During a tunnel construction project, engineers used explosives to excavate partway into a mountain. because of time constraints and environmental concerns, they later used a tunnel boring machine (tbm) to excavate the rest of the tunnel. the table shows the length of the completed tunnel, y, after different numbers of days, x, since the tbm started working. number of days length of tunnel (feet) 0 225 5 350 20 725 30 975 55 1,600 the length of the completed tunnel can be calculated using what equation . if the project will be completed 86 days after the tbm was introduced, the length of the completed tunnel will be feet.

The given values lie on a line with slope

... m = (975 -725)/(30 -20) = 250/10 = 25

The initial value shown gives the y-intercept, so the length can be calculated using the equation

... y = 25x +225

The length after 86 days will be

... y = 25·86 +225 = 2375 . . . feet

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value