Use Euclid’s Ladder (or a factor tree) to write the prime factorization.

Mathematics

2 answers:

Veseljchak [2.6K]3 years ago

5 0

Answer:

Step-by-step explanation:

the answer is 64 hope this helps

alekssr [168]3 years ago

4 0

I can’t do factor trees on here, but I’ll try my best

64 =
32, 2 =
16, 2, 2 =
8, 2, 2, 2 =
4, 2, 2, 2, 2 =
2, 2, 2, 2, 2 =
2^5

100 =
50, 2 =
25, 2, 2 =
5, 5, 2, 2 =
2^2 * 5^2

54 =
27, 2 =
9, 3, 2 =
3, 3, 3, 2 =
3^3 * 2

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A seamstress needs to cut 15-inch pieces of ribbon from a roll of ribbon that is 9 feet length. What is the greatest number of 1

yan [13]

STEP 1:
Divide the length of the ribbon by the size of the pieces.

12 inches= 1 foot

= 9 ft ÷ 15 inch pieces
convert ft to inches
= (12)(9) ÷ 15
= 108 ÷ 15
= 7.2 pieces from one roll

STEP 2:
multiply the number of pieces that can be cut from one roll by the number of rolls

= 7.2 pieces * 5 rolls
= 36 pieces total from 5 rolls

ANSWER: The greatest number of 15-inch pieces that can be cut from five 9-foot rolls is 36.

Hope this helps! :)

4 0

3 years ago

what is the best approximation of the solution to the system to the nearest valus 2x-3y=-6 and x+2y=8

Trava [24]

Given:
2x - 3y = -6 ⇒ identified as 1st equation
x + 2y = 8 ⇒ identified as 2nd equation

Let us first get the value of x using the 2nd equation.
x + 2y = 8
x = 8 - 2y

Substitute x in the 1st equation with its value and find the value of y.
2x - 3y = -6
2(8-2y) - 3y = -6
16 - 4y -3y = -6
-4y - 3y = -6 -16
-7y = - 22
y = -22/-7
y = 22/7 simplified to 3 1/7

Substitute the value of y in the 2nd equation.
x = 8 - 2y
x = 8 - 2(22/7)
x = 8 - 44/7
x = (8 * 7/7) - 44/7
x = 56/7 - 44/7
x = (56-44)/7
x = 12/7 simplified to 1 5/7

To check: x = 12/7 and y = 22/7 *we need to use the improper fractions.
2x - 3y = -6
2(12/7) - 3(22/7) = -6
24/7 - 66/7 = -6
(24-66)/7 = -6
-42/7 = -6
-6 = -6

x + 2y = 8
12/7 + 2(22/7) = 8
12/7 + 44/7 = 8
(12+44)/7 = 8
56/7 = 8
8 = 8

8 0

3 years ago

Write an expression for the 12th partial sum of the series 3/2+7/3+19/6+... using summation notation

lapo4ka [179]

Answer:

$S_{12}=\sum_{i=1}^{12} [\frac{3}{2}+(i-1)\times \frac{5}{6}]$

$S_{12}=73$

Step-by-step explanation:

$First\ term\ of\ the\ series(a_1)=\frac{3}{2}\\\\Second\ term\ of\ the\ series(a_2)=\frac{7}{3}\\\\Third\ term\ of\ the\ series(a_3)=\frac{19}{6}\\\\a_2-a_1=\frac{7}{3}-\frac{3}{2}=\frac{5}{6}\\\\a_3-a_2=\frac{19}{6}-\frac{7}{3}=\frac{5}{6}\\\\Hence\ it\ is\ an\ Arithmetic\ Series\ with\ first\ term=\frac{3}{2}\ and\ constant\ difference=\frac{5}{6}$

$a_1=\frac{3}{2}+0\times \frac{5}{6}\\\\a_2=\frac{3}{2}+1\times \frac{5}{6}\\\\a_3=\frac{3}{2}+2\times \frac{5}{6}\\\\.\\.\\.\\a_n=\frac{3}{2}+(n-1)\times \frac{5}{6}\\\\S_n=a_1+a_2+a_3+......+a_n\\\\S_n=(\frac{3}{2}+0\times \frac{5}{6})+(\frac{3}{2}+1\times \frac{5}{6})+(\frac{3}{2}+2\times \frac{5}{6})+....+(\frac{3}{2}+[n-1]\times \frac{5}{6})\\\\S_n=\sum_{i=1}^n [\frac{3}{2}+(i-1)\times \frac{5}{6}]\\\\S_n=(\frac{3}{2}+\frac{3}{2}+\frac{3}{2}+...n\ times)+\frac{5}{6}(1+2+3+4+...+(n-1))\\\\$