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Svetllana [295]
3 years ago
7

A shark is swimming 28 ft below sea level. If the angle of depression from a boat on the water to the shark is 19 degrees, what

is the horizontal distance between the boat and the shark?
Mathematics
1 answer:
Orlov [11]3 years ago
3 0

Answer:

81,3 ft to the nearest tenth.

Step-by-step explanation:

Tan 19 = 28 / h  where h = the horizontal distance.

h = 28 / tan 19

h = 81.3 ft.

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What is the slope in the table below
eduard

Answer:

<h2>The table does not show a linear function</h2>

Step-by-step explanation:

\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{From the table we have:}\\\\(5,\ 24),\ (10,\ 21),\ (15,\ 17),\ (20,\ 13)\\\\\text{Check}\\\\\dfrac{21-24}{10-5}=\dfrac{-3}{5}=-\dfrac{3}{5}\\\\\dfrac{17-21}{15-10}=\dfrac{-4}{5}=-\dfrac{4}{5}\\\\-\dfrac{3}{5}\neq-\dfrac{4}{5}

3 0
3 years ago
HELP PLZ The Multiplication of Polynomials
vampirchik [111]

Answer:

x⁴ + 3x³ - 5x + 1

Step-by-step explanation:

(x - 1)(x³ + 4x² + 4x - 1)

Same as writing....

x(x³ + 4x² + 4x - 1) - 1(x³ + 4x² + 4x - 1)

x⁴ + 4x³ + 4x² - x - x³ - 4x²- 4x + 1

x⁴ + 3x³ - 5x + 1

3 0
4 years ago
How to express each of the following pairs of
vichka [17]

Answer:

<em>a) 3<x<8</em>

<em>b) -4<x<-2</em>

<em>c) -6<x<5</em>

<em>d) -21/4 < x-8/3</em>

<em>e) 0<x<7</em>

Step-by-step explanation:

Given the following inequalities

a)  x > 3, 2x - 3 < 15

Solve 2x - 3 < 15

2x < 15+3

2x<18

x<18/2

x<8

Combine x>3 and x<8

If x>3, then 3<x

On combining, we have:

3<x<8

b) For the inequalities 25 > 1 - 6x, 1 > 3x + 7

25 > 1 - 6x

25-1>-6x

24>-6x

Divide through by -6:

24/-6 > -6x/-6

-4 <x

For the inequality 1 > 3x + 7

1-7>3x

-6>3x

-6/3 > 3x/3

-2 > x

x < -2

Combining both results i.e -4 <x and x < -2, we will have:

-4<x<-2

c) For the inequalities 2x - 7<3< 27 + 4x

On splitting:

2x - 7<3 and 3< 27 + 4x

2x < 3+7

2x<10

x<5

Also for 3< 27 + 4x

3-27<4x

-24<4x

-24/4 < 4x/4

-6<x

Combining both solutions i.e x<5 and -6<x will give;

<em>-6<x<5</em>

d) For the inequalities 3x + 8 <0 < 21 + 4x

3x + 8 <0

3x < -8

x < -8/3

Also for 0 < 21 + 4x

0-21<4x

-21<4x

-21/4 < 4x/4

-21/4 < x

Combining -21/4 < x and x < -8/3 will give;

<em>-21/4 < x-8/3</em>

<em></em>

e) For the inequalities 5x - 36 < -1 < 2x – 1​

Split:

5x - 36 < -1

5x < -1+36

5x<35

5x/5 < 35/5

x < 7

For the expression -1 < 2x – 1​

-1+1 < 2x

0 < 2x

0<x

Combining both inequalities 0<x and x < 7 will give:

<em>0<x<7</em>

7 0
3 years ago
A box contains four 10 nf and eight 100 nf capacitors. (a) what is the probability of obtaining at least two 10 nf capacitors if
grigory [225]

there are 4 of the 10-nf and 8 of the 100-nf capacitors which is a total of 12 items.

the probability of drawing a 10-nf is: 4 out of 12 = \frac{1}{3}

the probability of drawing a 100-nf is: 8 out of 12 =  \frac{2}{3}

(a)  "at least two" means: 2 or 3 or 4

Probability of 2 (10's) and 2 (100's):  \frac{1}{3} x \frac{1}{3} x \frac{2}{3} x \frac{2}{3} = \frac{4}{81}

Probability of 3 (10's) and 1 (100's):  \frac{1}{3} x \frac{1}{3} x \frac{1}{3} x \frac{2}{3} = \frac{2}{81}

Probability of 4 (10's) and 0 (100's):  \frac{1}{3} x \frac{1}{3} x \frac{1}{3} x \frac{1}{3} = \frac{1}{81}

2 or 3 or 4: \frac{4}{81} + \frac{2}{81} + \frac{1}{81} = \frac{7}{81}

(b) without replacement

Probability of 2 (10's) and 2 (100's):  \frac{4}{12} x \frac{3}{11} x \frac{8}{10} x \frac{7}{9} = \frac{4 x 3 x 8 x 7}{12 x 11 x 10 x 9}

Probability of 3 (10's) and 1 (100's):  \frac{4}{12} x \frac{3}{11} x \frac{2}{10} x \frac{8}{9} = \frac{4 x 3 x 2 x 8}{12 x 11 x 10 x 9}

Probability of 4 (10's) and 0 (100's):  \frac{4}{12} x \frac{3}{11} x \frac{2}{10} x \frac{1}{9} = \frac{4 x 3 x 2 x 1}{12 x 11 x 10 x 9}

2 or 3 or 4: \frac{4 x 3 x 8 x 7}{12 x 11 x 10 x 9} + \frac{4 x 3 x 2 x 8}{12 x 11 x 10 x 9} + \frac{4 x 3 x 2 x 1}{12 x 11 x 10 x 9} = \frac{672 + 192 + 24}{12 x 11 x 10 x 9} =  \frac{888}{12 x 11 x 10 x 9}  =  \frac{111}{1485}


8 0
3 years ago
Read 2 more answers
Help fast i have to leave in like 10 min please!
liubo4ka [24]
6. C
answer is 65 your answer is C
7.A
15.5
4 0
3 years ago
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