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finlep [7]
2 years ago
8

Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph

slower than Cynthia's. At the end of one hour, they are 70 miles apart. Find Cynthia's average speed. (Round your answer to the nearest tenth.)
Mathematics
1 answer:
RSB [31]2 years ago
6 0

Answer:

  54.2 mph

Step-by-step explanation:

Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...

  70² = c² +(c -10)²

  4900 = 2c² -20c +100 . . . . eliminate parentheses

  c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form

  (c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form

  c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical

  c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution

Cynthia's average speed was 54.2 miles per hour.

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2 years ago
2 1/3 + 3/7 divided by 2 1/3 x 1 3/7​
oee [108]

Answer: \frac{29}{35}

Step-by-step explanation:

1. Make sure all your denominators are the same, you can do this by multiplying them all by 3 or 7, 2 and 1/3 would become 2 7/21, 3/7 would become 9/21, 2 and 1/3, would become 2 and 7/21, and so on and so forth, leaving us with

2\frac{7}{21}+\frac{9}{21} / 2\frac{7}{21} * 1\frac{9}{21}

2. Now, I would go and solve each side of the equation because we divide them, we can add 2\frac{7}{21} and \frac{9}{21}  together to get  2\frac{16}{21}, because 7 + 9 = 16

2\frac{16}{21} / 2\frac{7}{21} * 1\frac{9}{21}

3. We can do the same thing to the other side, by multiplying the two of them. I'm going to convert both of them to just fractions, 2\frac{7}{21} becomes \frac{49}{21} and 1\frac{9}{21} becomes \frac{30}{21}

\frac{49}{21} *  \frac{30}{21}

Now we can reduce them, and for our first fraction divide the top and bottom by 7, giving us  \frac{7}{3} and the second one by 3, which gives us  \frac{10}{7}

\frac{7}{3} * \frac{10}{7} now we cross divide, where we replace the 7's with ones because they're right across from each other to get  \frac{1}{3} and  \frac{10}{1}, or just 10.

\frac{1}{3} * 10 =  \frac{10}{3}

4. So now we can do a similar thing with the first half of our equation and convert it into a fraction and not a mixed number.

\frac{58}{21} / \frac{10}{3}

Now we multiply divide them, and the easiest way I learned how to do this was by keep the first fraction in its place, and flipping the denominator and numerator of the second, and multiplying them.

so   \frac{58}{21} * \frac{3}{10} which if we multiply both sides, you get \frac{174}{210}

I'll save you some times and simplify it for you, the greatest common factor is 6 so we divide the top and bottom by 6 to get

\frac{29}{35}

4 0
2 years ago
Two similar cylinders have heights of 3 cm and 6 cm respectively. If the volume of the smaller cylinder is 30 cm3, find the volu
Otrada [13]

Answer:

the ans is

Step-by-step explanation:

V=πr2h=π·32·6≈169.646

8 0
2 years ago
Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per
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Answer:

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Step-by-step explanation:

7 0
2 years ago
Plzz help I will mark brainliesttttt
ira [324]

Answer:

HOPE IT HELPED U .....

Step-by-step explanation:

a). f(5)= 2x +6

= 2 *5+6

= 10+6

=16

(b). g (9)= -12x+4

= -12*9+4

= -108 +4

=-104

(c). f(5)+f(9)= 16+(-104)

=-88

4 0
2 years ago
Read 2 more answers
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