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max2010maxim [7]
3 years ago
5

Your house is located at point T. Your grandma's house is located at point V. U is the midpoint of segment TV. How far do you ne

ed to travel to drive home from your grandma's house?

Mathematics
1 answer:
Vladimir [108]3 years ago
5 0

Answer:

70

Step-by-step explanation:

From the question given above, the following data were obtained:

TU = 8x + 11

UV = 12x – 1

Next, we shall determine the value of x.

From the question:

U is the midpoint. This means that TU and UV are equal i.e

TU = UV

With the above idea in mind, we shall determine the value of x as follow:

TU = UV

TU = 8x + 11

UV = 12x – 1

8x + 11 = 12x – 1

Collect like terms

11 + 1 = 12x – 8x

12 = 4x

Divide both side by the coefficient of x i.e 4

x = 12/4

x = 3

Next, we shall determine the length of TU and UV. This can be obtained as follow:

TU = 8x + 11

x = 3

TU = 8(3) + 11

TU = 24 + 11

TU = 35

UV = 12x – 1

x = 3

UV = 12(3) – 1

UV = 36 – 1

UV = 35

Finally we shall determine the length of TV. This can be obtained as follow:

TV = TU + UV

TU = 35

UV = 35

TV = 35 + 35

TV = 70

Therefore, the distance between my house and grandma's house is 70.

NOTE: Assume the distance is measured in kilometer (km)

This means that I will travel 70 km from grandma's house to my house.

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The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3
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==============================================

Work Shown:

a = first term

a*(2/3) = (2/3)a= second term

(2/3)a*(2/3) = (4/9)a = third term

note how I multiplied each previous term by the common ratio (2/3) to get the next term

Add up the three terms

a + (2/3)a + (4/9)a = (9/9)a + (6/9)a + (4/9)a = (19/9)a

Set this equal to 171, which is what we want the first three terms to sum to, then solve for 'a'

(19/9)a = 171

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------------------------------------

Checking the answer:

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(4/9)*a = (4/9)*81 = 36 = third term

adding up the three terms gets us

81+54+36 = 171

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