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3 years ago

Question 3

Mathematics

1 answer:

Papessa [141]3 years ago

4 0

Answer:

(a) The next 3 terms in the sequence are 17, -31, and 65

(b) The 3 terms that came before -7 are 2, -1, and 5

Step-by-step explanation:

a. To determine the next 3 terms in the sequence after -7,

From the question, the sequence follows the rule: multiply the previous number by-2 and add 3.

Then, for the next number after -7, we will get

-7 × -2 = 14; 14 + 3 = 17

For the second number after -7, we will get

17 × -2 = -34; -34 + 3 = -31

For the third number after -7, we will get

-31 × -2 = 62; 62 + 3 = 65

Hence, the next 3 terms are 17, -31, and 65

(b) For the 3 terms that came before -7 in the sequence, the rule will be reversed, that is: subtract 3 from the immediate number and divide by -2

Hence, the previous number to -7 (that is, the third term in the sequence)

-7 -3 = -10; -10 ÷ -2 = 5

Then, the second term will be

5 - 3 = 2; 2 ÷ -2 = -1

and the first term will be

-1 -3 = -4; -4 ÷ -2 = 2

Hence, the 3 terms that came before -7 are 2, -1, and 5

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2 years ago

Read 2 more answers

What is the y-intercept of the line perpendicular to (1,1) and (-3,-1) and passes through (-3,-2)

marin [14]

Answer:

-8

Step-by-step explanation:

Let's first establish the reference line (the one that the second line will be perpendicular to). We are told that this line passes through two points:

(1,1) and (-3,-1).

We'll find a line equation using the point slope form format to start:

(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.

(x,y) = (1,1)

(x1,y1) = (-3,-1)

Rearrange the equation:

(y - y1) = m * (x - x1)

m = (y - y1)/ (x - x1)

m = (1-(-1))/(1-(-3))

m = 2/4, or 1/2: The slope is 1/2. [This is "m."]

We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:

y = (1/2)x + b

Use either of the two given points. I'll use (1,1) since I have memorized the "1" math tables.

y = (1/2)x + b

1 = (1/2)(1) + b for (1,1)

b = 1/2

This makes the reference line: y = (1/2)x+(1/2)

===

The line perpendicular must have a slope that is the negative inverse of (1/2). This would be -(2/1), or -2.

We can then write y = -2x + b

To find be, enter the one given point for this line: (-3,-2)

y = -2x + b

-2 = -2(-3) + b

-2 = 6 + b

b = -8

The perpendicular line is thus:

y = -2x - 8

It has a y-intercept of -8

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