Determine which of the following statements is/are true: #1: 3⋅20=4(6+9) #2: 4×12=6×(8×2)12+6⋅64−−√=2⋅4⋅8 #3: 4⋅18−4⋅6=42+4⋅8 (1 point) Responses 1 1 1 and 3 1 and 3 1 and 2 1 and 2 2 and 3
The correct response is 1 and 3.
Explanation:
1. 3⋅20 does not equal 4(6+9) because 3⋅20 equals 60 and 4(6+9) equals 60 as well. Therefore, statement 1 is true.
2. 4×12 does not equal 6×(8×2)12+6⋅64−−√=2⋅4⋅8 because 4×12 equals 48 and 6×(8×2)12+6⋅64−−√=2⋅4⋅8 equals 468. Therefore, statement 2 is false.
3. 4⋅18−4⋅6 equals 60 and 42+4⋅8 equals 74. Therefore, statement 3 is false.
Which expression is A, in order to have a true equation A=5−113 ?(1 point) Responses A=123−13 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=−123+13 negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction A=123+13 negative 1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction A=153+13
The correct response is A=123−13.
Explanation:
To obtain the equation A=5−113, we want A to have the value of 5 minus 113. The expression A=123−13 would result in A having the value of 123 minus 13, which is not equal to 5 minus 113. The other options are also not correct. Therefore, the correct expression is A=123−13.
Consider the following expressions: −6+3⋅5 ______ 16−−√+32÷8 . Which operator can be inserted to make the statement true? (1 point) Responses > greater than ≤ less-than-or-equal-to < less than =
To make the statement true, the suitable operator that can be inserted is ≤ (less-than-or-equal-to).
Explanation:
Considering the given expressions:
−6+3⋅5 ≤ 16−−√+32÷8
We need to compare the results of both expressions. By simplifying them, we get:
−6+15 ≤ 16−−√+4
Further simplifying, we have:
9 ≤ 16−−√+4
As we can see, 9 is indeed less than or equal to 16−−√+4. Therefore, the suitable operator to make the statement true is ≤ (less-than-or-equal-to).
When the value of r is 23, the equation 3r−47.5=21.5 is a true statement. Which of the following values of r makes the inequality 3r−47.5>21.5 a true statement? (1 point) Responses 22 22 23.5 23.5 23 23 22.5
To find the value of r that makes the inequality 3r−47.5>21.5 a true statement, we need to solve the inequality.
Given that the equation 3r−47.5=21.5 is true when r=23, we can substitute this value into the inequality:
3(23)−47.5>21.5
69−47.5>21.5
21.5>21.5
This statement is not true, as 21.5 is not greater than 21.5.
Therefore, none of the given values of r make the inequality 3r−47.5>21.5 a true statement.
Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?(1 point) Responses 8 8 9 9 10 10 9.5 9.5
To determine which value for x makes the inequality 4x+1−−√ ≤ 5.83 true, we need to solve the inequality.
Starting with the inequality:
4x+1−−√ ≤ 5.83
Subtracting 1 from both sides:
4x ≤ 4.83
Dividing by 4 from both sides:
x ≤ 1.2075
The value for x that satisfies the inequality is any value less than or equal to 1.2075.
Among the given responses, none of them satisfy the inequality because none of them are less than or equal to 1.2075.
Therefore, none of the given values for x make the inequality 4x+1−−√ ≤ 5.83 true.
To determine which of the provided statements are true, let's evaluate each one step by step.
Statement #1:
3⋅20 = 4(6+9)
To solve this equation, we simplify both sides:
60 = 4(15)
60 = 60
Since both sides of the equation are equal, statement #1 is true.
Statement #2:
4×12 = 6×(8×2)12+6⋅64−√ = 2⋅4⋅8
Let's start by simplifying the left-hand side of the equation:
48 = 6×(16)12+6⋅64−√ = 2⋅4⋅8
Next, we simplify the right-hand side of the equation:
48 = 6×16+6⋅64−√ = 64−√ = 2⋅4⋅8
We continue by simplifying further:
48 = 96+64−√ = 64−√ = 2⋅4⋅8
Finally, simplifying the last expression:
48 = 160−√ ≠ 64
Since the final expression does not hold true, statement #2 is false.
Statement #3:
4⋅18−4⋅6 = 42+4⋅8
Let's solve this equation:
72−24 = 42+32
Simplifying both sides further:
48 = 74
The equation is not balanced, as both sides do not equal each other. Therefore, statement #3 is false.
So, the correct statement(s) are:
Statement #1: 3⋅20=4(6+9)
Therefore, the correct response is: 1