unit 1 milestone.docx

18/21 that's 86% RETAKE 18 questions were answered correctly . 3 questions were answered incorrectly . 1 What is the following expression equivalent to?     RATIONALE First, apply the Power of a Power Property of Exponents, which states that when an exponent is another exponent, you can multiply the exponents. Therefore, multiply 2 and 4 to evaluate the . is equivalent to . Next, combine the two terms. The Product Property of Exponents st expressions with the same base are multiplied together, you can add the exponents. Add the e and 3 to evaluate the two terms. 8 plus 3 is 11, which becomes the final exponent. CONCEPT Properties of Exponents Report an issue with this question 2

Evaluate the expression by finding the absolute value. |10| – |‐5| + |‐3|  18  12  2  8 RATIONALE Evaluate each absolute value first. Absolute value is always non-negative. Rewrite the number negative sign if there was one. The absolute value of 10 is 10. The absolute value of -5 is 5. The absolute value of -3 is 3. Now and subtract these numbers following the order of operations. 10 minus 5 is 5. Next, we can add 3. 5 plus 3 is 8. CONCEPT Introduction to Absolute Value Report an issue with this question 3 Jayla bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 12 cups of soup. A quick Google search told her that this was 173.3 cubic inches. She hoped the soup pot below would be big enough. The soup pot is 8 inches tall with a radius of 3 inches. What is the volume of the soup pot? Answer choices are rounded to the nearest whole cubic inch.  226 cubic inches  56 cubic inches

 603 cubic inches  150 cubic inches RATIONALE Recall that the volume of the pot can be represented with the formula for the volume of a cylin the value, r is the radius of the base, and h is the height. First, substitute 3 for r and 8 for h. Once we have the given values plugged into the appropriate places, we can evaluate the formu Order of Operations, we will first square the radius of 3. 3 squared equals 9. Next, we can multiply the remaining values. Using a calculator with a pi bu the most accurate; otherwise we can use the value 3.14. Multiplying π times 9 times 8 is 226, when rounded to the nearest whole cubic inch. The volume pot is 226 cubic inches. CONCEPT Volume Report an issue with this question 4 Consider the following expression: What is the value of this expression when x = -8?     RATIONALE To find the value of this expression when x = -8, begin by substituting -8 for every instance of x expression.

Once all instances of x have been substituted with -8, we can evaluate the expression. The divi as a grouping symbol, separating the expression in the numerator, 2|-8|, from the expression in denominator, -8. Evaluate them separately before dividing, starting with evaluating the absolut Recall that the absolute value of a number is the non-negative value. The absolute value of -8 i the numerator, we can multiply 2 by 8. 2 times 8 is 16. Finally, divide 16 by -8. 16 divided by -8 is -2. CONCEPT Operations as Grouping Symbols Report an issue with this question 5 Perform the indicated operations and write your result as a single number.  39  43  63  91 RATIONALE For this expression, there is a lot to consider here. Follow the order of operations, and evaluate inside parentheses and other grouping symbols first. There are two groups. First, the radical sy (11 × 2 – 6), and a set of parentheses groups . Let's evaluate what is under the radical firs Under the radical, there is multiplication and subtraction. Multiplication comes before subtractio of operations, so we multiply 11 by 2 to get 22. Next, evaluate the subtraction. 22 minus 6 is 16. Now we can take the square root of 16. The square root of 16 is 4. This is the simplified expression underneath the radical. Next, we ha the operations in the set of parentheses. Exponents comes before subtraction in the order of op we square 4 first.

4 squared equals 16. Next, we subtract 9 from 16. 16 minus 9 equals 7. Now that we have eliminated the grouping symbols, we can evaluate the of 5 and 7. 5 times 7 equals 35. Finally, we can add 4 and 35. 4 plus 35 is equal to 39. The expression simplifies to 39. CONCEPT Order of Operations: Exponents and Radicals Report an issue with this question 6 Theresa bought a new desktop computer. One side of the desktop screen is 14 inches and the other side is 18 inches. What is the length of the diagonal of the desktop screen? Answer choices are rounded to the nearest inch.  20 inches  23 inches  16 inches  11 inches RATIONALE We can use the Pythagorean Theorem to calculate the length of a diagonal. The variables a and the sides of the computer, and c represents the diagonal. First, substitute 14 for a and 18 for b could also substitute 18 for a and 14 for b). Once we have the given values plugged into the Pythagorean Theorem, we can evaluate the ex 14 squared is 196, and 18 squared is 324. Now we can add these values together. 196 plus 324 is equal to 520. Finally, we can take the square root of both sides to find the value When we have a squared term, such as c², taking the square root of both sides will cancel this

The square root of 520 is approximately 23. The length of the diagonal, rounded to the nearest inches. CONCEPT Calculating Diagonals Report an issue with this question 7 Simplify the following radical expression.     RATIONALE To simplify this expression, we can use the Product Property of Radicals to separate the expres radicals. The cube root of can be written as the cube root of 27 times the cube root of . Next, w each radical expression using a fractional exponent in order to simplify. The index of the radica the denominator of the fractional exponent. The index here is 3, so each expression underneat will be raised to the power. Now that we have changed our original expression from a radical to fractional exponents, we ca and simplify the two expressions that are raised to the power. 27 to the power of evaluates to 3 because 3 raised to the 3rd power is 27 ( ). To simpl multiply the two exponents together. 3 times equals 1 and is simply x. The expression simplifies to 3x. CONCEPT

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help