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Answer:
There are <u>1240</u> students who attended Washington Middle School.
Step-by-step explanation:
Given:
Students who attend Washington Middle School are either in seventh or eighth grade.
At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.
Seventh graders represented 60% of the students on the honor roll.
If 124 students on the honor roll were in eighth grade.
Now, to find the students attend Washington Middle School.
Let the total number of students be
So, the students at Washington Middle School were on the honor roll:
<u><em>25% of </em></u><u><em /></u>
As, given seventh graders represented 60% of the students.
So, the students on the honor roll represented as seventh graders:
As, 124 students on the honor roll were in eighth graders.
Thus,
According to question:
<em>Multiplying both sides by 4 we get:</em>
<em>Dividing both sides by 0.4 we get:</em>
Therefore, there are 1240 students who attended Washington Middle School.
Answer:
FD≈25.94.. rounded = 26
Step-by-step explanation:
FD²=12²+(4x+11)²
FD²=144+16x²+88x+121
FD²=265+16x²+88x
also
FD²=12²+(13x-16)²
FD²=144+169x²-416x+256
FD²=400+169x²-416x
thus
265+16x²+88x = 400+169x²-416x
16x²-169x²+88x+416x+265-400 = 0
-153x²+504x-135 = 0
we will solve this quadratic equation by suing the quadratic formula to find x
x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)
x=(-504±)/2(-153)
x=(-504±)/-306
x=(-504±)/-306
x=(-504±414)/-306
x=(-504+414)/-306 and x=(-504-414)/-306
x=-90/-306 and x=-918/-306
x= 5/17 , 3
substituting x by the roots we found
check for 5/17:
4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..
13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..
check for 3:
4x+11 = 4×3+11 = 12+11 = 23
13x-16 = 13×3-16 = 23
thus 3 is the right root
therfore
ED=23 and CD=23
FD²=FE²+ED² or FD²=FC²+CD²
FD²=12²+23²
FD²=144+529
FD²=673
FD=√673
FD≈25.94.. rounded = 26