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3 years ago

What is the length of the missing side FP? Round the answer to the nearest tenth please.

Mathematics

2 answers:

Sauron [17]3 years ago

8 0

Answer:

Step-by-step explanation:

Considering the given triangle KFP, to determine FP, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

KP/SinF = FP/SinK

Therefore

66/Sin 85 = FP/Sin 49

Cross multiplying, it becomes

FPSin85 = 66Sin49

0.996FP = 66 × 0.755

0.996FP = 66 × 0.755 = 49.83

FP = 49.83/0.996

FP = 50.0 yards

kirill [66]3 years ago

5 0

Answer:

Step-by-step explanation:

Xem xét các tam giác cho KFP, để xác định FP, chúng tôi áp dụng các quy tắc sine. Nó được thể hiện như a/SinA = b/SinB = c/SinCWhere a, b và c là chiều dài của mỗi bên của tam giác và góc A, Angle B và góc C là các góc tương ứng của hình tam giác. So sánh nó với tam giác nhất định, biểu hiện becomesKP/SinF = FP/SinKTherefore66/Sin 85 = FP/Sin 49Cross nhân, nó becomesFPSin85 = 66Sin 490.996 FP = 66 × 0.7550.996 FP = 66 × 0,755 = 49.83 FP = 49.83/0.996 FP = 50,0 yards

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Dado dos ángulos complementarios, uno mide (2x + 10) y el otro (x + 20),

rusak2 [61]

Answer:

El valor de x es igual a 20 o x = 20.

Step-by-step explanation:

Lo primero que se debe saber es que dos ángulos complementarios suman un ángulo recto o 90º.

Supongamos que el valor de un ángulo $\\ \alpha$ y un ángulo $\\ \beta$ valen:

$\\ \alpha = 2x + 10$ [1]

$\\ \beta = x + 20$ [2]

Como la suma de $\\ \alpha + \beta = 90$ [3]

Entonces

$\\ \alpha + \beta = (2x + 10) + (x + 20) = 90$

Sumamos los factores comunes entre si:

$\\ (2x + x) + (10 + 20) = 90$

Para la primera expresión debemos recordar que se suman sólo los coeficientes. Así:

$\\ (2 + 1)x + (10 + 20) = 90$

$\\ 3x + 30 = 90$

Para despejar la incógnita x, debemos tener en cuenta que una igualdad no se altera si se suma, se resta, se multiplica o divide un mismo valor a cada lado de ella. Por esta razón, para despejar 3x, lo primero que podemos hacer es sumar -30 a cada lado de la expresión (lo que es igual a restar 30 a cada lado de la misma). Así tenemos:

$\\ 3x + 30 - 30 = 90 - 30$

$\\ 3x + 0 = 90 - 30$

$\\ 3x = 60$

Ahora dividimos cada miembro de la igualdad entre 3 (o multiplicamos cada lado de la igualdad por $\\ \frac{1}{3}$ ):

$\\ \frac{3}{3}x = \frac{60}{3}$

Como sabemos que:

$\\ \frac{3}{3} = 1$

Entonces:

$\\ 1*x = \frac{60}{3}$

$\\ x = \frac{60}{3}$

$\\ x = 20$

De esta manera, el valor de x es igual a 20 o x = 20.

Lo anterior lo podemos comprobar considerando las ecuaciones [1], [2] y [3]. Así tenemos que:

$\\ \alpha = 2x + 10$ [1]

Sustituimos x por el valor de 20:

$\\ \alpha = 2*20 + 10 = 40 + 10 = 50$

$\\ \beta = x + 20$ [2]

Hacemos lo mismo para [2]:

$\\ \beta = 20 + 20$

$\\ \beta = 40$

De esta manera:

$\\ \alpha + \beta = 90$ [3]

$\\ 50 + 40 = 90$

4 0

3 years ago

Consider the toss of four coins. There are 16 (i.e., 24) possible outcomesin one toss. (a)Calculate the probabilities that there

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Answer:

See answers below

Step-by-step explanation:

If 4 coins are tossed. the total possible outcomes are;

H H H H , H H H T, H H T H, H T H H, T H H H , H H T T, H T T H, T T H H, H T H T, T H T H, T H H T , H T T T, T H T T, T T H T, T T T H and T T T T

Total outcomes = 16

1) zero head = T T T T = 1 outcome

Probability = Expected/Total outcome

Pr(zero head) = 1/16

2) one head = H T T T, T H T T, T T H T, T T T H = 4 outcomes

Probability = Expected/Total outcome

Probability = 4/16

Pr(one head) = 1/4

3) two heads = H H T T, H T T H, T T H H, H T H T, T H T H, T H H T = 6 outcomes

Probability = Expected/Total outcome

Pr(two head) = 6/16

Pr(two head) = 3/8

4) three heads = H H H T, H H T H, H T H H, T H H H = 4 outcomes

Probability = Expected/Total outcome

Pr(three heads) = 4/16

Pr(two head) = 1/4

5) four heads appearing on the four coins = H H H H = 1 outcome

Pr(four heads) = 1/16

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zubka84 [21]

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Answer:

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