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Firdavs [7]
2 years ago
14

The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer l

eg. Find the side lengths of the triangle.
Mathematics
1 answer:
Licemer1 [7]2 years ago
6 0

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

<u>Pythagorean Theorem</u>

c^2 = a^2 + b^2

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x

Now let's factorize to get solutions for x.

0 = x(x-20)

First solution:

x = 0

Second solution:

x - 20 = 0\\x = 20

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

You might be interested in
4 times a number is 16​
andrey2020 [161]

Answer:

4 times 4 equals 16

Step-by-step explanation:

4 times 1= 4

4 times 2= 8

4 times 3= 12

4 times 4= 16

you add 4 after each result.

4 0
3 years ago
Which number sentence is true? O A) 2.3 x 102 &gt; 2000 OB) 3.45 &gt; 1-4.35| OC) 345 &gt; 5:33 825 OD 13​
OLEGan [10]

Answer:

D) -2.14< root10 <|-2.8|

Step-by-step explanation:

the value for -2.14 is as plain as you can see, the negative version of 2.14.

The square root of 10 is 3.16227766.

The lines next to -2.8 is asking for the absolute value of -2.8, or the distance between that number and zero. The distance between -2.8 and 0 is positive 2.8, because distance can't be negative.

The 3 numbers taken from the explanations are -2.14, 3.16, and 2.8. Ranking them from least to greatest would give you -2.14, 2.8, 3.16, or -2.14< root10 <|-2.8|

7 0
3 years ago
A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average
marysya [2.9K]

Answer:

a) player’s expected payoff is $ 240

b) probability the player loses $1000 or more is 0.1788

c)  probability the player wins is 0.3557

d) probability of going broke is 0.0594

Step-by-step explanation:

Given:

Since there are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 * 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

a)

Solution:

Expected payoff is basically the expected mean

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss =  μ

                        = ∑ x P(x)

                        = 50 * P(win) - 50 * P(lose)

                        = 50 * P(win) + (-50) * (1 - P(win))

                         = 50 * 0.49 - 50 * (1 - 0.49)

                        = 24.5 - 50 ( 0.51 )

                        = 24.5 - 25.5

                        = -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 * 1 = $ 240

b)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 110.5 - 117.6 / √117.6(1-0.49)

  = −7.1/√117.6(0.51)

  = −7.1/√59.976

  = −7.1/7.744417

  =−0.916789

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110

Using normal probability table:

P(X≤110) = P(X<110.5)

             = P(Z<-0.916)

             = 0.1788

c)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 120.5 - 117.6 / √117.6(1-0.49)

  = 2.9/√117.6(0.51)

  = 2.9/√59.976

  = 2.9/7.744417

  =0.374463

Here the player wins when he wins at least 120 of 240 hands

Using normal probability table:

P(X>120) = P(X>120.5)

              = P(Z>0.3744)  

             =  1 - P(Z<0.3744)

             = 1 - 0.6443

             = 0.3557

d)

Player goes broke when he loses $1500

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 105.5 - 117.6 / √117.6(1-0.49)

  = -12.1/√117.6(0.51)

  = -12.1/√59.976

  = -12.1/7.744417

  =−1.562416

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

             = P(Z<-1.562)

             = 0.0594

7 0
3 years ago
Solve each equation you must use
n200080 [17]

1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.

2)The solution for b² - 4b + 4 = 0 is x=2.

<u>Step-by-step explanation</u>:

The general form of quadratic equation is ax²+bx+c = 0

where

  • a is the coefficient of x².
  • b is the coefficient of x.
  • c is the constant term.

<u>To find the roots :</u>

  • Sum of the roots = b
  • Product of the roots = c

1) The given quadratic equation is m² - 5m - 14 = 0.

From the above equation, it can be determined that b = -5 and c = -14

The roots are -7 and 2.

  • Sum of the roots = -7+2 = -5
  • Product of the roots = -7\times2 = -14

The solution is given by (x-7) (x+2) = 0.

Therefore, the solutions are x=7 and x= -2.

2) The given quadratic equation is b² - 4b + 4 = 0.

From the above equation, it can be determined that b = -4 and c = 4

The roots are -2 and -2.

  • Sum of the roots = -2-2 = -4
  • Product of the roots = -2\times-2 = 4

The solution is given by (x-2) (x-2) = 0.

Therefore, the solution is x=2.

5 0
3 years ago
Charles has six times as many action figures as ben together the action figures total more than 75 how many does each have
seropon [69]

Answer:

We have been given that Charles has six times as many action figures as Ben

Let Ben has x action figures

So according to question Charles will have 6x.

together the action figures total more than 75

x+6x>75

7x>75

x>\frac{75}{7}

So Ben will have more than \frac{75}{7} action pictures.

And 6x>6\frac{75}{7}

6x>\frac{450}{7}

Charles will have more than \frac{450}{7}.

7 0
3 years ago
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