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AveGali [126]
3 years ago
5

Lois rode her bike to visit a friend. she traveled at 10 mi/h. Her friend drove her home in a car traveling at 25 mi/h. Lois too

k 1.5 hours longer to go to her friend's than to return home. How many hours did it take Lois to ride to her friend's house?
Mathematics
1 answer:
igor_vitrenko [27]3 years ago
5 0

Speed of Lois' bike = 10 miles/h

Speed of Lois' friend's car = 25 miles/h

Time taken by Lois to reach via car = t hours

Time taken by Lois to reach via bike = 1.5 + t

We know that the distance traveled in both the cases is the same

Hence, distance traveled by car = distance traveled by bike

⇒ Speed of car × time taken by car = Speed of bike × time taken by bike

⇒ 25 × t = 10 × (t+1.5)

⇒ 25t = 10t + 15

⇒ 15t = 15

⇒ t = 1

Hence, Lois took t + 1.5, i.e. 2.5 hours to reach his friend's house.

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Which statement is true
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2 years ago
What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 ti
Marat540 [252]

Answer:

x = \frac{5 + \sqrt{53}}{2}  or  x = \frac{5 - \sqrt{53}}{2}

Step-by-step explanation:

Given

x^2 - 5x - 7 = 0

Required

Solve for x using:

x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}

First, we need to identify a, b and c

The general form of a quadratic equation is:

ax^2 + bx + c = 0

So, by comparison with x^2 - 5x - 7 = 0

a = 1     b = -5      c = -7

Substitute these values of a, b and c in

x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}

x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}

x = \frac{5 \± \sqrt{25 +28}}{2}

x = \frac{5 \± \sqrt{53}}{2}

Split the expression to two

x = \frac{5 + \sqrt{53}}{2}  or  x = \frac{5 - \sqrt{53}}{2}

To solve further in decimal form, we have

x = \frac{5 + 7.28}{2}  or  x = \frac{5 - 7.28}{2}

x = \frac{12.28}{2}  or  x = \frac{-2.28}{2}

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3 years ago
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Romashka-Z-Leto [24]
Find the LCD and then combine


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Read 2 more answers
Let x and y be any numbers at all with x ≤ y. Show that the number of integers between x and y is [y] - [x] +1.That is show that
ddd [48]

Answer:

the explanation is given below.

Step-by-step explanation:

  • Here what is applied is assumption of range of values of number from say 1 - 100
  • In total, i stopped at 100 on the dot.

from this, the lowest number is 1 and the highest number is 100

  • hence the range of the numbers = Difference between Highest and Lowest
  • range = 100 - 1 = 99, the 99 gotten as the range is indicative that a number has been missing.

  • In order to make up the 100, an integer is added to the difference = 99, i.e 99 is added to 1 to make up the 100.

  • Furthermore, if 0 is exclusively out when numbers are counted up 100 with 0 inclusive, in such case, the first and last number are excluded from the counting. as such the integers will be {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20.........., 99} since both 0 and 100 are not included.

  • Here, if we try to get the range = highest - lowest = 99 - 1 = 98, it implies that to make up the 99, an integer is added to the result of the difference = 98+1 = 99

  • As such, the number of integers between two numbers is the difference between the highest and the lowest number plus 1 i.e highest - lowest + 1 = y - x +1 = (the floor of y) - ( the ceiling of x) + 1
5 0
3 years ago
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