The circle is inscribed in triangle PRT. Which statements about the figure are true? Select two options.​

"The length of the line segment PR is 13 units" and TU=TS

Step-by-step explanation:

"The perimeter of the triangle is 19 units"

False - if you add up the marked measurements (8,6, and 5), you already get 19, so the perimeter is more than 19 units.

TU=TS

Call the centre of the circle C.

TC=TC

UC=SC (radius)

∠TCU=∠SCT (TC bisects ∠UCS)

∴ΔTUC is congruent to ΔTCS

∴TU=TS=6, TRUE

PU=TU

False -  PU=8, TU=6, 8≠6

"The length of the line segment PR is 13 units"

ΔRQC=ΔRSC (QC=SC, RC=RC, ∠QSC=∠CRS)

∴RS=RQ=5

ΔPUC=ΔPQC (UC=QC, PC=PC, ∠UPC=∠CPQ)

∴PU=PQ=8

PR=PQ+QR=8+5=13, TRUE

"The length of the segment TR is 10 units"

False

ΔTSC=ΔTUC (UC=SC,TC=TC,∠UCT=∠SCT)

∴TU=TS=6

TR=TS+SR=6+5=11

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.