1 1 1 2
2 -3 1 -11 -2R1 + R2 → R2
-1 2 -1 8 R1 + R3 → R3
1 1 1 2
0 -5 -1 -15 R2 ⇔ R3
0 3 0 10
1 1 1 2
0 3 0 10 -R3
0 -5 -1 -15
1 1 1 2
0 3 0 10 1/3 R2
0 5 1 15
1 1 1 2 -R2 + R1
0 1 0 10/3 -5R2 + R3
0 5 1 15
1 0 1 -4/3
0 1 0 10/3 -R3 + R1
0 0 1 -5/3
1 0 0 1/3
0 1 0 10/3
0 0 1 -5/3
Therefore, x = 1/3, y = 10/3, z = -5/3
4/5x + 4/3 = 2x....there are 2 ways to do this...one with fractions, one without.
with :
4/5x + 4/3 = 2x
4/3 = 2x - 4/5x
4/3 = 10/5x - 4/5x
4/3 = 6/5x
4/3 * 5/6 = x
20/18 = x
10/9 = x
without :
4/5x + 4/3 = 2x....multiply by common denominator of 15
12x + 20 = 30x
20 = 30x - 12x
20 = 18x
20/18 = x
10/9 = x
Hope this helps..................
Answer:
Adult tickets =125
Child tickets = 128
Step-by-step explanation:
Let the number of adult and children tickets sold be x and y respectively
So that
x+y= 253--------1
Since total sales/receipt is $2,771
And given that tickets for a dance recital cost $15 for adults and $7 for children hence
15x+7y= 2771-------2
Solving equation 1 and 2 simultaneously we have
x+y= 253---------------1
15x+7y= 2771----------2
Let us multiply equation 1 by 15 to get equation 3 to eliminate x and subtract equation 2 from 3
15x+15y=3795---------3
-{15x+7y= 2771----------2
0+8y=1024
8y= 1024
y= 1024/8
y= 128 tickets
So solve for x let us put y= 128 in equation 1
x+ 128=253
x=253-128
x= 125 tickets
The complete sentence should be:
<span><em>Composite</em> numbers can be written as a product of <em>prime</em> factors. This is called the prime factorization of a number.
A prime number is a number that can't be divided by any other number other than 1 or itself. Otherwise, that is a composite number. For example, 50 is a composite number. Through prime factorization,
50
/ \
10 5
/ \
5 2
The prime factors of composite number 50 are 5, 5 and 2.</span>
