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tamaranim1 [39]
3 years ago
9

Find the first term, a1, of an arithmetic sequence if a12 = 38 and a45 = 170.

Mathematics
1 answer:
snow_lady [41]3 years ago
8 0
Standard formula for arithmetic sequence:
an = a0 + d(n-1)

if we use the two terms given, setting a12 as starting term and a45 as the end term an.

170 = 38 + 33d 
170 - 38 = 33d
132 = 33d

132/33 = d
This is the common difference, use it to find the first term.

38 = a0 + (132/33)(12-1)
38 = a0 + (132/33)(11)
38 = a0 + 132/3
38 - 132/3 = a0
38 - 44 = a0
-6 = a0

The starting term is -6

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Answer:

x = 47°

y = 10

z = 5

Step-by-step explanation:

They share the middle line which is one side. It's given that side y is congruent to the side with a value of 5. Angle X and the non labeled angel are also congruent to each other. Using SAS (side angle side) we can conclude the 2 triangles are congruent, which means all angles and sides are congruent and equal.

The angles of a triangle add to 180.

x+90+43=180

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z is congruent/equal to 5 since they are congruent and equal triangles. Therefore z=5

Y is congruent to side 10, which also means it is equal to 10. Therefore y=10

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3 years ago
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lbvjy [14]

Answer:

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Step-by-step explanation:

when x=-4

x²-5x+6=(-4)²-5×-4+6=16+20+6=42

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2 years ago
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mel-nik [20]

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5 0
3 years ago
Stephanie has 60 tickets to the carnival.She used 3/4 of her 60 tickets to play games.Then she used 1/5 of her remaining tickets
Lera25 [3.4K]

Answer:

<h2>She gave her brother 6 tickets</h2>

Step-by-step explanation:

This problem is on fractional numbers.

given that she has 60 tickets

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=(3/4)*60

=180/4

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She is left with (60-45)= 15 tickets

2. She used 1/5 of her remaining tickets for rides

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   =15/5

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She is left with (15-3)= 12 tickets

3. She gave half of her tickets to her brother.

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  =12/2

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She gave her brother 6 tickets

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Length=6 ft

Step-by-step explanation:

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