Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.
i)
"A radio station plays a total of 272 pop, rock, and hip-hop songs during a day"
means that : P+R+H=272
ii)
"The number of pop songs is 3 times the number of rock songs. "
so, P=3R
iii)
"The number of hip-hop songs is 32 more than the number of rock songs."
means: H=32+R
iv)
since both P and H can be written in terms of R, we have:
P+R+H=272
(3R)+R+(32+R)=272
3R+R+32+R=272
5R+32=272
5R=272-32=240
R=240/5=48
vi)
thus: P=3R=3*48=144, H=32+R= 32+48=80
Answer:
48 Rock, 144 Pop and 80 Hip-hop
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
<h3>Right angled triangle</h3>
A right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.
For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.
Find the slopes of AB, BC and AC
Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5
Slope of BC = 0-5/7-1
Slope of BC = -5/6
Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11
Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
Learn more on right angle triangle here: brainly.com/question/22790996
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She has 501 more pennies than nickles.
