Clay can run one lap around the track in 1/4 of an hour. How many hours will it take him to run 5 1/3 laps around the track?

In the diagram, P1P2 and Q1Q2 are the perpendicular bisectors of line AB and BC , respectively. A1A2 and B1B2 are the angle bise

Aliun [14]

I hope I can show the image, but I hope this may help you, the answer is:

The center of the inscribed circle of ΔABC is point S , and the center of the circumscribed circle of ΔABC is point P.

4 0

2 years ago

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12. A cyclist travels 40 km at a speed of x km/h. Find the time

GREYUIT [131]

Answer:

Step-by-step explanation:

distance = rate times time, so

distance

time = --------------

rate

Here the distance is 40 km and the rate is x. Then

40 km

time = -------------- = (40/x) hr

x km/hr

If the speed is reduced by 2 km/hr, we get:

40 km 40 km 40

time = ------------------------------- or time = ----------------------- = --------- hr

(x km/hr - 2 km/hr) (x - 2) (km/hr) x - 2

The difference between the times is:

40 40

-------- - --------- = 1 hr Solve this for the original speed, x

x - 2 x

40x - 40x + 80 80

----------------------- = 1 hr or ------------ = 1 or 80 = x^2 - 2x

x(x - 2) x(x - 2)

Rewriting this in standard quadratic form: x^2 - 2x - 80 = 0

Here a = 1, b = -2 and c = -80, and so the discriminant b^2 - 4ac is:

(-2)^2 - 4(1)(-80) = 324

The solutions are:

-(-2) ± √324 2 ± 18

x = -------------------- = ------------ = 1 ± 9, or 10 (discard the other root)

2 2

The original speed was 10 km/hr

7 0

1 year ago

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What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, –0.04, –0.14,

TiliK225 [7]

0.10
is the answer for that

5 1

2 years ago

a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet

tangare [24]

Answer:

50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

Step-by-step explanation:

Suppose, the number of Chef's salad is $x$ and the number of Caesar salad is $y$

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are: $40\leq x\leq 60$ and $35\leq y\leq 50$

The total number sold has never exceed 100 salads. So, another constraint will be: $x+y\leq 100$

According to the graph of the constraints, the vertices of the common shaded region are: $(40,35), (60,35), (60,40), (50,50)$ and $(40,50)$ (Refer to the attached image for the graph)

The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be: $P=0.75x+1.20y$

For (40, 35) , $P=0.75(40)+1.20(35)=72$

For (60, 35) , $P=0.75(60)+1.20(35)=87$

For (60, 40) , $P=0.75(60)+1.20(40)=93$

For (50, 50) , $P=0.75(50)+1.20(50)=97.5$ (Maximum)

For (40, 50) , $P=0.75(40)+1.20(50)=90$

Profit will be maximum when $x=50$ and $y=50$

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

6 0

2 years ago

Gino has a stick of pepperoni that is 26 1/2 inches long. He wants to cut 1/2 inch pieces to put on his large pizza. How many pi

ikadub [295]

Answer:57 pieces

Step-by-step explanation:

If the pepperoni is 26 1/2 inches long and he is cutting then 1/2 in slices. You are going to get 2 slices per inch. So multiply 26 x 2 which is 56 then add 1 for the half inch which gives you 57 slices

4 0

2 years ago