Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than 1/4 the
2 answers:
Answer: only true statement is ---The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right
Step-by-step explanation:
Let Brain and Damien both scored x while Chris scored y then
According to the first relation
where x and y are less than or equal to 20 .
For y=20 , x=19 possible value
According to the second relation
where x and y are less than or equal to 20 .
For y=20 , x= 23 not possible
so only true statement is ---The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right
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Given :
A bike path is 3 miles long. there are distance markers every path one fourth mile to the end of the path.
To Find :
Which number line correctly models this situation and the total number of distance markers.
Solution :
It is given that their are markers every 1/4 part of mile.
So, their are 4 markers per mile.
Numbers of markers in 3 miles long path is :
Therefore, the total number of distance markers in 3 mile path is 12.
Hence, this is the required solution.
one way would be to factor
I can't factor it so we will have to use Descartes' Rule of Signs which is helpful for finding how many real roots you have
it goes like this:
for a polynomial with real coefients, consider .
after arranging the terms in decending order in terms of degree, count how many times the signs of the coeffients change direction and minus 2 from that number until you get to 1 or 0. that will be the number of even roots the function can have
We have (-, -, +, +). the signs changed 1 times, so it has 1 real positive root
to get the negative roots, we evaluate f(-x) and see how many times the root changes
signs are (-, -, -, +). there was 1 change in sign
so the function has 1 real negative root
a total of 2 real roots
a function of degree can have at most,
roots
our function is degree 6 so it has 6 roots
if 2 are real, then the others must be complex
6-2=4 so there are 4 complex roots
you can also show that there are only 2 real roots by using a graphing utility to see that there are only 2 real roots