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nordsb [41]
3 years ago
5

The general term of an arithmetic sequence is tn = 32 + 3n, where n ∈N and n ≥ 1. The sequence is

Mathematics
1 answer:
Debora [2.8K]3 years ago
4 0

Answer:

D) 35, 38, 41, 44, 47, 50,...

Step-by-step explanation:

The general term of an arithmetic sequence is

t_n=32+3n, where n ∈N and n ≥ 1.

When n=1,

t_1=32+3(1)=35

When n=2,

t_2=32+3(2)=38

When n=3,

t_3=32+3(3)=41

When n=4,

t_4=32+3(4)=44

When n=5,

t_5=32+3(5)=47

When n=6,

t_6=32+3(6)=50

Hence the sequence is 35, 38, 41, 44, 47, 50,...

The correct answer is D

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Diagram shows two perpendicular straight lines,OB and CBD,drawn on a Cartesian plane.
Tems11 [23]

Answer: (a) y = -3x + 10

               \bold{(b)\x=\bigg(\dfrac{10}{3},0\bigg)}  

<u>Step-by-step explanation:</u>

The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.

Step 1: Find the slope of OB using the formula: m=\dfrac{y_2-y_1}{x_2-x_1}

(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)

m=\dfrac{1-0}{3-0} = \dfrac{1}{3}

Step 2: Find the slope of CD (opposite and reciprocal of OB)

m = \dfrac{1}{3}\qquad m_\perp=-\bigg(\dfrac{3}{1}\bigg) = -3

Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)

(x₁, y₁) = (3, 1) because it is the point the line will pass through

y - 1 = -3(x - 3)

y - 1 = -3x + 9      <em>distributed -3 into (x - 3)</em>

y      = -3x + 10    <em>added 1 to both sides</em>

***********************************************************************

The x-intercept of DQ is the same x-intercept as CD.  The x-intercept is when y = 0

y = -3x + 10

0 = -3x + 10

-10 = -3x       subtracted 10 from both sides

\dfrac{10}{3}=x    <em>divided both sides by -3</em>


3 0
2 years ago
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