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2 years ago

The net below is for a number cube. What are the three sums of the numbers on opposite surfaces of the cube?

1 answer:

7 0

I think the way you do it is you just add the numbers that are opposite of each other. A way you can figure it out is by imagining the net folding into a cube. The numbers that are opposite each other are 5 and 6, 2 and 4, and 1 and 3. 5+6=11, 4+2=6, and 1+3=4. 11, 6, and 4 are your answers.

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the graph shows the first five terms in a geometric sequence what is the iterative rule for the sequence

algol [13]

The iterative rule for the sequence is a_n = 8 · ( 0.5 )ⁿ ⁻ ¹

<h3>Further explanation</h3>

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>d = common difference between adjacent numbers</em>

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>r = common ratio between adjacent numbers</em>

Let us now tackle the problem!

<u>Given:</u>

a₁ = 8

a₂ = 4

a₃ = 2

a₄ = 1

<u>Solution:</u>

<em>Firstly , we find the ratio by following formula:</em>

$r = a_2 \div a_1 = 4 \div 8 = 0.5$

$\texttt{ }$

<em>The iterative rule for the sequence:</em>

$a_n = a_1 \cdot~ r^{n-1}$

$a_n = 8 \cdot~ (0.5)^{n-1}$

$\texttt{ }$

<h3>Learn more</h3>

Geometric Series : brainly.com/question/4520950
Arithmetic Progression : brainly.com/question/2966265
Geometric Sequence : brainly.com/question/2166405

<h3>Answer details</h3>

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

6 0

2 years ago

Write an equation from the information given: A rectangle is twice as long as it is wide. The perimeter of the rectangle is 18.

Agata [3.3K]

Let width = x, Therefore the length must equal 2x

Therefore insert these values on the sides of a rectangle.

Add: 2x + 2x + x + x = 18

Therefore 6x = 18

x = 3

3 0

3 years ago

Help&EXPLAIN <br> •••••••••••••••••••<br> Help plz

Stolb23 [73]

Answer:

diameter = 2.5 feet

Step-by-step explanation:

Circumference of a circle is given as C = πd

Circumference of the tree trunk = 7.85 ft

π = 3.14

Diameter of the tree trunk = d

Thus:

7.85 = 3.14*d

Divide both sides by 3.14

7.85/3.14 = 3.14*d/3.14

2.5 = d

d = 2.5 ft

3 0

2 years ago

1.When two variables are proportional which of the following is constant?

grin007 [14]

Answer:

Their Ratio

Step-by-step explanation:

You switched the numbers 2 and 3 btw

5 0

2 years ago

A group of four boys (Alex, Bryan, Chris, and David) and five girls (Megan, Nancy, Olivia, Pauline, and Rebecc?

aliina [53]

Answer:

a) P = 362880 ways

b) P = 2880 ways

Step-by-step explanation:

a) We have four boys and five girls, they are going to sit together in a row of 9 theater seats, without restrictions

We have a permutation of 9 elements

P = 9!

P = 9*8*7*6*5*4*3*2*1

P = 362880 ways

b) Boys must seat together, we have two groups of people

4 boys they can seat in 4! different ways

P₁ = 4!

P₁ = 4*3*2*1

P₁ = 24

And girls can seat in 5! dfferent ways

P₂ = 5!

P₂ = 5*4*3*2*1

P₂ = 120

To get total ways in the above mentioned condition, we have to multiply P₁*P₂

P = 24*120

P = 2880 ways

4 0

2 years ago