To simplify the expression (10−6)2 + 8 − 2'2, let's first evaluate the parentheses:
(10−6)2 = 4² = 16
Now let's simplify the remaining expression:
16 + 8 − 2'2
Next, let's evaluate the exponent:
2'2 = 2 × 2 = 4
Now we can substitute the values back into the expression:
16 + 8 - 4
Finally, let's perform the addition and subtraction:
= 24 - 4
= 20
Therefore, the simplified expression is 20.
Simplify (10−6)2 + 8 − 2'2
17 answers
Simplify: 12
(16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8)
(16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8)
To simplify the expression (16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8), let's work through the calculations step by step:
First, perform the division inside the parentheses:
(16 ÷ 4 = 4 + 4) ÷ (6 × 4 ÷ 8)
= (4 + 4) ÷ (6 × 4 ÷ 8)
= 8 ÷ (6 × 4 ÷ 8)
Next, perform the multiplication inside the parentheses:
8 ÷ (6 × 4 ÷ 8)
= 8 ÷ (24 ÷ 8)
= 8 ÷ 3
Finally, perform the division:
8 ÷ 3 = 2.6667 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 2.6667.
First, perform the division inside the parentheses:
(16 ÷ 4 = 4 + 4) ÷ (6 × 4 ÷ 8)
= (4 + 4) ÷ (6 × 4 ÷ 8)
= 8 ÷ (6 × 4 ÷ 8)
Next, perform the multiplication inside the parentheses:
8 ÷ (6 × 4 ÷ 8)
= 8 ÷ (24 ÷ 8)
= 8 ÷ 3
Finally, perform the division:
8 ÷ 3 = 2.6667 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 2.6667.
Simplify: 1/2
(16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8)
(16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8)
To simplify the expression (16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8), let's work through the calculations step by step:
First, perform the division inside the parentheses:
(16 ÷ 4 = 4 + 4) ÷ (6 × 4 ÷ 8)
= (4 + 4) ÷ (6 × 4 ÷ 8)
= 8 ÷ (6 × 4 ÷ 8)
Next, perform the multiplication inside the parentheses:
8 ÷ (6 × 4 ÷ 8)
= 8 ÷ (24 ÷ 8)
= 8 ÷ 3
Finally, perform the division:
8 ÷ 3 = 2.6667 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 2.6667.
However, please note that the original expression does not involve a fraction or the number 1/2. If there was an error in formatting the expression, please provide the correct expression for further simplification.
First, perform the division inside the parentheses:
(16 ÷ 4 = 4 + 4) ÷ (6 × 4 ÷ 8)
= (4 + 4) ÷ (6 × 4 ÷ 8)
= 8 ÷ (6 × 4 ÷ 8)
Next, perform the multiplication inside the parentheses:
8 ÷ (6 × 4 ÷ 8)
= 8 ÷ (24 ÷ 8)
= 8 ÷ 3
Finally, perform the division:
8 ÷ 3 = 2.6667 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 2.6667.
However, please note that the original expression does not involve a fraction or the number 1/2. If there was an error in formatting the expression, please provide the correct expression for further simplification.
Simplify: 1/2 (16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8)
To simplify the expression 1/2 (16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8), let's work through the calculations step by step:
First, perform the division inside the parentheses:
16 ÷ 4 = 4 + 4
= 8
Next, apply the multiplication and division outside the parentheses:
1/2 (8) ÷ (6 × 4 ÷ 8)
= 1/2 × 8 ÷ (6 × 4 ÷ 8)
= 4 ÷ (6 × 4 ÷ 8)
Now, perform the division:
4 ÷ (6 × 4 ÷ 8)
= 4 ÷ (24 ÷ 8)
= 4 ÷ 3
Finally, perform the division:
4 ÷ 3 = 1.3333 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 1.3333.
First, perform the division inside the parentheses:
16 ÷ 4 = 4 + 4
= 8
Next, apply the multiplication and division outside the parentheses:
1/2 (8) ÷ (6 × 4 ÷ 8)
= 1/2 × 8 ÷ (6 × 4 ÷ 8)
= 4 ÷ (6 × 4 ÷ 8)
Now, perform the division:
4 ÷ (6 × 4 ÷ 8)
= 4 ÷ (24 ÷ 8)
= 4 ÷ 3
Finally, perform the division:
4 ÷ 3 = 1.3333 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 1.3333.
Simplify: 1/2 (16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8)
Responses
A 1/2
B 1
C 4/3
D 3
Responses
A 1/2
B 1
C 4/3
D 3
To simplify the expression 1/2 (16 ÷ 4 + 4) ÷ (6 × 4 ÷ 8), let's work through the calculations step by step:
First, perform the division inside the parentheses:
16 ÷ 4 = 4 + 4
= 8
Next, apply the multiplication and division outside the parentheses:
1/2 (8) ÷ (6 × 4 ÷ 8)
= 1/2 × 8 ÷ (6 × 4 ÷ 8)
= 4 ÷ (6 × 4 ÷ 8)
Now, perform the multiplication and division:
4 ÷ (6 × 4 ÷ 8)
= 4 ÷ (24 ÷ 8)
= 4 ÷ 3
Finally, perform the division:
4 ÷ 3 = 1.3333 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 1.3333.
