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inessss [21]
3 years ago
14

Let the smallest of 4 consecutive odd numbers be 2 n + 1 , where n is an integer. Show, using algebra, that the sum of any 4 con

secutive odd numbers is always a multiple of 8. Give your answer as an expression that makes explicit that it is a multiple of 8.
Mathematics
1 answer:
andrey2020 [161]3 years ago
7 0

Answer:

Expression is 8(n+2)

Step-by-step explanation:

smallest of 4 consecutive odd numbers =2n + 1

consecutive odd integers are found by adding 2 to the any given odd numbers

Thus, 2nd consecutive odd integers  = 2n + 1 + 2 = 2n + 3

3rd consecutive odd integers  = 2n + 3 + 2 = 2n + 5

2nd consecutive odd integers  = 2n + 5 + 2 = 2n + 7

Thus, 4 consecutive odd integers are

2n + 1 ,2n + 3,2n + 5,2n + 7

sum of these numbers are = 2n + 1 +2n + 3 + 2n + 5+2n + 7 = 8n+16

sum of these numbers are = 8(n+2)

Thus, we see that the sum of numbers are 8(n+2)

As, 8 is common for n+2, whatever is value of n, the number will be multiple of 8 .

thus expression is 8(n+2)

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Unit 2 (12 points)
klio [65]
1+3=4

A counterexample is an a example that proves the statement false.

1+3 are not even numbers but they equal an even one, so it just proved the statement wrong.
3 0
2 years ago
The triangular pyramid shown is made up of four congruent triangles. The length of the base is 8 inches, and the height of the b
Aneli [31]

Answer:

(B) Talia is correct. The lateral area can be found by approximating one large triangle, which can be found using the expression 4 (one-half (8) (6.9))

Step-by-step explanation:

Base of the Pyramid = 8 Inches

Height of the Triangular Face = 6.9 Inches

In any solid shape, the Lateral surface area is the sum of all sides except its top and bottom bases.

Since the four triangles are congruent:

Lateral Surface Area = 4 X Area of One Triangle

Area of a Triangle = \frac{1}{2}$ X Base X Height

Area of one Triangular Face = \dfrac{1}{2}(8)(6.9)

Therefore:

Lateral Surface Area = 4\left(\dfrac{1}{2}(8)(6.9)\right)

Therefore, Talia is correct.

8 0
3 years ago
X is increased by 50% and decreased by 30%. What is the result?
omeli [17]

Answer:

its the same as increasing x by 5 percent

4 0
2 years ago
3+2x+x-1=2x+x-2<br> answer?
konstantin123 [22]
It’d be 2=-2 ... but then subtract two from both side and the answer is a null set. Also known as “no solution”..

Best of luck in your studies :)
-Nicky
8 0
3 years ago
Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. R
Mrac [35]

Answer:

Midpoint (-2,4)

distance nearest tenth = 8.9

The approximate distance = 9

Step-by-step explanation:

Formulas

PQ midpoint = (x2 + x1)/2, (y2 + y1)/2

distance d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

Givens

x2 = -4

x1 = 0

y2 = 1

y1 = 7

Solution

M(PQ) = (-4+0)/2, (1 + 7)/2

M(PQ) = -2, 4

The midpoint is -2,4

The distance = sqrt( (4 - 0)^2 + (1 + 7)^2 )

The distance = sqrt(16 + 64)

The distance = sqrt(80)

The distance = 4√5           exactly

The distance = 8.94    

The distance = 8.9            To the nearest tenth

Question 2

The distance is rounded to the nearest whole number which is 9.

6 0
3 years ago
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