Answer:
Step-by-step explanation:
consider 6x^2-8x +k
disc .=(-8)^2-4*6*k=64-24k
it has no solution if 64-2k<0
or 64<2k
or 2k>64
k>32
it has two zeros if 64-2k≥0
or 64≥ 2k
or 2k≤64
or k≤ 32
it has one zero if Disc. =0
64-2k=0
2k=64
k=32
Answer:
SSS~
RQP
Step-by-step explanation:
36/15 = 2.4
48/20 = 2.4
72/30 = 2.4
Triangles are similar by SSS~.
triangle JKL is similar to triangle RQP
Hi there
So, if the track is 1/8 of a mile, let's call every lap a "one-eighth mile" run. We know John ran 24 laps, or that he ran 24 "one-eighth miles," just consecutive, one right after another. Let's stop worrying about rates or tricks or math for a second, and just ask: how many real miles is 24 "one-eighth" miles? We know it's less than 24---a lot less, since you have to go around 8 times just to get to 1 mile. Well wait, if we go around 8 times, we get 1 mile. That means if we go around 28, or 16 times, we get 2 miles; And let's just think to the next full mile---if we go 38, or 24 times, we get 3 miles. He did go around 24 times, so he must have run 3 miles on a 1/8 track.
Division and multiplication are inverses of each other. So we solved this by looking for an intuition for how many full miles corresponded to how many laps, with a bunch of steps of multiplication. But you can cut right to the chase and solve it faster with division---24 laps * 1 mile per 8 laps, means:
total distance = 24 Lap (1 mi / 8 Lap) total distance = 24/8 total distance = 3
So, first you must find the remaining angle measure. To do this add 25 and 90 then subtract from 180. The remaining angle measure is 65 degrees.
Next, use tangent, cosine, or sine to find the remaining side lengths.
I used sine of 25 which is opposite of hypo. which is sine 25 = y/43.
Multiply both side by 43 and you get y=18.17
Do the same to find x, but use the sine of 65, and you get sine 65 = x/43.
Multiply both sides by 43 and you get x=38.97
Hope this helped!
Answer:
∠TAR = 35°
Step-by-step explanation:
∠TAR = ∠CAR - ∠CAT = (9x + 7) - 5x = 4x + 7
AT bisect ∠CAR ∠TAR = ∠CAT
4x + 7 = 5x
x = 7
∠TAR = 4 x 7 + 7 = 35
