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Mamont248 [21]
3 years ago
10

Write in point-slope form an equation of the line that passes through the point

Mathematics
1 answer:
AnnyKZ [126]3 years ago
7 0

A horizontal line through y=−53. Explanation: Write the equation in the form y=mx+c because then we can read off the slope and the y-intercept ...

Answer:

Step-by-step explanation:

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What length is the shorter leg of a right triangle that has hypotenuse 50 in long and its perimeter is 112 inches?
Brut [27]
The length of the shorter leg is 14 inches.

We will set up two equations for this; first, for the perimeter.  We will call the legs a and b:

a + b + 50 = 112

Subtract 50 from both sides:
a + b + 50 - 50 = 112 - 50
a + b = 62

We will isolate a, so we can use substitution.  Subtract b from both sides:
a + b - b = 62 - b
a = 62 - b

Now we will set up our Pythagorean theorem equation:
a² + b² = 50²
a² + b² = 2500

We will substitute our value for a from the first equation into this one:
(62-b)² + b² = 2500
(62 - b)(62 - b) + b² = 2500

Multiplying the binomials, we have:
62*62 - b*62 - b*62 -b(-b) + b² = 2500
3844 - 62b - 62b + b² + b² = 2500

Combining like terms:
3844 - 124b + 2b² = 2500

To set it equal to 0 and solve, we subtract 2500 from both sides:
3844 - 124b + 2b² - 2500 = 2500 - 2500
1344 - 124b + 2b² = 0

In standard form, we have
2b² - 124b + 1344 = 0

Using the quadratic formula, 
\frac{--124\pm \sqrt{(-124)^2-4(2)(1344)}}{2(2)}
\\
\\=\frac{124\pm \sqrt{15376-10752}}{4}
\\
\\=\frac{124\pm \sqrt{4624}}{4}=\frac{124\pm 68}{4}=\frac{124+68}{4}\text{ or }\frac{124-68}{4}
\\
\\=\frac{192}{4}\text{ or }\frac{56}{4}=48\text{ or }14

The shorter leg is 14 and the longer one is 48.
8 0
3 years ago
Read 2 more answers
2) Working alone, Rob can dig a 10 ft by 10 ft hole in ten hours. Shayna can dig the same hole in seven hours. Find how long it
Free_Kalibri [48]

rob can dig 1/10ft in one hour

Shayna can dig 1/7ft in one our

together they can dig

1/10+1/7

(7+10)/70 in one hour

17/70

in for hours they can dig

17/70×4

68/70

the left work is 2/70

in 60 minutes they can dig 17/70

1/70 work can be done in 60 minutes/17

2/70 work can be done in 60/17×2 minutes

7.088 minutes

for the entire work they take 4hours and 7 minutes

8 0
2 years ago
A pie tin has an area of 81 pi square inches. Which choice below is closest to its
Brrunno [24]

Answer:

can i have the choices

Step-by-step explanation:

7 0
2 years ago
If a football team plays A games. and loses B games. what was their winning percentage
Leona [35]
The answer would be  (B/A)*100%
3 0
3 years ago
A vendor sells pizza and soft drinks. A customer buys 6 slices of pizza and 5 drinks for $31.60. Another customer buys 5 slices
Irina-Kira [14]
let the price of a slice of pizza be 'p' and that of soft drink be 's'

   6 p + 5 s = 31.60............equation (i)
   5 p + 4 s = 26.02............equation (ii)

6 p + 5 s = 31.60............×4
5 p + 4 s = 26.02............×5

24 p + 20 s = 126.4
25 p + 20 s = 130.1

p = 3.7

   Answer = 3.7 Dollars
6 0
3 years ago
Read 2 more answers
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