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rusak2 [61]
3 years ago
5

PLEASE HELP!!! In a large marathon, runners start the race in stages. Sophia started in group E and ran at a rate of 4.8 miles p

er hour. During the race she was passed by Josefina who ran at a rate of 5.3 miles per hour and started in group H, 25 minutes after Sophia started. How far did Sophia run before she was passed by Josefina?
Mathematics
1 answer:
Xelga [282]3 years ago
7 0

Answer:

she ran 1.2 miles

Step-by-step explanation:

take 4.8 and divide it by .25

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A bridge constructed over a bayou has a supporting arch in the shape of an inverted parabola. Find the equation of the parabolic
babymother [125]

Answer: f(x) = -0.016x² + 1.6x

Step-by-step explanation:

If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.

So, we have

(0,0) (50,40) (100,0)

A quadratic function is always on the form: f(x) = ax² + bx + c

0 = a0² + b0 + c

40 = a50² + b50 + c

0 = a100² + b100 + c

0 = a0² + b0 + c → c = 0 ∴

40 = a50² + b50

0 = a100² + b100

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2500a + 50b = 40 (*2)

10000a + 100b = 0

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5000a + 100b = 80

10000a + 100b = 0 (-)

__________________________

-5000a = 80

-a=80/5000

a=-0.016

∴

2500a + 50b = 40

2500.(-0.016) + 50b = 40

-40 + 50b = 40

50b = 80

b = 80/50

b = 1.6

This way f(x) = -0.016x² + 1.6x

6 0
3 years ago
Whats the perimeter and area of this shape?
stich3 [128]

Answer:

<u>60+14.35=88.27</u>

Step-by-step explanation:

5x12 for the rectangle on the right, then for the circle, using the formula A=πr², I get 28.27, which you divide by 2 because you only need half of the circle, and you get 88.27. I calculated the radius by subtracting 12-6 and then dividing that in half because the radius is half of the distance to the other end of the circle. Then you get the radius of 3, then plug it into the formula to get π(3)², which is just 3.14(9), and you get 28.27.

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3 years ago
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Maksim231197 [3]

Answer:

C=\frac{5F-160}{9}

Step-by-step explanation:

Let's solve for C.

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Step 1: Flip the equation.

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Step 2: Add -32 to both sides.

\frac{9}{5} C+32+-32=F+-32

\frac{9}{5}C=F-32

Step 3: Divide both sides by \frac{9}{5}.

\frac{\frac{9}{5}C}{\frac {9} {5}}=\frac{F-32}{\frac{9}{5} }

C=\frac{5F-160}{9}

Answer:

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