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PtichkaEL [24]
3 years ago
14

Please I will give brainylest if the answer is correct

Mathematics
1 answer:
Luba_88 [7]3 years ago
8 0

Answer:

a^n +3

Step-by-step explanation:

simpify: a^na^3:\quad a^{n+3}

a^{n+3}

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6) Two coastguard stations P and Q are 17km apart, with due East of P. A ship S is observed in distress on a bearing 048° fromP
adelina 88 [10]

Answer:

The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.

Step-by-step explanation:

Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.

But,

<P = 048°

<Q = 360^{o} - 324^{o}

     = 036^{o}

Sum of angles in a triangle = 180^{o}

<P + <Q + <S = 180^{o}

048° + 036^{o} + <S = 180^{o}

84^{o} + <S = 180^{o}

<S  = 180^{o} -  84^{o}

    = 96^{o}

<S = 96^{o}

Applying the Sine rule,

\frac{y}{Sin P} = \frac{x}{Sin Q} = \frac{z}{Sin S}

\frac{y}{Sin P} = \frac{z}{Sin S}

\frac{y}{Sin 48^{o} } = \frac{17}{Sin 96^{o} }

\frac{y}{0.74314} = \frac{17}{0.99452}

⇒ y = \frac{12.63338}{0.99452}

       = 12.703

y = 12.70 km

\frac{x}{Sin Q} = \frac{z}{Sin S}

\frac{x}{Sin 36^{o} } = \frac{17}{Sin 96^{o} }

\frac{x}{0.58779} = \frac{17}{0.99452}

⇒ x = \frac{9.992430}{0.99452}

      = 10.0475

x = 10.05 km

Thus,

the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.

6 0
3 years ago
Which graph shows the image of the triangle reflected across the line of reflection shown?
olga55 [171]

Answer:

D .points (2,2) (4,4) (0,9)

Step-by-step explanation:

5 0
3 years ago
From a standard deck of cards, a 5-card hand is dealt. Calculate the number of hands that contain 4 diamonds and 1 black king
rjkz [21]

Answer:

1430

Step-by-step explanation:

Given that a standard deck of cards is 52 cards, we have 13 Diamonds and we need 4 diamonds.

Hence, we have 13C4.

Also, we have 4 kings in a standard deck of cards, and in which we have 2 black kings but we need 1 king.

Hence we have a 2C1

Therefore:

13C4 * 2C1

=> 13! ÷ [4! (13 - 4)!] * 2! ÷ [1! (2-1)!]

=> 13! ÷ [4! (9)!]

=> (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13) ÷ [(1 x 2 x 3 x 4) (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)]

=> (10 x 11 x 12 x 13) ÷ 24

=> (17160 ÷ 24) * (24 ÷ 6)

=> 715

2! ÷ [1! (2-1)!]

=> 2

Hence, we have 715 * 2

=> 1430

Hence, in this case, the correct answer to the question is 1430

7 0
3 years ago
Solve each equation (quadratic pattern)
dusya [7]

Answer:  x = 2

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

2^{2x}-2^x-12=0\\\\\text{Let u = }2^x\\\\u^2-u-12=0\\(u-4)(u+3)=0\\\\u-4=0\quad and\quad u+3=0\\u=4\qquad and\quad u=-3\\\\\text{Substitute u with }2^x\\2^x=4\qquad and \quad 2^x=-3\\2^x=2^2\quad and\quad \text{not possible}\\\boxed{x=2}

********************************************************************************

Answer:  x = 0

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

3^{2x}+3^{x+1}-4=0\\\\3^{2x}+3^x\cdot3^1-4=0\\\\\text{Let u = }3^x\\u^2+3u-4=0\\\\(u+4)(u-1)=0\\\\u+4=0\quad and\quad u-1=0\\u=-4\qquad and\quad u=1\\\\\text{Substitute u with }3^x\\3^x=-4\qquad and\quad 3^x=1\\\text{not possible}\ and\quad 3^x=3^0\\.\qquad \qquad \qquad \qquad \boxed{x=0}

********************************************************************************

Answer:  No Solution

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

4^x+6\cdot 2^x+8=0\\\\2\cdot 2^x+6\cdot 2^x+8=0\\\\\text{Let u = }2^x\\2u+6u+8=0\\8u+8=0\\8u=-8\\u=-1\\\\\text{Substitute u with }2^x\\2^x=-1\\\text{not possible}

********************************************************************************

Answer:  No Solution

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

<u>9^x=3^x-6\\\\3\cdot 3^x=1\cdot 3^x-6\\\\\text{Let u = }3^x\\\\3u=u-6\\2u=-6\\u=-3\\\\\text{Substitute u with }3^x\\3^x=-3\\\text{not possible}</u>

<u />

6 0
3 years ago
Which simplified fraction is equal to 0.53 repeat ? A.24/46 B.8/15 C.42/90 D.5/9
murzikaleks [220]

Answer:

To see how these fractions are equal, I divided the numerators by the denominators. For instance, you could have 4 over 5 (4/5) and divide 4 by 5 (4/5) to get 0.8. Now you'll do the same thing for the fractions given

24/45=0.533...

8/15=0.533...

48/90=0.533...

5/9=0.5556

As you can see, the only fraction that doesn't equal 0.53, or the outlier, is 5/9 or 0.5556

Step-by-step explanation:

8 0
3 years ago
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