QP=24 cm
RS=11.25 cm
QS=18.75 cm
<u>Explanation</u>:
Given that TQ bisects <RTP
(1)
consider ΔRQS and ΔRPT
QS||PT,RP and RT are transversals
(alternate angles)(2)
comparing (1) and (2)
and triangle SQT is isocelus
Therefore SQ=ST(sides opposite to equal angles in an isocelus triangle)
Therefore <RQS=<RPT(corresponding angles)
<RSQ=<RTP(corresponding angles)
therefore by AA criterion for similarity
ΔRQS~ΔRPT
According to the property of similar triangles


An important rule of logs is a*log b = log b^a.
Thus, 2 (log to the base 5 of )(5x^3) = (log to the base 5 of ) (5x^3)^2, or
(log to the base 5 of ) (25x^6).
Next, (1/3) (log to the base 5 of ) (x^2+6) = (log to the base 5 of ) (x^2+6)^(1/3).
Here, the addition in the middle of the given expression indicates multiplication:
2Log5(5x^3)+1/3log5(x^2+6) = (log to the base 5 of ) { (5x^3)^2 * (x^2+6)^(1/3) }.
Here we've expressed the given log quantity as a single log.
Hey there! :)
Answer:
x = -6.
Step-by-step explanation:
Given:
![\sqrt[3]{5x-4} = \sqrt[3]{7x + 8}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B5x-4%7D%20%3D%20%5Csqrt%5B3%5D%7B7x%20%2B%208%7D)
Cube both sides:
5x - 4 = 7x + 8
Subtract 5x from both sides:
-4 = 2x + 8
Subtract 8 from both sides:
-12 = 2x
x = -6.
Answer:
The answer is 6 1/5 feet in width.
Step-by-step explanation:
Since the formula for area is <em>wl</em> or <em>width </em>x <em>length</em>, we can utilize our reversive property to find our width by dividing the Area we are given by our length, giving us the missing width in return. Dividing 46.5 square feet by 7.5 feet gives us 6.2 feet, or 6 1/5 feet.
Hope this helps!