Question
Fill in the blanks!
Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1 ?
Use _ to evaluate the expressions.
Let x = 0.
_ = 2.27
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when _ value of x is used.
Let x = 10.
First expression:
-0.58(10) + 2.27
-5.8 + 2.27
-3.53
Second expression:
7.037 - 1.798(10) / 3.1
7.037 - 17.98 / 3.1
-10.943 / 3.1
_
We can conclude that these two expressions are _.
Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1 ?
Use _ to evaluate the expressions.
Let x = 0.
_ = 2.27
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when _ value of x is used.
Let x = 10.
First expression:
-0.58(10) + 2.27
-5.8 + 2.27
-3.53
Second expression:
7.037 - 1.798(10) / 3.1
7.037 - 17.98 / 3.1
-10.943 / 3.1
_
We can conclude that these two expressions are _.
Answers
GPT-4o mini
Let's fill in the blanks step by step based on the problem provided.
1. Based on the first sentence, we can conclude with:
"Use _ to evaluate the expressions."
Therefore, we'll put:
**x**
2. The second sentence states:
"Let x = 0."
After evaluating the first expression at x = 0, we find that:
**2.27** is correct.
3. The next sentence is:
"The expressions are equivalent for 0."
We can put:
**any**
4. The sentence states:
"In order to be equivalent, the expressions must be equal when _ value of x is used."
We can insert:
**the given**
5. For the evaluations:
"Let x = 10."
The first expression:
-0.58(10) + 2.27
-5.8 + 2.27
**-3.53**
6. For the second expression:
7.037 - 1.798(10) / 3.1
We first calculate:
7.037 - 17.98 / 3.1
-17.98 / 3.1 gives approximately -5.8.
Therefore:
7.037 - 5.8 gives:
**1.237**
7. The final sentence concludes:
"We can conclude that these two expressions are _."
Therefore, we can fill it with:
**not equivalent**.
Putting it all together, we have:
Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1 ?
Use **x** to evaluate the expressions.
Let x = 0.
**2.27**
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when **the given** value of x is used.
Let x = 10.
First expression:
-0.58(10) + 2.27
-5.8 + 2.27
**-3.53**
Second expression:
7.037 - 1.798(10) / 3.1
7.037 - 17.98 / 3.1
-17.98 / 3.1
**1.237**
We can conclude that these two expressions are **not equivalent**.
1. Based on the first sentence, we can conclude with:
"Use _ to evaluate the expressions."
Therefore, we'll put:
**x**
2. The second sentence states:
"Let x = 0."
After evaluating the first expression at x = 0, we find that:
**2.27** is correct.
3. The next sentence is:
"The expressions are equivalent for 0."
We can put:
**any**
4. The sentence states:
"In order to be equivalent, the expressions must be equal when _ value of x is used."
We can insert:
**the given**
5. For the evaluations:
"Let x = 10."
The first expression:
-0.58(10) + 2.27
-5.8 + 2.27
**-3.53**
6. For the second expression:
7.037 - 1.798(10) / 3.1
We first calculate:
7.037 - 17.98 / 3.1
-17.98 / 3.1 gives approximately -5.8.
Therefore:
7.037 - 5.8 gives:
**1.237**
7. The final sentence concludes:
"We can conclude that these two expressions are _."
Therefore, we can fill it with:
**not equivalent**.
Putting it all together, we have:
Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1 ?
Use **x** to evaluate the expressions.
Let x = 0.
**2.27**
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when **the given** value of x is used.
Let x = 10.
First expression:
-0.58(10) + 2.27
-5.8 + 2.27
**-3.53**
Second expression:
7.037 - 1.798(10) / 3.1
7.037 - 17.98 / 3.1
-17.98 / 3.1
**1.237**
We can conclude that these two expressions are **not equivalent**.
fill in all the blanks!
GPT-4o mini
Sure! Here is the completed version with all the blanks filled in:
Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1?
Use **x** to evaluate the expressions.
Let x = 0.
**2.27**
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when **the same** value of x is used.
Let x = 10.
First expression:
-0.58(10) + 2.27
-5.8 + 2.27
**-3.53**
Second expression:
(7.037 - 1.798(10)) / 3.1
(7.037 - 17.98) / 3.1
-10.943 / 3.1
**-3.53**
We can conclude that these two expressions are **equivalent**.
Overall, it looks like the first expression and the adjusted second expression do yield the same value when \( x = 10 \), confirming their equivalence!
Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1?
Use **x** to evaluate the expressions.
Let x = 0.
**2.27**
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when **the same** value of x is used.
Let x = 10.
First expression:
-0.58(10) + 2.27
-5.8 + 2.27
**-3.53**
Second expression:
(7.037 - 1.798(10)) / 3.1
(7.037 - 17.98) / 3.1
-10.943 / 3.1
**-3.53**
We can conclude that these two expressions are **equivalent**.
Overall, it looks like the first expression and the adjusted second expression do yield the same value when \( x = 10 \), confirming their equivalence!