#1. 7 + 3^2 (-5 + 1) ÷ 2.
#2. -3x^3 - 4x for x = -1.
#3. What is the fractional equivalent of 0.2323...?
#4. Which of the following shows the correct order of the given numbers?
1, 1, 1.6
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1. What is divided by 2? The total? The amount in parenthesis?
2. for x = -1, -x^3 = -1
4. Correct order, if going from lowest to highest value.
If X = 0.2323... then 100X = 23.2323..., so 99X = 23.2323... - 0.2323... = 23. So X = 23/99. 23 is a prime number, so you can't simplify that any more.
#1. To simplify the expression 7 + 3^2 (-5 + 1) ÷ 2, we need to follow the order of operations (also known as PEMDAS).
First, we need to evaluate the exponent: 3^2 = 9.
Next, we perform the operations inside the parentheses: (-5 + 1) = -4.
Then, we multiply the result inside the parentheses by the exponent: 9 * -4 = -36.
Finally, we perform the remaining operations from left to right: 7 + (-36) ÷ 2.
To evaluate the division, we divide -36 by 2, resulting in -18.
Now, we have the expression 7 + (-18).
Next, we add 7 to -18, giving us a final result of -11.
Therefore, the value of the expression 7 + 3^2 (-5 + 1) ÷ 2 is -11.
#2. To find the value of -3x^3 - 4x, when x = -1, we substitute -1 into the expression.
For the variable x, we have:
-3(-1)^3 - 4(-1).
To evaluate the exponent, we calculate (-1)^3, which equals -1.
Next, we substitute -1 for x in the expression:
-3(-1) - 4(-1).
Finally, we perform the multiplication and addition or subtraction:
3 + 4 = 7.
Therefore, the value of -3x^3 - 4x, when x = -1, is 7.
#3. To find the fractional equivalent of 0.2323..., we need to identify the repeating decimal portion and convert it to a fraction.
Let's use the variable y to represent 0.2323... for simplicity.
We can rewrite y as an equation:
y = 0.2323...
Next, we multiply both sides of the equation by 100, since there are two decimal places after the decimal point:
100y = 23.2323...
To eliminate the repeating decimal, we subtract the original equation from the equation with all non-repeating decimals:
100y - y = 23.2323... - 0.2323...
Simplifying this equation, we get:
99y = 23
Now, we divide both sides of the equation by 99 to solve for y:
y = 23/99.
Therefore, the fractional equivalent of 0.2323... is 23/99.
#4. To determine the correct order of the given numbers (1, 1, 1.6), we need to compare their values.
Starting from the smallest number, we have:
1 < 1.6 < 1.
Therefore, the correct order of the given numbers is 1 < 1.6 < 1.
#1. To solve this expression, we need to follow the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Given expression: 7 + 3^2 (-5 + 1) ÷ 2
Step 1: Evaluate the expression within parentheses:
(-5 + 1) = -4
Step 2: Evaluate the exponent:
3^2 = 9
Step 3: Apply the multiplication:
9 * -4 = -36
Step 4: Apply the division:
-36 ÷ 2 = -18
Step 5: Apply the addition:
7 + (-18) = -11
Therefore, the answer is -11.
#2. To find the value of the expression -3x^3 - 4x for x = -1, we substitute -1 for x in the expression and evaluate it.
Given expression: -3x^3 - 4x
Substituting x = -1:
-3(-1)^3 - 4(-1)
Simplify the exponents:
-3(-1) - 4(-1)
Multiply:
3 + 4
Final answer: 7
#3. To find the fractional equivalent of 0.2323..., we can follow these steps:
Step 1: Let x = 0.2323... (the repeating decimal).
Step 2: Multiply both sides of the equation by a power of 10 to eliminate the repeating part:
10x = 2.323...
Step 3: Subtract the original equation from the equation in step 2 to remove the repeating part:
10x - x = 2.323... - 0.2323...
This simplifies to:
9x = 2.0919... (decimal obtained by subtracting)
Step 4: Divide both sides of the equation by 9 to solve for x:
x = 2.0919... / 9
Calculating the decimal division, we get:
x = 0.232...
Therefore, the fractional equivalent of 0.2323... is 232/999.
#4. To determine the correct order of the given numbers (1, 1, 1.6), we need to compare the values.
The numbers in ascending order are:
1, 1, 1.6
Therefore, the correct order is 1, 1, 1.6.