since ΔQRS similar to ΔQRP, then
SR/QR = QR/PR
x/12 = 12/(3.5+x)
x(3.5+x) = 12²
x² + 3.5x = 144
x² + 3.5x - 144 = 0
approximately 10.38
Step-by-step explanation:
first a little help, how they got the equations :
in total they need 15 liters.
so, whatever x and y are, but together they must be 15 L.
x + y = 15
then, we are mixing x liters of 20% alcohol with y liters of 100% alcohol, that have to result in a 40% solution of (x+y) liters :
0.2x + y = 0.4(x+y)
we know from the first equation that x+y = 15, so the second equation is actually
0.2x + y = 0.4 × 15 = 6
so, we have
x + y = 15
0.2x + y = 6
do you notice something ? there is a "+ y" in both equations.
so we can actually subtract the second equation from the first, eliminate y and solve for the remaining x. and then use one of the original equating to get also y :
x + y = 15
- 0.2x + y = 6
---------------------
0.8x 0 = 9
0.8x = 9
x = 9/0.8 = 11.25 liters
x + y = 15
11.25 + y = 15
y = 15 - 11.25 = 3.75 liters
Her cousin is 27 and Taylor is 18 years old
Answer:
12 beats per minute after 30minutes
Step-by-step explanation:
Since we are told by how much his heartrate increased in 20 minutes, we can simply calculate how much it increased in 10 minutes and add that amount to the current heart rate to know how much his heartrate increased after 30 minutes of working out. Since 10minutes would be half of the 20minutes we simply divide the beats per minute by 2.
8 / 2 = 4 beats per minute after 10 minutes
Now we simply add this to the beats per minute at the 20minute mark to calculate the beats per minute at 30minutes
8 + 4 = 12 beats per minute after 30minutes
If the distance from R to S is only half then the other half is S to T. The distance between R and S is (5,2). that should give you the answer
