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netineya [11]
2 years ago
15

If /61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triang

Mathematics
1 answer:
Ghella [55]2 years ago
8 0

Answer:

A. 5

Step-by-step explanation:

The longest side of the right triangle is the hypotenuse and it is √61 units. The other legs of the triangle is x unit and (x + 1) units.

From Pythagoras theorem for right angle triangle, the square of the hypotenuse is equal to the sum of the square of the other sides of the triangle. This implies that:

(√61)² = (x)² + (x + 1)²

x² + x² + 2x + 1 = 61

2x² + 2x + 1 - 61 = 0

2x² + 2x -60 = 0

Dividing through by 2 gives:

x² + x - 30 = 0

x² + 6x - 5x - 30 = 0

x(x + 6) -5(x + 6) = 0

(x-5)(x+6) = 0

x-5 = 0 or x+6 = 0

x = 5 or x = -6

Since the length of a side cannot be negative, x = 5 units

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Suppose each runner ran at the rate given in the table above for 3.1 miles. How much time will elapse between the first place fi
Scilla [17]
You didn't include the table but I found this table for the same statement, so I will answer you based on the next table:

Runner         distance           time

Arabella        7,299 feet        561 seconds
Bettina          3,425 yards     13 minutes, 12 seconds
Chandra       8,214 feet        0,195 hours
Divya            1,62 miles        732 seconds

To answer the question you must find the rate for each runner and then calculate the time to run 3.1 miles at each rate.

First you need to convert the data to obtain the rate in miles per second.

These are the main conversion identities:

1 mile = 5280 feet

1 mile = 1760 yards

1 hour = 3600 seconds

1 hour = 60 minutes

1 minute = 60 seconds

Arabella:

rate: 7,229 feet / 561 seconds * (1 mile / 5280 feet)  =

= 0.00244 mile/second

Time to run 3.1 miles: V = d / t => t = d / V = 3.1 miles / 0.00244 mile/second = 1270 seconds

Bettina:

13 minutes + 12 seconds = 13*60 seconds +12 seconds = 792 seconds

rate = 3425 yards / 792 seconds * 1 mile / 1760 yards = 0.00246 mile/seconds

Time to run 3.1 miles = 3.1 miles / 0.00246 mile/second = 1260 seconds

Chandra:

rate = 8214 feet / 0.195 hours * 1 mile / 5280 feet * 1hour / 3600 seconds =

= 0.00222 seconds

Time = 3.1 mile / 0.00222 seconds = 0.389 hour = 1396 seconds

Divya:

rate = 1.62 miles / 732 seconds = 0.00221 seconds

Time = 3.1 mile / 0.00221 seconds = 1403 seconds

Now you can find the difference between fhe last and the first 1403 seconds - 1260 seconds = 143 seconds

That is equivalent to 2.38 seconds.
6 0
3 years ago
Consider two histograms that can be constructed from the frequency distribution below; the first will have 12 classes with a cla
beks73 [17]

Answer:

okb-joye-ngv

C O m e t o l e a r n s e x

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3 years ago
SOS I NEED ANSWER RIGHT NOW SOMEONE PLEASE HELP ME :(
laila [671]

Answer:

The functions share a y intercept of -1

Step-by-step explanation:

Both functions cross the y axis and y=-1 and x=0

They both have the same y intercept

3 0
3 years ago
The cost, in dollars, of adding s ingredients is f(s) = 6.75 +0.50s. Which<br> statement is correct?
Ganezh [65]
Is there more to this question or no?
4 0
2 years ago
Tickets to a show cost $5.50 for adults and $4.25 for students and families purchasing two adult tickets and three student ticke
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Answer:

$23.75

Step-by-step explanation:

Add 5.50+5.50

and the add 4.25+4.25+4.25

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2 years ago
Read 2 more answers
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