PLEASE HELP!

Mathematics

1 answer:

inn [45]3 years ago

6 0

2*(-11) if its multiple choice but im not sure

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Joe scored 10 more than half his normal average at the basketball game tonight. If he scored 24 times, what is his usual average

KIM [24]

Answer: His usual average = 28.

Step-by-step explanation:

Let x = usual average at the basketball game tonight.

As per given,

$\dfrac{x}{2}+10=24$

Subtract 10 from both sides , we get

$\dfrac{x}{2}+10-10=24-10\\\\\Rightarrow\ \dfrac{x}{2}=14\\\\\Rightarrow\ x=14\times2=28$

Hence, his usual average = 28.

8 0

3 years ago

Lily swims for 5 hours in stream that has a current of 1 mph. She leaves her dock, swims upstream for 2 miles and then swim back

antiseptic1488 [7]

Answer:

Swimming speed in still water is approximately 1.5 mph

Step-by-step explanation:

Given the speed of the current = 1 mph

distance she swims upstream =2 miles,

the total time = 5 hours.

She swam 2 miles upstream against the current and 2 miles back to the dock with the current. The formula that relates distance, time, and rate is $d = r t\ \ \ \ or \ \ \ t= \frac{d}{r}$

Let x be the speed in still water.

Then her speed with the current is x + 1, and

her speed against the current is x – 1.

Total time is equal to 2 miles with upstream and 2 miles downstream.

$\frac{2}{x+1}+\frac{2}{x-1}=5\\\\\frac{2(x-1)}{(x+1)(x-1)}+\frac{2(x+1)}{(x-1)(x+1)}=5\\\\\frac{2x-2}{(x^2-1)}+\frac{2x+2)}{(x^2-1)}=5\\\\\frac{2x-2+2x+2)}{(x^2-1)}=5\\\\4x=5(x^2-1)\\4x= 5x^2-5\\0= 5x^2-4x-5$

Now Using quadratic formula to solve above equation we get;

$x= \frac{-b \±\sqrt{b^2-4ac}} {2a}\\\\here \ \ a= 5,b=-4,c=-5\\\\x= \frac{-(-4) \±\sqrt{(-4)^2-4\times 5\times-5}} {2\times5}\\\\x=\frac{4 \±\sqrt{16+100}} {10}\\\\x=\frac{4 \±\sqrt{116}} {10}=x=\frac{4 \±2\sqrt{29}} {10}= x=\frac{2 \±\sqrt{29}} {5}\\ x \approx 1.5 \ or \ x = -0.7$