Sophia uses 18 beads to make a necklace. Three sixths of the beads are purple. How many beads are purple?
1 answer:
Answer:
9 beads are purple
Step-by-step explanation:
we know that
To find out how many beads are purple, multiply the total beads by the fraction of the beads that are purple
so
therefore
9 beads are purple
Another way to solve the problem is convert the fraction in percentage
we have
so
If the total are 18 beads
50% is 9 beads
therefore
9 beads are purple
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Answer:
The system of linear equations has infinitely many solutions
Step-by-step explanation:
Let's modified the equations and find the answer.
Using the first equation:
we can multiply by 2 in both sides, obtaining:
which can by simplified as:
which is equal to:
Considering the second equation:
Taking into account that from the first equation we know that: , we can express the second equation as:
, which can be simplified as:
Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:
if
This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.
For example, if k=0 then
which give us y=-4, and, because:
if y=-4 then
Now let's try with k=-1, then:
which give us y=-8, and, because:
if y=-8 then
.
Then, the system of linear equations has infinitely many solutions