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3 years ago

Paul jogged for 2/10 of an hour. Ones jogged for 5/8 of an hour. Who jogged for a longer period of time? How much longer?

Mathematics

1 answer:

AleksandrR [38]3 years ago

6 0

Ones jogged for a longer period of time.
by 17/40

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What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth

EleoNora [17]

Check the picture below.

so... you can pretty much see how long RS and QT are, you can just count the units off the grid.

now, let's find QR's length

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&Q&(~ 8 &,& 8~) 
% (c,d)
&R&(~ 14 &,& 16~)
\end{array}~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
QR=\sqrt{(14-8)^2+(16-8)^2}\implies QR=\sqrt{6^2+8^2}
\\\\\\
QR=\sqrt{36+64}\implies QR=\sqrt{100}\implies QR=10$

and let's also find the length for ST

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ 20 &,& 16~) 
% (c,d)
&T&(~ 22 &,& 8~)
\end{array}~ 
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
ST=\sqrt{(22-20)^2+(8-16)^2}\implies ST=\sqrt{2^2+(-8)^2}
\\\\\\
ST=\sqrt{4+64}\implies ST=\sqrt{68}\implies ST=\sqrt{4\cdot 17}
\\\\\\
ST=\sqrt{2^2\cdot 17}\implies ST=2\sqrt{17}$

so, add the lengths of all sides, and that's the perimeter of the trapezoid.

8 0

3 years ago

Read 2 more answers

A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still w

prohojiy [21]

Step-by-step explanation:

Given that,

A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,

We know that,

Speed = distance/time

The rate while moving downstream $=\dfrac{60}{3}=20\ mph$

The rate while moving upstream $=\dfrac{60}{5}=12\ mph$

The rate of the boat in still water is the average of these:

$v_s=\dfrac{20+12}{2}=16\ mph$

The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph

Hence, this is the required solution.

7 0

3 years ago

Event tickets cost $20 each. A student ordered some tickets online. There was a service charge of $2.50 per ticket. The total co

antiseptic1488 [7]

(20+2.5)x = cost

when x equals number of tickets

(20+2.5)24 = 540

8 0

3 years ago

1/2(6а + в) <br> Please answer

Tom [10]

Answer:

12a + .5B

B= -6a

a=.042B

Step-by-step explanation:

1/2(6a+B)= 12a+.5B

1/2(6a+B)=0

-12a=.5B

-6a=B

12a=-.5B

a=.042B

7 0

3 years ago

Kellan’s lemonade recipe uses 4 scoops of lemonade powder for every 2.5 cups of water. Kellan uses 10 scoops of lemonade powder

Rina8888 [55]

Answer:

6.25 cups of water

Step-by-step explanation:

So I first write out the rates: 4:2.5 and also 10:?

So let's find out how the scoops changed, as in how did you get 4 to become 10 so you can do the same thing to 2.5 and get ?.

To go from 4 to 10 you MULTIPLY/DIVIDE. DON'T ADD OR SUBTRACT. 10 divided by 4 (to see what you multiplied by) is 2.5.

So we multiplied 4 by 2.5 to get 10. So if we multiply 2.5 by 2.5 we get 6.25.

So 4:2.5 = 10:6.25

?=6.25

Hope this helps!

3 0

3 years ago