So the correct answer choice is C) 4/3.
First, perform the division inside the parentheses:
16 ÷ 4 = 4 + 4
= 8
Next, apply the multiplication and division outside the parentheses:
1/2 (8) ÷ (6 × 4 ÷ 8)
= 1/2 × 8 ÷ (6 × 4 ÷ 8)
= 4 ÷ (6 × 4 ÷ 8)
Now, perform the multiplication and division:
4 ÷ (6 × 4 ÷ 8)
= 4 ÷ (24 ÷ 8)
= 4 ÷ 3
Finally, perform the division:
4 ÷ 3 = 1.3333 (rounded to 4 decimal places)
Therefore, the simplified expression is approximately 1.3333.
So the correct answer choice is C) 4/3.
Which expression is equivalent to 1/3
+ (3/4
+ 2/3
)?
Responses
A (13
+ 34
) + 23
( 1 3 + 3 4 ) + 2 3
B 13
(34
+ 23
)1 3 ( 3 4 + 2 3 )
C 13
− 23
+ 34
1 3 − 2 3 + 3 4
D 34
− 23
+ 13
+ (3/4
+ 2/3
)?
Responses
A (13
+ 34
) + 23
( 1 3 + 3 4 ) + 2 3
B 13
(34
+ 23
)1 3 ( 3 4 + 2 3 )
C 13
− 23
+ 34
1 3 − 2 3 + 3 4
D 34
− 23
+ 13
To simplify the expression 1/3 + (3/4 + 2/3), let's work through the calculations step by step:
First, let's find a common denominator for the fractions within the parentheses:
1/3 + (9/12 + 8/12)
Next, let's add the fractions within the parentheses:
1/3 + 17/12
To combine these fractions, we need a common denominator:
4/12 + 17/12 = 21/12
Now, let's simplify the expression:
1/3 + (3/4 + 2/3) = 21/12
To further simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (3):
21/12 ÷ 3/3 = 7/4
Therefore, the expression 1/3 + (3/4 + 2/3) is equivalent to 7/4.
So the correct answer choice is D) 34 - 23 + 13.
First, let's find a common denominator for the fractions within the parentheses:
1/3 + (9/12 + 8/12)
Next, let's add the fractions within the parentheses:
1/3 + 17/12
To combine these fractions, we need a common denominator:
4/12 + 17/12 = 21/12
Now, let's simplify the expression:
1/3 + (3/4 + 2/3) = 21/12
To further simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (3):
21/12 ÷ 3/3 = 7/4
Therefore, the expression 1/3 + (3/4 + 2/3) is equivalent to 7/4.
So the correct answer choice is D) 34 - 23 + 13.
What is the distance between -45 and -98 on a number line?
Responses
A -67-67
B 5353
C 6767
D 133133
E 143
Responses
A -67-67
B 5353
C 6767
D 133133
E 143
To find the distance between -45 and -98 on a number line, we consider the absolute difference between the two numbers.
The difference between -45 and -98 is obtained by subtracting -45 from -98:
-98 - (-45) = -98 + 45 = -53
However, since we want the distance, we take the absolute value of the difference:
|-53| = 53
Therefore, the distance between -45 and -98 on a number line is 53.
So the correct answer choice is B) 53.
The difference between -45 and -98 is obtained by subtracting -45 from -98:
-98 - (-45) = -98 + 45 = -53
However, since we want the distance, we take the absolute value of the difference:
|-53| = 53
Therefore, the distance between -45 and -98 on a number line is 53.
So the correct answer choice is B) 53.
A hot air balloon reaches its maximum height of 1,260 feet within 15 minutes of liftoff. After descending 235 feet, it rises 147 feet. Which statements are correct for this situation?
Responses
A The balloon's final height is 1,025 feet.The balloon's final height is 1,025 feet.
B After its first descent, the balloon's height is 1,245 feet.After its first descent, the balloon's height is 1,245 feet.
C After its first descent, the balloon's height is 1,025 feet.After its first descent, the balloon's height is 1,025 feet.
D The balloon's final height is 88 feet below its maximum height.The balloon's final height is 88 feet below its maximum height.
E Calculating 1,260 − 235 + 147 determines the balloon's final height.
Responses
A The balloon's final height is 1,025 feet.The balloon's final height is 1,025 feet.
B After its first descent, the balloon's height is 1,245 feet.After its first descent, the balloon's height is 1,245 feet.
C After its first descent, the balloon's height is 1,025 feet.After its first descent, the balloon's height is 1,025 feet.
D The balloon's final height is 88 feet below its maximum height.The balloon's final height is 88 feet below its maximum height.
