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loris [4]
3 years ago
12

Part A: What is the shortest distance between the gymnasium and the library? Round your answer to the nearest tenth of a kilomet

er.
Part B: Gabe walks the shortest distance from his house to the gymnasium, then the shortest distance to the library. What is the total distance Gabe walked?
Mathematics
1 answer:
Oxana [17]3 years ago
4 0

Answer:

4.5 km

10.3 km

Step-by-step explanation:

The shortest distance from gymnasium to library:

Each square box representing 1 unit

1unit = 1 km

A.)

Distance, d ;

Using Pythagoras :

d = sqrt(2² + 4²)

d = sqrt(4 + 16)

d = sqrt(20)

d = 4.47

d = 4.50 (nearest tenth)

Shortest Distance from gymnasium to library

B.)

shortest distance from his house to the gymnasium, then the shortest distance to the library

House to gymnasium (d1) :

d1 = sqrt(3² + 5²)

d1 = sqrt(9 + 25)

d1 = sqrt(34)

d1 = 5.83

Gymnasium to Library (d2) :

d2 = sqrt(2² + 4²)

d2 = sqrt(4 + 16)

d2 = sqrt(20)

d2 = 4.47

Total distance = (d1 + d2) = (5.83 + 4.47) = 10.3km

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Paladinen [302]

Answer <u>(assuming it is allowed to be in point-slope format)</u>:

y-4 = \frac{2}{3}(x-1)

Step-by-step explanation:

1) First, determine the slope. We know it has to be perpendicular to the given equation, y = -\frac{3}{2} x-4. That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since -\frac{3}{2} is in place of the m in the equation, that must be the slope of the given line.

Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be \frac{2}{3}.  

2) Now, use the point-slope formula, y-y_1 = m (x-x_1) to write the new equation with the given information. Substitute m, x_1, and y_1 for real values.

The m represents the slope, so substitute \frac{2}{3} in its place. The x_1 and y_1 represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for x_1 and 4 for y_1. This gives the following equation and answer:

y-4 = \frac{2}{3}(x-1)

3 0
3 years ago
What is the value of x?
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Answer:

180-45= 135

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7 0
3 years ago
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If f(x) =7 +4x and g(x) =1/2 what is the value of (f/g)
saw5 [17]

Answer:

10.8

Step-by-step explanation:

To find (f/g)(5), find f(5) and (g5) then divide the values.

f(5) = 7 + 4(5) = 27

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27/2.5 = 10.8

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Line b passes through points (5, 5) and (10, 8). Line c passes through points (4, 8) and (1, 13). Are line b and line c parallel
lora16 [44]

Answer:

Step-by-step explanation:

In going from (5, 5) to (10, 8), x (the run) increases by 5 and y (the rise) increases by 3.  Thus, the slope of the line connecting the first two points is m = 3/5.

In going from (1, 13) to (4, 8), x (the run) increases by 3 and y (the rise) decreases by 5.  Thus, the slope of the line connecting the first two points is m = -5/3

Because these results are negative reciprocals of one another, the two lines are PERPENDICULAR to one another.

3 0
3 years ago
What is the slope of the line that passes through the points (-4, -1) and (4, 5)?
andreyandreev [35.5K]

Answer:

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Step-by-step explanation:

Since we have two points, we can use the slope formula

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   = ( 5+1)/(4+4)

   = 6/8

   = 3/4

7 0
2 years ago
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