3 lines are shown. A line with points M, H, K intersects with a line with points J, H, L at point H. Another line extends from p

Answer:

- 128 Superscript StartFraction 3 Over x EndFraction

- (4RootIndex 3 StartRoot 2 EndRoot)x

- (4 (2 Superscript one-third Baseline) ) Superscript x

Step-by-step explanation:

Considerando la ecuación dada

De acuerdo con una de las leyes de índices,

Aplicando esta ley a la pregunta;

128 Superscript StartFraction 3 Over x EndFraction

(4RootIndex 3 StartRoot 2 EndRoot)x

(4 (2 Superscript one-third Baseline) ) Superscript x

Answer: Zeno consumed 51 hot dogs.

The total number of hot dogs consumed was 676.

Step-by-step explanation:

Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.

The formula for finding the nth term in an arithmetic series is given by

Tn = a + (n - 1)d

Where

a denotes the first term in the sequence.

d signifies the common difference.

n stands for the total terms in the sequence.

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs

The formula to calculate the sum of n terms in an arithmetic sequence is

Sn = n/2[2a + (n - 1)d]

Hence, to find the total number of hot dogs consumed by 26 contestants, S26 is calculated as

S26 = 26/2[2 × 1 + (26 - 1)2]

S26 = 13[2 + 50]

S26 = 13 × 52 = 676 hot dogs

Response:

a)12 b)12 c)36

Detailed steps:

a) Identify the least common multiple. The quantity of marbles corresponds to that value multiplied by n (with n representing an integer)

b) The least common multiple is calculated as 4*3=...

c)12*3 =?

Afterward, simply divide by 2, 3, and 4 to find the solution