Step-by-step explanation:
![6\sqrt3\cdot\dfrac{\sqrt3}{3}=\dfrac{(6\sqrt3)(\sqrt3)}{3}\\\\\text{use the associative property}\ (a\times b)\times c=a\times(b\times c)\\\\=\dfrac{(6)(\sqrt3\cdot\sqrt3)}{3}\\\\\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\\\\=\dfrac{(6)(\not3)}{\not3}\qquad\text{cancel 3}\\\\=6](https://tex.z-dn.net/?f=6%5Csqrt3%5Ccdot%5Cdfrac%7B%5Csqrt3%7D%7B3%7D%3D%5Cdfrac%7B%286%5Csqrt3%29%28%5Csqrt3%29%7D%7B3%7D%5C%5C%5C%5C%5Ctext%7Buse%20the%20associative%20property%7D%5C%20%28a%5Ctimes%20b%29%5Ctimes%20c%3Da%5Ctimes%28b%5Ctimes%20c%29%5C%5C%5C%5C%3D%5Cdfrac%7B%286%29%28%5Csqrt3%5Ccdot%5Csqrt3%29%7D%7B3%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%5Csqrt%7Ba%7D%5Ccdot%5Csqrt%7Ba%7D%3Da%5C%5C%5C%5C%3D%5Cdfrac%7B%286%29%28%5Cnot3%29%7D%7B%5Cnot3%7D%5Cqquad%5Ctext%7Bcancel%203%7D%5C%5C%5C%5C%3D6)
Answer:
See below.
Step-by-step explanation:
Part A:
triangle QPR and triangle PSR are similar
Part B:
Triangle QPR is a right triangle with right angle QPR.
Triangle SPR is a right triangle with right angle PSR.
Angle QPR of triangle QPR corresponds to and is congruent to angle PSR of triangle PSR.
Angle R of triangle QSR corresponds to and is congruent to angle R of triangle PSR.
The similar triangles by AA Similarity are
triangle QPR and triangle PSR
Part C:
QR/PR = PR/SR
16/PR = PR/4
PR² = 16 * 4
PR² = 64
PR = 8
Part 1:
A.53 =53
B.3^5/3^-6 =177147
C.(1/4)^3 • (1/4)^2 = 1
/1024
D.(-7)^5/(-7)^7 = 1/49
I tried my best for part 2 but i'm pretty sure it's not right. I think 1/1024 and 1/49 has a value between 0 and 1
Answer:
equation:x*1/5=9/20
answer=9/4
Step-by-step explanation:
9/20÷1/5=9/20×5/1 in word form you multiply 9/20 by its reciprocal.
first you want to simplify and change 9/20 to 9/4 and change 5/1 to 1/1 and then multiply to get 9/4