E Calculating 1,260 − 235 + 147 determines the balloon's final height.
Let's evaluate each statement one by one:
A) The balloon's final height is 1,025 feet.
To find the final height, we start with the maximum height of 1,260 feet. Then, the balloon descends 235 feet and rises 147 feet.
1,260 - 235 + 147 = 1,172 feet
Therefore, statement A is incorrect.
B) After its first descent, the balloon's height is 1,245 feet.
This statement is not mentioned in the given information and cannot be determined. Hence, statement B is incorrect.
C) After its first descent, the balloon's height is 1,025 feet.
To find the height after the first descent, we start with the maximum height of 1,260 feet and subtract the descent of 235 feet.
1,260 - 235 = 1,025 feet
Therefore, statement C is correct.
D) The balloon's final height is 88 feet below its maximum height.
To determine if this statement is correct, we need to find the difference between the maximum height of 1,260 feet and the final height.
1,260 - 1,172 = 88 feet
Therefore, statement D is correct.
E) Calculating 1,260 − 235 + 147 determines the balloon's final height.
Calculating 1,260 - 235 + 147 gives us:
1,260 - 235 + 147 = 1,172 feet
Therefore, statement E is incorrect.
In summary, statements C and D are correct for this situation.
A) The balloon's final height is 1,025 feet.
To find the final height, we start with the maximum height of 1,260 feet. Then, the balloon descends 235 feet and rises 147 feet.
1,260 - 235 + 147 = 1,172 feet
Therefore, statement A is incorrect.
B) After its first descent, the balloon's height is 1,245 feet.
This statement is not mentioned in the given information and cannot be determined. Hence, statement B is incorrect.
C) After its first descent, the balloon's height is 1,025 feet.
To find the height after the first descent, we start with the maximum height of 1,260 feet and subtract the descent of 235 feet.
1,260 - 235 = 1,025 feet
Therefore, statement C is correct.
D) The balloon's final height is 88 feet below its maximum height.
To determine if this statement is correct, we need to find the difference between the maximum height of 1,260 feet and the final height.
1,260 - 1,172 = 88 feet
Therefore, statement D is correct.
E) Calculating 1,260 − 235 + 147 determines the balloon's final height.
Calculating 1,260 - 235 + 147 gives us:
1,260 - 235 + 147 = 1,172 feet
Therefore, statement E is incorrect.
In summary, statements C and D are correct for this situation.
wrong
Apologies for the incorrect response. Let's revaluate each statement:
A) The balloon's final height is 1,025 feet.
To find the final height, we start with the maximum height of 1,260 feet. Then, the balloon descends 235 feet and rises 147 feet.
1,260 - 235 + 147 = 1,172 feet
Therefore, statement A is incorrect.
B) After its first descent, the balloon's height is 1,245 feet.
To find the height after the first descent, we subtract 235 feet from the maximum height of 1,260 feet.
1,260 - 235 = 1,025 feet
Therefore, statement B is incorrect.
C) After its first descent, the balloon's height is 1,025 feet.
As calculated above, the height after the first descent is indeed 1,025 feet.
Therefore, statement C is correct.
D) The balloon's final height is 88 feet below its maximum height.
To determine if this statement is correct, we need to find the difference between the maximum height of 1,260 feet and the final height.
1,260 - 1,025 = 235 feet
Therefore, the balloon's final height is 235 feet below its maximum height. Hence, statement D is incorrect.
E) Calculating 1,260 − 235 + 147 determines the balloon's final height.
Calculating 1,260 - 235 + 147 gives us:
1,260 - 235 + 147 = 1,172 feet
Therefore, statement E is incorrect.
In summary, only statement C is correct for this situation.
A) The balloon's final height is 1,025 feet.
To find the final height, we start with the maximum height of 1,260 feet. Then, the balloon descends 235 feet and rises 147 feet.
1,260 - 235 + 147 = 1,172 feet
Therefore, statement A is incorrect.
B) After its first descent, the balloon's height is 1,245 feet.
To find the height after the first descent, we subtract 235 feet from the maximum height of 1,260 feet.
1,260 - 235 = 1,025 feet
Therefore, statement B is incorrect.
C) After its first descent, the balloon's height is 1,025 feet.
As calculated above, the height after the first descent is indeed 1,025 feet.
Therefore, statement C is correct.
D) The balloon's final height is 88 feet below its maximum height.
To determine if this statement is correct, we need to find the difference between the maximum height of 1,260 feet and the final height.
1,260 - 1,025 = 235 feet
Therefore, the balloon's final height is 235 feet below its maximum height. Hence, statement D is incorrect.
E) Calculating 1,260 − 235 + 147 determines the balloon's final height.
Calculating 1,260 - 235 + 147 gives us:
1,260 - 235 + 147 = 1,172 feet
Therefore, statement E is incorrect.
In summary, only statement C is correct for this situation.