Mathematics, 02.09.2020 07:01, Tellyy8104

Point M is the midpoint of FG. Can the value of variable a be determined? Explain. a
G(24,30+3)
M(3,5)
F[b+1 a+2)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. To determine the value of a, set up and solve a system of equations in two variables. The value of a is
B. To determine the value of a, set the x- and y-coordinates of G and Fequal to each other and solve for a The value of a is
C. To determine the value of a, divide each coordinate of M by 2. Then add each quotient to the x-and y-coordinates of M. The value of a is
D. Not enough information is given for the value of a to be determined.

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answered: jayycruz59

A. To determine the value of a, set up and solve a system of equations in two variables. The value of a is 2

Step-by-step explanation:

Given the coordinates F(b+1, a+2, M(3,5) and G(2a, 3b+3), if M is the midpoint of F and G then, to get the value of a and b we will use the formula for calculating the midpoint a shown;

M(X, Y) = (x₁+x₂/2, y₁+y₂/2)

X = x₁+x₂/2 and Y = y₁+y₂/2

From the given coordinates x₁ = b+1, y₁ = a+2, x₂ = 2a, y₂ = 3b+3, X = 3 and Y = 5

Substituting the given parameters into the formula, we can form up a simultaneous equation and get the value of a.

To determine the value of a, set up and solve a system of equations in two variables

For the X coordinates;

X = x₁+x₂/2

3 = b+1+2a/2

6 = 2a+b+1

2a+b = 5 1 * 1

For the Y coordinates;

5 = a+2+3b+3/2

cross multiply

10 = a+2+3b+3

collect like terms

a+3b = 10-2-3

a+3b = 5 2 * 2

Solving the resulting simultaneous equation to get the value of a

multiply equation 1 by 1 and 2 by 2 to have the resulting equations;

2a+b = 5 3

2a +6b = 10 4

subtract 3 from 4

(2a-2a)+(b - 6b) = 5-10

0-5b = -5

b = -5/-5

b = 1

substitute b =1 into equation 1 to get a;

2a + b = 5

2a + 1 = 5

2a = 5-1

2a = 4

a = 2

From the calculation above it is seen that the value of variable a can be determined and it is equivalent to 2

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step-by-step explanation:

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answered: Guest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$