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
2 and 3
1 and 2
1 and 3
To determine which statements are true, we can evaluate each statement individually.
For statement #1:
3⋅20=4(6+9)
60=4(15)
60=60
This statement is true.
For statement #2:
4×12=6×(8×2)
48=6×16
48=96
This statement is false.
For statement #3:
4⋅18−4⋅6=42+4⋅8
(4⋅18)-(4⋅6)=42+(4⋅8)
72-24=42+32
48=74
This statement is false.
Therefore, the true statement(s) are:
1
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=153+13
Start Fraction 15 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
To determine which expression is A in order to have a true equation A = 5 - 113, we substitute each expression for A and check which one results in the equation being true.
For expression A = 123 - 13:
A = 123 - 13
A = 110
This does not result in A = 5 - 113, so this expression is not the correct one.
For expression A = (2/3) - (1/3):
A = (2/3) - (1/3)
A = 1/3
This does not result in A = 5 - 113, so this expression is not the correct one.
For expression A = -123 + 13:
A = -123 + 13
A = -110
This does not result in A = 5 - 113, so this expression is not the correct one.
For expression A = 15/3 + 1/3:
A = (15/3) + (1/3)
A = 16/3
This does not result in A = 5 - 113, so this expression is not the correct one.
For expression A = 123 + 13:
A = 123 + 13
A = 136
This also does not result in A = 5 - 113, so this expression is not the correct one.
None of the given expressions for A result in A = 5 - 113. Therefore, none of the given options are correct.
Consider the following expressions:
−6+3⋅5______16−−√+32÷8.
Which operator can be inserted to make the statement true?
(1 point)
Responses
=
equals
>
greater than
≤
less-than-or-equal-to
<
To determine which operator can be inserted to make the statement true, we can evaluate the expressions on both sides of the operator and compare them.
Expression before the operator: -6 + 3 * 5
= -6 + 15
= 9
Expression after the operator: 16 - √(16) + 32 ÷ 8
= 16 - 4 + 4
= 16
From the evaluations, we can see that 9 is not equal to 16. Therefore, the correct operator to make the statement true is:
> (greater than)
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
23.5
23
22
22.5
To determine which value of r makes the inequality 3r - 47.5 > 21.5 a true statement, we can substitute each value of r into the inequality and check if it holds true.
Let's substitute the values:
For r = 23.5:
3(23.5) - 47.5 > 21.5
70.5 - 47.5 > 21.5
23 > 21.5
This is true, but we are looking for values that make the inequality strictly greater than, not just equal to. So we can exclude this option.
For r = 23:
3(23) - 47.5 > 21.5
69 - 47.5 > 21.5
21.5 > 21.5
This is not true, as 21.5 is not strictly greater than 21.5.
For r = 22:
3(22) - 47.5 > 21.5
66 - 47.5 > 21.5
18.5 > 21.5
This is not true, as 18.5 is not greater than 21.5.
For r = 22.5:
3(22.5) - 47.5 > 21.5
67.5 - 47.5 > 21.5
20 > 21.5
This is not true, as 20 is not greater than 21.5.
None of the given values of r make the inequality 3r - 47.5 > 21.5 a true statement. Therefore, none of the given options are correct.