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10 months ago

15. Which rule was used to create the arithmetic sequence below?

Mathematics

1 answer:

Nikolay [14]10 months ago

4 0

The rule used to create the arithmetic sequence -2, -4, -6, -8,.. is an = -2 - 2(n-1)

The arithmetic sequence is

-2, -4, -6, -8,...

The initial term = -2

The common difference = The second term - The first term

= -4 - (-2)

= -4 + 2

= -2

The nth term of the arithmetic sequence is

an = a+ (n-1) d

Where a is the initial term

an is the nth term

d is the common difference

Substitute the values in the equation

an = -2 + (n-1)(-2)

Rearrange the terms

an = -2 -2(n-1)

Hence, the rule used to create the arithmetic sequence -2, -4, -6, -8,.. is an = -2 - 2(n-1)

Learn more about arithmetic sequence here

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Midpoint (10,4) Endpoint (9,-4), find the coordinates of the other endpoint.

mestny [16]

Answer:

(11, 12)

Step-by-step explanation:

Mid point coordinates:

x = (x₁ + x₂)/2
y = (y₁ + y₂)/2

Since midpoint and one endpoint given (10, 4) and (9, -4), the other endpoint:

x₂ = 2x - x₁ = 2*10 - 9 = 11
y₂ = 2y - y₁ = 2*4 - (-4) = 12

So the other endpoint is: (11, 12)

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3 years ago

A’B’C’ is a dilation image if ABC which is the correct description of the dilation

Sav [38]

Answer:

The dilation is an enlargement

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

In this problem Triangles A'B'C' and ABC are similar by AA Similarity Postulate

Let

z------> the scale factor

$z=\frac{A'C'}{AC}$

substitute the values

$z=\frac{2+8}{2}$

$z=\frac{10}{2}=5$

The scale factor is greater than 1

therefore

The dilation is an enlargement

3 0

3 years ago

Read 2 more answers

SOLVE APPLICATION USING ALGEBRA. TYPE THE EQUATION OR INEQUALITY AND PLEASE SHOW WORK. a) A rectangle with perimeter 18 cm has l

alekssr [168]

Answer:

$w=2\\l=7$

Step-by-step explanation:

$l+l+w+w=18\\\\2w+3=l\\\\2w+3+2w+3+w+w=18\\6w+6=18\\6w=12\\w=2\\\\2w+3=l\\2*2+3=l\\4+3=l\\l=7$

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3 years ago

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Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Jos

rusak2 [61]

Answer: Josh borrowed $ 876 to buy the computer.

Step-by-step explanation:

Formula for simple interest : I = Prt

, where P = principal amount

r= rate of interest ( in decimal)

t=time (in years)

Total amount with simple interest to pay : A = P+I

⇒ A = P +Prt

⇒ A = P(1 +rt) (i)

As per given , A = $1,244.34

r= 12.4% = 0.124

t= 3 years

Now, put these values in (i) , we get

$1244.34=P(1+0.124)^3\\\\\Rightarrow\ 1244.34=P(1.124)^3\\\\\Rightarrow\ 1244.34=P(1.420034624)\\\\\Rightarrow\ P=\dfrac{1244.34}{1.420034624}\\\\\Rightarrow\ P=876.27$

Hence, Josh borrowed $ 876 to buy the computer.

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2 years ago

A square cake is cut into 16 equal parts. ben ears 7/16 of the cake. bell eats ¼ of the cake. what fraction of the cake is left?

Alexxx [7]

Set both fraction to a common denominator

7/16 and 4/16

now add them together

7/16 + 4/16 = 11/16

now subtract that from a full cake

16/16 - 11/16 = 5/16

there are 5/16 of the cake left

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3 years ago