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Arada [10]
3 years ago
11

Factor completely 96-6x^2

Mathematics
1 answer:
kotegsom [21]3 years ago
7 0

Answer:

96 - 6x²

= 6(16 - x²)    (Factor 6)

= 6(4² - x²)    (Rewrite 16)

= 6(4 + x)(4 - x)  (Difference of squares)

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How many solutions does the system of equations below have?
soldier1979 [14.2K]

Answer:

One solution                    

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

\dfrac{ -60x  }{ -60  }   =   \dfrac{ -106  }{ -60  }

Simplify

x =   \dfrac{ 53  }{ 30  }

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

\mathrm{So\:it\:would\:look\:like\:this:\ y =  -5 \left(  \dfrac{ 53  }{ 30  }    \right)  +8}

\mathrm{Now\:lets\:solve\:for\:"y"\:then}

y =  -5 \left(  \dfrac{ 53  }{ 30  }    \right)  +8}

\mathrm{Express\: -5 \times   \dfrac{ 53  }{ 30  }\:as\:a\:single\:fraction}

y =   \dfrac{ -5 \times  53  }{ 30  }  +8

\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }

y =   \dfrac{ -265  }{ 30  }  +8

\mathrm{Simplify\:  \dfrac{ -265  }{ 30  }    \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }

y =   \dfrac{ -265 \div  5  }{ 30 \div  5  }  +8

\mathrm{Simplify}

y =  - \dfrac{ 53  }{ 6  }  +8

\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53  }{ 6  }}

\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}

\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}

\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48  }{ 6  }}

y =  - \dfrac{ 53  }{ 6  }  + \dfrac{ 48  }{ 6  }

\mathrm{Since\: - \dfrac{ 53  }{ 6  }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}

y =   \dfrac{ -53+48  }{ 6  }

\mathrm{Add\: -53 \: and\: 48\: to\: get\:  -5}

y =  - \dfrac{ 5  }{ 6  }

\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53  }{ 30  }, - \dfrac{ 5  }{ 6  })}

So there is only one solution to the equation.

5 0
2 years ago
Angle 1 and angle 3 are ___ angles.
slega [8]

Angles 1 and 3 are vertical lines and because they are vertical, both angles equal each other.

4 0
2 years ago
Evaluate<br> 4(x+5)(2+1)<br> (2+3)(2-3)<br> for x = 5.
zaharov [31]

Answer:

-600

Step-by-step explanation:

4 x 10 x 3 x 5 x -1

40 x 15 x -1

600 x -1 = -600

7 0
2 years ago
Help please. Will put brainliest
Murrr4er [49]

Answer:

  • 17,750
  • 1737

Step-by-step explanation:

A suitable table or calculator is needed.

One standard deviation from the mean includes 68.27% of the total, so the number of bottles in the range 20 ± 0.16 ounces will be ...

  0.6827·26,000 = 17,750 . . . . . within 20 ± 0.16

__

The number below 1.5 standard deviations below the mean is about 6.68%, so for the given sample size is expected to be ...

  0.66799·26,000 = 1737 . . . . . below 19.76

_____

<em>Comment on the first number</em>

The "empirical rule" tells you that 68% of the population is within 1 standard deviation (0.16 ounces) of the mean. When the number involved is expected to be expressed to 5 significant digits, your probability value needs better accuracy than that. To 6 digits, the value is 0.682689, which gives the same "rounded to the nearest integer" value as the one shown above.

4 0
3 years ago
Simplify (-7x+5)-(2x^2-8x+6) in standard form
Zarrin [17]

Answer: -2x² - 15x + 11

Step-by-step explanation:

8 0
1 year ago
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