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Alex777 [14]
3 years ago
13

A certain arithmetic sequence has the following explicit formula for the nth term: an = 3 + (n - 1)(8) The same sequence has the

following recursive formula: an = an-1 + _____ What number belongs in the blank space in the recursive formula? A. 5 B. 3 C. 8 D. 24
Mathematics
1 answer:
zhuklara [117]3 years ago
6 0
From the explicit formula:
an=3+(n-1)8
simplifying this we get:
an=3+8n-8
an=8n-5
thus 
the recursive formula is:
an=an-1+
the missing part is the common difference which is 8
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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
Select the Correct Answer Consider the following Equation 12w - 27 = -34 + 14 Which Equation has the same solution as the equati
cricket20 [7]
12w - 27 = -34 + 14
w = 7/12

A -2w+21=-8w+36
w=17/8

B -5/6 w + 2 = -34+14w
w=216/89

C -47-10w=-9w-40-3w
w= 7/2

D 8/7w=13/14w+2
w=28/5


6 0
3 years ago
Biking at 12 mph, it takes Kristen hour to reach the train station to go to work. Kristen then takes the train to work, and it t
LenKa [72]

Answer:

d = 19 mi

Step-by-step explanation:

Total dist = bike dist + train dist

d = 12(.5) + 20(.5)

d = 6 + 13

d = 19 mi

4 0
3 years ago
If an angle is acute, then the measure of its complement must be greater than the measure of its
salantis [7]

Answer: acute angles are higher that 0° and smaller than 90°

Step-by-step explanation: obtuse are between 90° and 180°

5 0
3 years ago
When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary l
Volgvan

Answer:

See Below

Step-by-step explanation:

The boundary line follows the graph of y = 2x - 4 because it represents the line of maximum or minimum values the graph could take. y = 2x - 4 has a y-intercept of -4 because it is in slope-intercept form. It also has a slope of 2, so to find another point on the line, you can go up two and right one. Also, this inequality has a solid line because it is "less than or equal to" and a solid line represents the values that equal.

6 0
3 years ago
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