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Mama L [17]
3 years ago
5

The altitude of an equilateral triangle is 22 inches. Find the perimeter of the equilateral triangle. Leave answer as a simplifi

ed radical.
Mathematics
1 answer:
torisob [31]3 years ago
3 0

The perimeter of the equilateral triangle will be 76.2 in

<u>Explanation:</u>

Altitude of an equilateral triangle, H = 22 in

Perimeter, p = ?

Let a be the side of the triangle

We know:

H = \frac{a\sqrt{3} }{2} \\\\22 = \frac{a\sqrt{3} }{2} \\\\a = 25.4 in

Perimeter = 3a

P = 3 X 25.4 in

P = 76.2 in

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Find the roots of h(t) = (139kt)^2 − 69t + 80
Sonbull [250]

Answer:

The positive value of k will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80, roots are those values of t so that h(t) = 0. That is:

19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0 (1)

Roots are determined analytically by the Quadratic Formula:

t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}

t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }

The smaller root is t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }, and the larger root is t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }.

h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80 has one real root when \frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0. Then, we solve the discriminant for k:

\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}

k \approx \pm 0.028

The positive value of k will result in exactly one real root is approximately 0.028.

7 0
2 years ago
A factory makes tennis balls. Every tennis ball must meet a quality standard, or it will be rejected. The percentage that meets
Anettt [7]
The answer you're looking for is 40 tennis balls.
Hope this helped!
3 0
3 years ago
Find the value of x
olya-2409 [2.1K]

Answer:

A) 33

Step-by-step explanation:

180 - 105= 75

75 + 72 + x = 180

147 + x = 180

x= 33

3 0
2 years ago
A store pays $365.84 for a fountain. The store marks up the price by 10%.
Ann [662]

Answer:

The store marks up the fountain by adding $ 36.58 to its original cost, bringing its retail price to $ 402.42.

Step-by-step explanation:

Given that a store pays $ 365.84 for a fountain, and then the store marks up the price by 10%, to determine the amount of the mark-up the following calculation must be performed:

365.84 x 10/100 = X

3,658.4 / 100 = X

36,584 = X

36.584 + 365.84 = 402.424

Thus, the store marks up the fountain by adding $ 36.58 to its original cost, bringing its retail price to $ 402.42.

4 0
3 years ago
HELPPPPPPPP ASAPPPPP PLSSSS
balu736 [363]
The answer to this should be 101!
7 0
2 years ago
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