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
The correct answer is A. Jimmy is running late, so he starts to run to school but needs to take breaks.
Explanation:
The graph shows the distance in axis y and the time in axis x. Additionally, the graph presents different sections from A to E. In this, the sections A, C, and E show an increase in the distance from home, this implies there was movement. Moreover, the speed (distance traveled in time) is higher in sections C and E than in A because the distance increases in a shorter time. Also, in sections D and B there is no movement as time continues but the distance is the same. In this context, the description that best matches the graph is "Jimmy is running late, so he starts to run to school but needs to take breaks" because this is the only option that includes the breaks or lack of movement in sections B and D. Also, the changes in speed are likely to occur in this scenario.
<u>Answer-</u>
<em>The values of x and y are </em><em>13</em><em> and </em><em>24</em><em>, respectively.</em>
<u>Solution-</u>
From the attachment, l and m are parallel lines and
---------------------1
As, when a traversal line intersects two parallel lines, same-side interior angles are supplementary, or they add up to 180 degrees.
---------------------2
As, an exterior angle is equal to the sum of the opposite interior angles.
Adding equation 1 and 2, we get,
Putting the value of x in equation 1, we get
Answer:
<em>Exact Form:
</em>
<em>Decimal Form:
</em>
1.875
<em>Mixed Number Form:
</em>
