What value of Y would make the expression YB − 6 + 7 + 2B − 3B + 1 equivalent to 5B + 2?

Bot GPT 3.5 Bot GPT 3.5 answered

To simplify the expression YB − 6 + 7 + 2B − 3B + 1, we can combine like terms:

YB + 2B − 3B + 7 + 1 − 6.

Combining the similar terms, we have:

(Y + 2 - 3)B + (7 + 1 - 6).

Simplifying further, we get:

(Y - 1)B + 2.

We want this expression to be equivalent to 5B + 2, so,

(Y - 1)B + 2 = 5B + 2.

Since the two expressions are equal, their coefficients must be the same:

Y - 1 = 5.

To find the value of Y, we add 1 to both sides:

Y = 5 + 1.

Therefore, the value of Y that makes the two expressions equivalent is Y = 6.

Generate an expression equivalent to: 4 ( h + 2 ) + 2 ( h + 1 ). The answer should be in simplest form.(1 point)

__h +__

Bot GPT 3.5 Bot GPT 3.5 answered

To simplify the expression 4(h + 2) + 2(h + 1), we distribute the numbers outside the parentheses:

4 * h + 4 * 2 + 2 * h + 2 * 1

Simplifying further, we multiply:

4h + 8 + 2h + 2

Now, we add the like terms:

(4h + 2h) + (8 + 2)

Combine the similar terms:

6h + 10.

Therefore, an expression equivalent to 4(h + 2) + 2(h + 1) in simplest form is:

6h + 10.

Generate an expression equivalent to: 5+6b+12c+10b−4c−2 . In the simplest form of the equivalent expression, what is the coefficient of variable b ?(1 point

Bot GPT 3.5 Bot GPT 3.5 answered

To simplify the expression 5 + 6b + 12c + 10b - 4c - 2, we can combine like terms:

(6b + 10b) + (12c - 4c) + (5 - 2)

Combine the similar terms:

16b + 8c + 3

Therefore, in the simplest form of the equivalent expression, the coefficient of the variable b is 16.

Use the properties of operations to write an expression equivalent to 2(k+4)+5 . The answer should be in simplest form. What is the constant value (no variables) in the equivalent expression?(1 point)

Bot GPT 3.5 Bot GPT 3.5 answered

To simplify the expression 2(k + 4) + 5, we can distribute the number outside the parentheses:

2 * k + 2 * 4 + 5

Simplifying further, we multiply:

2k + 8 + 5

Now, we add the like terms:

2k + 13

Therefore, an expression equivalent to 2(k + 4) + 5 in simplest form is:

2k + 13.

In the equivalent expression, the constant value (no variables) is 13.

Apply the properties of operations to determine which expression is equivalent to a+b+c(d+2) .(1 point)

Responses

2abcd
2 a b c d

a+b+cd+2c
a plus b minus c d minus 2 c

a+b+cd+c
a plus b minus c d plus 2 c

a+b+cd+2

Bot GPT 3.5 Bot GPT 3.5 answered

The expression that is equivalent to a+b+c(d+2) is:

a+b+cd+2c.

Are the expressions 3+(4x+1) and 4−4x equivalent?(1 point)

Responses

No, they are not because 3+(4x+1) simplifies to 4+4x , which is not equivalent to 4−4x.
No, they are not because 3 minus left parenthesis 4 x plus 1 right parenthesis simplifies to 2 minus 4 x , which is not equivalent to 4 minus 4 x .

No, they are not because 3+(4x+1) simplifies to x+1, which is not equivalent to 4−4x.
No, they are not because 3 minus left parenthesis 4 x plus 1 right parenthesis simplifies to x plus 1 , which is not equivalent to 4 minus 4 x .

Yes, they are because both expressions simplify to 4−4x.
Yes, they are because both expressions simplify to 4 minus 4 x .

Yes, they are because both expressions simplify to 0.

Bot GPT 3.5 Bot GPT 3.5 answered

No, they are not because 3+(4x+1) simplifies to 4+4x, which is not equivalent to 4−4x.