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3 years ago

What is the common difference of the arithmetic sequence-20,-16,-12,-18

Mathematics

1 answer:

Paul [167]3 years ago

8 0

Answer:

common difference = 4

Step-by-step explanation:

common difference is the difference between the successive term and its preceding term.

let's take the successive term of -20 that is - 16

common difference (d) = successive term - preceeding term

= -16 -(-20)

= -16 + 20

= 4

if we take the successive term of -16 that is -12

we'll get the same common difference.

d = -12 -(-16)

d = -12 + 16

d = 4

this means that the common difference for an AP remains constant.

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Type the correct answer In each box.

Verizon [17]

9514 1404 393

Answer:

A: x = -1 and y = 3

B: x = 12 and y = 16

Step-by-step explanation:

In each case, you can add the opposite of the constant to find the variable.

Equation A

(x +yi) +(4 -7i) = (3 -4i)

(x +yi) +(4 -7i) -(4 -7i) = (3 -4i) -(4 -7i) . . . . . add -(4-7i) to both sides

x +yi = (3 -4) +(-4-(-7))i = -1 +3i

x = -1 and y = 3

Equation B

(x +yi) -(-6 +14i) = (18 +2i)

(x +yi) -(-6 +14i) +(-6 +14i) = (18 +2i) +(-6 +14i) . . . . . add (-6 +14i) to both sides

x + yi = (18 -6) +(2 +14)i = 12 +16i

x = 12 and y = 16

8 0

3 years ago

Read 2 more answers

I’m failing this class please help

Jlenok [28]

Answer:

I think it is 4

Step-by-step explanation:

also if you need more help, go to khanacademy.org (100% free) and take the lesson on your topic

7 0

3 years ago

Each of the sides of a pentagon is 12 cm long. Two ants are walking from point A to point D along the sides of the pentagon. One

AVprozaik [17]

Answer:

The average speed of the second ant is 2 cm/s

Step-by-step explanation:

The details of the ants moving on the sides of the pentagon are;

The length of the sides of the pentagon = 12 cm

The path of the first ant = A to B, B to C, then C to D

The average speed of the first ant = 3 cm/s

The path of the second ant = A to E, and E to D

The time of arrival of the second ant at the point D = The time of arrival of the first ant at the point D

Given that both ants departed at the same time, from point A, we have;

The time it takes the first ant to arrive at the point D = The time it took the second ant to arrive at the point D

The distance from A to B = 12 cm

The distance from B to C = 12 cm

The distance from C to D = 12 cm

∴ The distance traveled by the first ant from A to D = 12 cm + 12 cm 12 cm = 36 cm

Average speed = (Total distance)/(Total Time)

Total time = (Total distance)/(Average speed)

Let 't' represent the time it takes the first ant to move from point A to point D, we have;

t = 36 cm/(3 cm/s) = 12 seconds

Therefore, the time it takes the first ant to move from point A to point D, t = 12 seconds = The time it takes the second ant to move from point A to point D through point E

The total distance traveled by the second ant from A to point E, then from point E to point D, $T_{d2}$ = 12 cm + 12 cm = 24 cm

The average speed of the second ant, v₂ = $T_{d2}$ /t

∴ v₂ = 24 cm/(12 seconds) = 2 cm/s

The average speed of the second ant, v₂ = 2 cm/s.

8 0

3 years ago

Factor this expression

Natasha_Volkova [10]

Answer:

6(3x−4y)

Step-by-step explanation:

6 0

2 years ago

A fence 6 ft high runs parallel to the wall of a house at a distance of 5 ft. Find the length of the shortest ladder that extend

Anettt [7]

Answer:

L = 15.53 ft

Step-by-step explanation:

using diagram which is attached below

now, using Pythagoras theorem

L² = b² + (5 + x)²...............(1)

using similarity of triangle

$\dfrac{x}{6}=\dfrac{5+x}{b}$

$b=\dfrac{5+x}{x}6$

from equation (1)

$L^2 = (\dfrac{5+x}{x}6)^2 + (5 + x)^2$

$= (5+x)^2(1+\dfrac{36}{x^2})$

$\frac{\mathrm{d} L^2}{\mathrm{d} x}= 2(5+x)(1+\dfrac{36}{x^2})+(5+x)^2(\dfrac{-2\times 36}{x^3})$

$\frac{\mathrm{d} L^2}{\mathrm{d} x}= (5+x)(2-\dfrac{72\times 5}{x^3})$

for maxima or minima

$\frac{\mathrm{d} L^2}{\mathrm{d} x}=0$

x = -5 and x = ∛190 = 5.74

on second derivative 5.74 is the value which comes out to be minimal value which is the distance between the fence and ladder

now,

L² = 241.38

L = 15.53 ft

7 0

3 years ago