Factoring and Multiples

To represent -2 x 3 on a number line, first calculate the product, which is -6. Then, locate the point -6 on the number line, which is 6 units to the left of 0. You can mark this point clearly, indicating that -6 is the result of multiplying -2 by 3.

To find the square root of 17424 by prime factorization, we first factor 17424 into its prime components. The prime factorization of 17424 is (2^4 \times 3^1 \times 7^2). Taking the square root involves taking half the exponent of each prime factor, resulting in (2^2 \times 3^{0.5} \times 7^1 = 4 \times 7 \times \sqrt{3} = 28\sqrt{3}). Therefore, the square root of 17424 is (28\sqrt{3}).

60 percent = 60 / 100

Cancel this down to its lowest terms, by dividing each side of the fraction by 20, you get 3 / 5.

To find the number of different factors of the number 75600, first, we need its prime factorization. The prime factorization of 75600 is (2^4 \times 3^3 \times 5^2 \times 7^1). To find the total number of factors, use the formula: ((e_1 + 1)(e_2 + 1)(e_3 + 1)(e_4 + 1)), where (e_i) are the exponents in the prime factorization. Thus, the number of factors is ((4+1)(3+1)(2+1)(1+1) = 5 \times 4 \times 3 \times 2 = 120).

The answer to 111111111 x 111111111 is 12,345,678,987,654,321. This multiplication can be observed as a pattern where the result is a palindrome, reflecting a symmetrical sequence of digits.

The GCF of 30, 50, and 70 is 10.

An odd multiple of 50 is not possible because all multiples of 50 are even (as 50 itself is an even number). However, double 18 in pounds is 36 pounds. Thus, while you can have a multiple of 50, it cannot be odd, and 36 pounds is simply double 18.

8,325 in expanded form using exponents is: (8 x 103) + (3 x 102) + (2 x 101) + (5 x 100).

Yes, 5 is a factor of 7565 because 7565 is divisible by 5.

1, 2, 3, 6, 13, 26, 39, 78

1, 3, 9, 13, 39, 117

x^(2) - 100 =>

x^(20 - 10^(2) =>

( x - 10)(x + 10) Done!!!!!

Well, isn't that just a happy little math problem we have here! To find out what times what equals 780, we can break it down by finding pairs of numbers that multiply together to equal 780. One pair that works is 30 times 26, but there are other combinations too. Just remember, there's no mistakes in math, only happy little accidents!

2 times 70 equals 140.

Catalan and Spanish are not mutually intelligible to the same degree as dialects of a single language, but they do share some similarities due to their common Latin roots. Speakers of one language may understand basic phrases or vocabulary in the other, especially if they have some exposure to it. However, the two languages have distinct grammatical structures, pronunciation, and vocabulary, which can make full comprehension challenging for speakers unfamiliar with the other language. Overall, while there is some overlap, they are considered separate languages.

To determine which set of ratios are equivalent, we can simplify each pair of numbers. The ratio of 36 to 918 simplifies to 1:25.5, while 47 to 48 simplifies to approximately 0.979. The ratio of 12 to 34 is approximately 0.353, and 216 to 116 simplifies to approximately 1.862. None of the ratios are equivalent to each other.

The multiples of 4 up to 100 are the numbers obtained by multiplying 4 by the integers from 1 to 25. This results in the sequence: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, and 100. Thus, the last multiple of 4 before reaching 100 is 100 itself.

The sequence 5, 10, 20, 40, 80 can be identified as a geometric progression where each term is multiplied by 2. The nth term can be expressed as ( a_n = 5 \times 2^{(n-1)} ), where ( a_n ) is the nth term. Thus, for any integer ( n ), you can find the term by substituting ( n ) into this formula. For example, the 1st term is 5, the 2nd term is 10, and so on.

The number of factors of a given number corresponds to the different ways that number can be expressed as a product of two integers, which represents the possible dimensions of rectangular arrays. For instance, if a number has six factors, it can be arranged into rectangular arrays of dimensions that multiply to that number, such as 1x6, 2x3, and 3x2. Each unique pair of factors gives a distinct arrangement, illustrating the relationship between factors and rectangular arrays. Thus, the total number of factors directly determines the number of unique rectangular configurations possible for that number.

18 = 6 x 3

24 = 6 x 4

54 = 6 x 9

Since '6' appears in all multiples then '6' is the GCF.

A community of people who share a common identity and common goals often forms around shared interests, values, or experiences. This can include cultural, ethnic, or social groups that come together to support one another, advocate for their needs, and celebrate their uniqueness. Such communities foster a sense of belonging and collective purpose, enabling individuals to work collaboratively towards achieving shared objectives. Examples include LGBTQ+ associations, cultural heritage organizations, and activist groups focused on social justice.

MDCCCCXX is the Roman numeral representation for the number 1920. In this notation, M represents 1000, D represents 500, C represents 100 (with four Cs making 400), and XX represents 20. Therefore, when combined, they total 1920.

No, 118 is not a multiple of 9. To determine if a number is a multiple of 9, you can sum its digits: 1 + 1 + 8 = 10. Since 10 is not divisible by 9, 118 is not a multiple of 9.

Opticians, optometrists, and ophthalmologists all work within the field of eye care and vision health, but they have different roles. Opticians primarily focus on fitting and dispensing eyewear based on prescriptions provided by optometrists or ophthalmologists. Optometrists are healthcare professionals who perform eye exams, diagnose vision problems, and prescribe corrective lenses, while ophthalmologists are medical doctors specializing in eye diseases and surgical interventions. Despite their distinct responsibilities, all three contribute to the overall management of eye health and vision correction.

To find the largest perfect cube factor of 189, we first need to factor it into its prime components. The prime factorization of 189 is (3^3 \times 7^1). The largest perfect cube that can be formed from these factors is (3^3), which equals 27. Therefore, the largest perfect cube factor of 189 is 27.