I need help with this question I'm reviewing for my final for next week. Thanks
Perform the indicated operation.
(84) ÷ [(-1) - (-7)]
AND
Find the GCF of the numbers using an appropriate method.
240, 10,000, and 4500
AND
Write the number in scientific notation.0.000 294
Thank you
1. Start by performing operations in the parentheses:
84 / [-1 + 7]
A negative multiplied by a negative is a positive.
Now we have 84/[6], which equals 14
2. Start by finding prime factors of the numbers:
240 = 4*6*10 = 2^2 * 2 * 3 * 2 * 5 = 2^4 * 3 * 5
10000 = 10^4 = 2^4 * 5^4
4500 = 9 * 5 * 100 = 3^2 * 5 * 10^2 = 3^2 * 5 * 2^2 * 5^2 = 3^2 * 5^3 * 2^2
Now look for common factors in the prime factorizations:
240 = 2^4 * 3 * 5
10000 = 2^4 * 5^4
4500 = 3^2 * 5^3 * 2^2
The greatest power of 2 shared by all of them is 2^2.
The greatest power of 3 shared is 3^0.
The greatest power of 5 shared is 5^1. Therefore, the GCF is 2^2 * 3^0 * 5^1 = 4*1*5 = 20
3. 0.000294. Multiply by 10 until there is a number in the units place:
.000294 * 10 = .00294
.00294 * 10 = .0294
.0294 * 10 = .294
.294 * 10 = 2.94
You multiplied by 10 four times. Therefore, the number is 2.94 x 10^(-4) in scientific notation.
Thank you so much it makes a lot more sense to me now. I have my final exam next week so I reviewing over my work. Once again thank you
I have a question what do you mean by ^ what does that symbol mean I know that * means multiplication.
^ means to the power of.
For instance, 4^2 is 4 squared and 5^3 is 5 to the third power or 5 cubed.
Has the content in this course allowed you to think of mathematics as a useful tool? If so, how? What concepts investigated in this course might apply to your personal and professional life?
what is the answer if I use lattice multiplication to find the product in 124 x 56
Sure! I'd be happy to help you with those questions.
1. Perform the indicated operation: (84) ÷ [(-1) - (-7)]
To solve this problem, you need to perform the operations in the parentheses first:
(-1) - (-7) = -1 + 7 = 6
Now you have: (84) ÷ 6
Simply divide 84 by 6: 84 ÷ 6 = 14
So, the answer to (84) ÷ [(-1) - (-7)] is 14.
2. Find the GCF of the numbers: 240, 10,000, and 4500
To find the greatest common factor (GCF), you can use the method of prime factorization.
Step 1: Find the prime factorization of each number:
- Prime factorization of 240: 2^4 * 3 * 5
- Prime factorization of 10,000: 2^4 * 5^4
- Prime factorization of 4500: 2^2 * 3^2 * 5^3
Step 2: Identify the common prime factors of all the numbers:
- The common prime factors of 240, 10,000, and 4500 are 2, 3, and 5.
Step 3: Determine the lowest exponent of each common prime factor:
- The lowest exponent of 2 is 2.
- The lowest exponent of 3 is 1.
- The lowest exponent of 5 is 1.
Step 4: Multiply the common prime factors with the lowest exponents:
2^2 * 3 * 5 = 60
Therefore, the GCF of 240, 10,000, and 4500 is 60.
3. Write the number in scientific notation: 0.000294
To express a number in scientific notation, you need to move the decimal point to the right until there is only one digit to the left of the decimal point, and then count the number of places you moved the decimal point.
For the number 0.000294:
Move the decimal point 4 places to the right to get 2.94. Since you moved the decimal point to the right, the exponent of 10 will be negative.
Therefore, 0.000294 in scientific notation is 2.94 x 10^(-4).
I hope this explanation helps! Let me know if you have any further questions.