Answer:
7
Step-by-step explanation:
(a squared) plus (b squared) equals (c squared)
(6 squared) plus (4 squared) equals (c squared)
36+16=c squared
c equals 7
Answer:
x = - 1
Step-by-step explanation:
3(x + 1) = - 2(x - 1) - 4 ← distribute parenthesis on both sides
3x + 3 = - 2x + 2 - 4
3x + 3 = - 2x - 2 ( add 2x to both sides )
5x + 3 = - 2 ( subtract 3 from both sides )
5x = - 5 ( divide both sides by 5 )
x = - 1
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.
_____
<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
X = number of singles matches
y = number of doubles mnathes
so we have the equation x + y = 13.......(1)
also
2x + 4y = 38 ...........(2)
(1) and (2) are the required equations
b) Find how many maches are in progress by solivng the above equations:-
x + y = 13 multiply this by -2:-
-2x - 2y = -26
2x + 4y = 38 Adding to removes the terms in x:-
2y = 12
y = 6
so x = 13-6 = 7
So the answer is 6 double matches and 7 singles are in progress.
