represent the total number of horses in the herd.

One fourth of the herd of horses was seen in the forest. This means that the number of horses that was seen in the forest would be

1/4 × x = x/4

Twice the square root of the herd had gone to the mountain slopes. This means that the number of horses that had gone to the mountain slopes would be

2 × √x = 2√x

Three times five horses remained on the riverbank. This means that the number that remained would be

3 × 5 = 15

Therefore

x/4 + 2√x + 15 = x

x - x/4 - 15 = 2√x

(4x - x - 60)/4 = 2√x

(3x - 60)/4 = 2√x

Cross multiplying,

3x - 60 = 8√x

Squaring both sides of the equation, it becomes

(3x - 60)(3x - 60) = 64x

9x² - 180x - 180x + 3600 = 64x

9x² - 360x - 64x + 3600 = 0

9x² - 424x + 3600 = 0

Applying the quadratic equation

x = (- b ±√b² - 4ac)/2a

x = ( - - 424 ± √-424² - 4(9 × 3600)/2 × 9

x = (424 ± √179776 - 129600)/18

x = (424 ±√50176)/18

x = (424 + 224)/18 or

x = (424 - 224)/18

x = 36 or x = 11.11

the number of horses must be whole number. Therefore, the number of horses is 36

5 0
3 years ago
What is the median of this list of numbers? 5, 10, 13, 7, 5
Eduardwww [97]
To find the median, you list the numbers in increasing order.
5, 5, 7, 10, 13.
Then you take the middle number. Every number has a pair except for seven in the middle, and the median is 7.  Hope it helps!
6 0
3 years ago
TIME LIMITED
mrs_skeptik [129]

Answer:

<h2>B.   9</h2>

Step-by-step explanation:

|<-------------- 27 ------------>|

L--------------M----------------N

       18                MN

LN = LM + MN

27 = 18 + MN

MN = 27 - 18

<h2>MN = 9</h2>
8 0
3 years ago
Jamie's truck has a 40-gallon gas tank.
andreev551 [17]

Answer:

$60.48

Step-by-step explanation:

hope this helps!!

5 0
3 years ago
Jessica has two salary options. She can earn a salary of $500 per week plus 2% of the weekly sales or a salary of $200 per week
Yuki888 [10]

Answer:

$500 + 0.02x = $200 + 0.05x  

Step-by-step explanation:

Jessica's first option:  J1 = $500 plus sales commission of 2%:

                                     J1 = $500 + 0.02x, where x:  weekly sales amount

Her second option:  J2 = $200 + 0.05x

Equating these two expressions, we get:

$500 + 0.02x = $200 + 0.05x  

... which is the same as the third answer choice.

5 0
3 years ago
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