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babymother [125]
3 years ago
7

A recursive rule for an arithmetic sequence is a₁=4;a_n=a_(n−1)−3 .

Mathematics
1 answer:
steposvetlana [31]3 years ago
3 0

The explicit formula of the arithmetic sequence:

a_n=a_1+(n-1)d

d - common difference

We have the recursive formula of an arithmetic sequence:

\left\{\begin{array}{ccc}a_1=4\\a_n=a_{n-1}-3\end{array}\right

Therefore we have:

a_1=4,\ d=-3

Substitute:

a_n=4+(n-1)(-3)=4-3n+3=7-3n

<h3>Answer: aₙ = 7 - 3n</h3>
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4m- t = m for m.......................................
Kruka [31]
4m-t=m Solution: collect d like term's 4m-m=t 3m=t m=t/3
7 0
3 years ago
Write an equation of the line that passes through (-5, -2) and is parallel to y=2/3x+1<br><br> y=?
Nutka1998 [239]

Answer:

<h2>          y = ²/₃x + ⁴/₃</h2>

Step-by-step explanation:

The point-slope form of the equation of line: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = 2/3x + 1   ⇒    m₁ = 2/3    ⇒    m₂ = 2/3

(-5, -2)    ⇒    x₁ = -5,  y₁ = -2

point-slope form:

y - (-2) = 2/3(x - (-5))

y + 2 = 2/3(x + 5)

y + 2 = 2/3x + 10/3               {subtact 2 from both sides}

y = 2/3x + 4/3         ←   slope-intercept form

4 0
3 years ago
Read 2 more answers
When a number is decreased by 25%, the result is 22. What is the original number to the nearest tenth?
Ilya [14]

The decrease is 25% so this means that 22 is 75% of the original number (100% - 25% = 75%)

Divide 22 by 75%:

22/ 0.75 = 29.3

The answer is 29.3

7 0
4 years ago
A square and a rectangle have the same perimeter. The rectangle is 13 cm long and 7 cm wide.
lorasvet [3.4K]

<u>Solving</u>

Knowing that we have the information needed we will first find the perimeter of the rectangle.

Rectangle:
Length: 13cm

Width: 7cm  

Formula: L+L+W+W

13+13+7+7 = 40cm

Meaning the perimeter is 40cm and we can use this to find the length of a square. From general knowledge we know that all sides of a square is equal.

So if we divide the 4 sides by 40 we will get our answer.

40 ÷ 4 = 10

So B would be our answer...

<u>Statement</u>

<u />

Therefore the length of a side of the square is 10cm, meaning answer B is correct.

5 0
2 years ago
What is the volume of the plastic rocket???
Snezhnost [94]

Answer:

A) 151 in³ or 151 cubic inches

Step-by-step explanation:

Volume of rocket = Volume of Cylinder + Volume of Cone

Step 1

Find the volume of the cylinder

Volume of a cylinder = πr²h

r = Diameter/2

= 5/2 = 2.5 inches

h = 6 inches

Hence,

π × 2.5² × 6

= 117.81 cubic inches

Step 2

Find the volume of the cone

Volume of a cone =1/3 πr²h

h = 11 inches - 6 inches

= 5 inches

r = 2.5 inches

Hence,

1/3 × π × 2.5² × 5

= 32.72 cubic inches

Therefore:

Volume of rocket = Volume of Cylinder + Volume of Cone

= 117.81 cubic inches + 32.72 cubic inches

= 150.53 cubic inches

Approximately to the nearest inch = 151 in³ or 151 cubic inches

Option A is correct

7 0
3 years ago
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