9514 1404 393
Answer:
- 12 boxes
- 10 pencils, 9 notebooks
Step-by-step explanation:
a) The number of boxes will be the greatest common divisor (GCD) of the numbers 120 and 108. That number is 12.
120 = 12×10
108 = 12×9 . . . . 12 is the greatest common divisor
Matthew can make 12 boxes with equal numbers of the items.
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b) 120 pencils divided by 12 will be 10 pencils per box.
108 notebooks divided by 12 will be 9 notebooks per box.
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<em>Additional comment</em>
It helps to be familiar with multiplication tables up to about 12×12.
The GCD can always be found using Euclid's algorithm. Look at the remainder when the larger number is divided by the smaller. If it is not zero, then replace the larger number with the remainder and repeat. If the remainder is zero, the divisor is the GCD.
Here, we have ...
120/108 = 1 r 12.
108/12 = 9 r 0 ⇒ 12 is the GCD
Answer:
(8, -8)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Terms/Coefficients
- Coordinates (x, y)
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = x - 16
5y = 2x - 56
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in <em>y</em>: 5(x - 16) = 2x - 56
- Distribute 5: 5x - 80 = 2x - 56
- [Subtraction Property of Equality] Subtract 2x on both sides: 3x - 80 = -56
- [Addition Property of Equality] Add 80 on both sides: 3x = 24
- [Division Property of Equality] Divide 3 on both sides: x = 8
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: y = x - 16
- Substitute in <em>x</em>: y = 8 - 16
- Subtract: y = -8
Answer:
Assuming you're referring to the sides of a right triangle, the missing side X would be 12.
Step-by-step explanation:
The Pythagorean Theorem states that the two legs of a right triangle squared and added together is equal to the hypotenuse squared. 
is 169, 
is 25, 169 - 25 = 144. Take the square root of 144 and you'll get 12, which is the missing side of the right triangle.
Answer:
The circle length is 90*pi which should be 3.14
So the circle length is 282.6
The central angle is 90 degree which is 1/4 part of 360 degree
From the theory of arc, the arc length should also be 1/4 part of circle length.
So the answer should be 1/4 * 282.6 = 70.65
Becasue it should be to the nearest tenth, so the answer should be 70.7
Step-by-step explanation:
Step-by-step explanation:
Work out the value of x.
<h3>#12</h3>
<u>The angles are supplementary as same side interior angles, sum to 180°:</u>
- x + x - 26 = 180
- 2x = 206
- x = 103
<h3>#13</h3>
<u>The angles are corresponding, hence congruent:</u>
- 3x - 5 = x + 55
- 3x - x = 55 + 5
- 2x = 60
- x = 30
<h3>#14</h3>
<u>The angles are supplementary as same side interior angles, sum to 180°:</u>
- 2x + 24 + x = 180
- 3x = 180 - 24
- 3x = 156
- x = 52
<h3>#15</h3>
<u>The angles are corresponding, hence congruent:</u>
- 4x - 12 = 3x + 6
- 4x - 3x = 6 + 12
- x = 18
<h3>#16</h3>
<u>Corresponding with the right angle:</u>
- 4x + 12 = 90
- 4x = 78
- x = 19.5
<h3>#17</h3>
<u>Vertical angle of the bottom angle is supplementary with the top angle:</u>
- 2x + 12 + 3x + 23 = 180
- 5x + 35 = 180
- 5x = 145
- x = 49
