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
2 and 3
2 and 3
1 and 2
1 and 2
1
1
1 and 3
9 answers
The correct answer is: 1 and 2.
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=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
A=−123+13
Responses
A=123−13
1 Start Fraction 2 over 3 End Fraction minus 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
A=−123+13
The correct answer 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
<
less than
≤
less-than-or-equal-to
=
equals
>
−6+3⋅5______16−−√+32÷8.
Which operator can be inserted to make the statement true?
(1 point)
Responses
<
less than
≤
less-than-or-equal-to
=
equals
>
The correct answer is > (greater than). The expression can be written as -6 + 3*5 > 16 - sqrt(16) + 32/8.
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
23.5
23
23
22
22
22.5
Responses
23.5
23.5
23
23
22
22
22.5
To determine which value of r would make the inequality 3r - 47.5 > 21.5 true, we need to solve the inequality.
Starting with 3r - 47.5 > 21.5, we can add 47.5 to both sides to isolate the variable:
3r > 21.5 + 47.5,
3r > 69.
Now, divide both sides by 3 to solve for r:
r > 69/3,
r > 23.
Therefore, any value of r that is greater than 23 would make the inequality 3r - 47.5 > 21.5 true.
The correct answer is: r > 23.
Starting with 3r - 47.5 > 21.5, we can add 47.5 to both sides to isolate the variable:
3r > 21.5 + 47.5,
3r > 69.
Now, divide both sides by 3 to solve for r:
r > 69/3,
r > 23.
Therefore, any value of r that is greater than 23 would make the inequality 3r - 47.5 > 21.5 true.
The correct answer is: r > 23.
Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?(1 point)
Responses
8
8
9.5
9.5
10
10
9
Responses
8
8
9.5
9.5
10
10
9
To determine which values of x make the inequality 4x + 1 ≤ √5.83 true, we need to solve the inequality.
Starting with 4x + 1 ≤ √5.83, we can subtract 1 from both sides to isolate the variable:
4x ≤ √5.83 - 1.
Next, we can square both sides to eliminate the square root:
(4x)^2 ≤ (√5.83 - 1)^2,
16x^2 ≤ 5.83 - 2√5.83 + 1.
Simplifying further:
16x^2 ≤ 6.83 - 2√5.83.
Now, divide both sides by 16 to solve for x:
x^2 ≤ (6.83 - 2√5.83) / 16.
To find the specific values of x, we need to determine the square root of 5.83 and evaluate the inequality. Using a calculator, we find that √5.83 is approximately 2.41. Substituting this value into the inequality:
x^2 ≤ (6.83 - 2 * 2.41) / 16,
x^2 ≤ (6.83 - 4.82) / 16,
x^2 ≤ 2.01 / 16,
x^2 ≤ 0.1256.
Taking the square root of both sides, we get:
x ≤ ±√0.1256.
Evaluating ±√0.1256, we find:
x ≤ ±0.3546.
Therefore, the values of x that make the inequality 4x + 1 ≤ √5.83 true are x ≤ 0.3546 and x ≥ -0.3546.
The correct answers are: 0.3546 and -0.3546.
Starting with 4x + 1 ≤ √5.83, we can subtract 1 from both sides to isolate the variable:
4x ≤ √5.83 - 1.
Next, we can square both sides to eliminate the square root:
(4x)^2 ≤ (√5.83 - 1)^2,
16x^2 ≤ 5.83 - 2√5.83 + 1.
Simplifying further:
16x^2 ≤ 6.83 - 2√5.83.
Now, divide both sides by 16 to solve for x:
x^2 ≤ (6.83 - 2√5.83) / 16.
To find the specific values of x, we need to determine the square root of 5.83 and evaluate the inequality. Using a calculator, we find that √5.83 is approximately 2.41. Substituting this value into the inequality:
x^2 ≤ (6.83 - 2 * 2.41) / 16,
x^2 ≤ (6.83 - 4.82) / 16,
x^2 ≤ 2.01 / 16,
x^2 ≤ 0.1256.
Taking the square root of both sides, we get:
x ≤ ±√0.1256.
Evaluating ±√0.1256, we find:
x ≤ ±0.3546.
Therefore, the values of x that make the inequality 4x + 1 ≤ √5.83 true are x ≤ 0.3546 and x ≥ -0.3546.
The correct answers are: 0.3546 and -0.3546.
1 answer