A school of salmon was swimming in the river 5 feet below the surface. To escape a hungry bear, they went down another 3 feet.
What is the position of the salmon now relative to the surface?

The angle of depression is the angle formed with the horizontal, when an object is viewed below the horizontal level. Thus, the height of the cliff is approximately 123.86 m.

Let the height of the cliff be represented by h, so that:

From the triangle 1, we have:

tan [tex]32^{o}[/tex] = [tex]\frac{h}{x}[/tex]

⇒ h = tan [tex]32^{o}[/tex]*x

    h = x tan [tex]32^{o}[/tex] ............. 1

Also, from the bigger triangle, we have:

tan [tex]24^{o}[/tex] = [tex]\frac{h}{80 + x}[/tex]

⇒ h = tan [tex]24^{o}[/tex] (80 + x) .........  2

Now equating the expressions for h in equations 1 and 2, we have:

x tan [tex]32^{o}[/tex] = tan [tex]24^{o}[/tex] (80 + x)

0.6249x = 0.4452 (80 + x)

               = 35.616 + 0.4452x

0.6249x - 0.4452x = 35.616

0.1797 x = 35.616

x = [tex]\frac{35.616}{0.1797}[/tex]

x = 198.2 m

Substitute the value of x in equation 1;

h = x tan [tex]32^{o}[/tex]

  = 198.2 * 0.6249

 = 123.8552

h = 123.86 m

Therefore, the height of the cliff is approximately 123.86 m.

A sketch to this question is attached.

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Answer:

not linear

Step-by-step explanation:

a linear function contains x and y only with the exponent 1.

this allows the function to be a line (hence the term "linear"), a constant ratio of y changes to x changes for any values of x which defines linear relation between x and y.

but this equation contains a term with x², which changes the size of change of y for every value of x.

e.g. when x changes by 1 from 1 to 2, y changes by 3 from 1² to 2² (1 to 4). but if x changes again by 1 from 2 to 3, y changes by 5 from 2² to 3² (4 to 9).

this is clearly not constant.

Answer:

8.x=7

7.x=12

Step-by-step explanation:

8.The two Base angles are equal

7. The exterior(outside) angle is equal to the sum of the two interior(inside) angles.

One apple cost $1.8 while the money that Philip has is $24.90

Let x represent the cost of each apple and y represent the money he has presently.

He can buy 15 apples if he had $2.10 more money than he has now, hence:

15x = y + 2.1

15x - y = 2.1     (1)

Also, if he buys 12 apples, how would have $3.30 left of the money he has now. Hence:

12x + 3.3 = y

12x - y = -3.3   (2)

Solving equations 1 and 2 gives:

x = 1.8, y = 24.9

Hence one apple cost $1.8 while the money that Philip has is $24.90

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Answer:

Step-by-step explanation:

Answer:

72 child

369 adult

48 senior

Answer:

box number 2 is 2. box number 3 is 7. box number 1 is product or sum

Using the concept of arithmetic sequence, the 5000th term can be obtained using the relation 4 + (5000 - 1)9

For an arithmetic sequence, the nth term is calculated using the relation :

Here,

First term, a = 4

Common difference = 2nd term - 1st term = 13 - 4 = 9

nth term = 5000th term

The expression would be :

The required expression would be : T(5000) = 4 + (5000 - 1)9

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Answer:

[tex](2,1)[/tex]

Step-by-step explanation:

Let's first write down the first in traditional form:

[tex]\left \{3x-y=5} \atop {2x+y=5}} \right.[/tex]

At this point, let's choose the order we want to do it.

Eliminating x: Let's multiply the first by 2, the second by 3, and subtract one from the other. Rest is simple algebra

[tex]2I-3II: 6x-2y -6x-3y = 10-15\\-5y=-5 \rightarrow y=1[/tex]

Eliminating y: Let's simply add the two equations together. Rest is simple algebra

[tex]I+II:3x-y+2x+y = 10\\5x=10 \rightarrow x = 2[/tex]

Answer:

J

Step-by-step explanation:

Answer:

answer attached

Step-by-step explanation:

Answer:

2 days

Step-by-step explanation:

12 - 4 = 8

8/3 = 2.7

Answer:

3 : 1

Step-by-step explanation:

The values must be in the same quantity

1 Kg = 1000 g

4.5 Kg = 4.5 × 1000 = 4500 g

Then

4.5 Kg : 1500 g

= 4500 g : 1500 g ( divide both parts by 1500 )

= 3 : 1 ( in simplest form )

The simplified form of the ratio, 4.5 kg : 1,500 g is 3 : 1

A ratio is a measure of the number of times one quantity is contained in or contains another quantity.

To write the the ratio 4.5 kg : 1,500 g as a ratio in its simplest form, both quantities are to be expressed in the same unit.

1 kg = 1,000g

Therefore, 4.5 kg = 1,000 g/kg × 4.5 kg = 4,500 g

The ratio 4.5 kg : 1,500 g can be written as follows;

4,500 g : 1,500 g

The above ratio can be simplified by dividing both terms by the greatest common divisor, (GCD). The GCD of 4,500 and 1,500 is 1,500, therefore, we divide both terms by 1,500 to get;

4,500 g : 1,500 g = (4,500 ÷ 1,500) : (1,500 ÷ 1,500)  = 3 : 1

Therefore, the ratio 4.5 kg : 1,500 g simplifies to 3 : 1

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Answer:

I think its 6/5 or 2/3

Step-by-step explanation:

Answer:

1. A

2. C

3. D

4. C

5. D

Step-by-step explanation:

You're welcome

Answer:

After 7 seconds it hits the ground.

h= -16^2 + 80x + 224

(I'm assuming this is what you meant, because these problems are generally quadratic)

Use quadratic formula to find when it hits the ground (get zeros)

x = -2, x = 7

After 7 seconds it hits the ground.

Answer:

w [tex]\leq[/tex] 3,600

Step-by-step explanation:

[tex]\leq[/tex]  means less than or equal to.

Answer:

A) Variable "x" is less than it equal to 1 because your domain can’t have [h(x)] because that’s your function and would be your range but in this case it’s your domain and your domain or else known as the variable "x" coordinate would have to be the number on the x axis that your line starts, your line begins on line 1 on the x axis which would be your domain

Hope this helps!

Answer:

[tex]m=\frac{-3}{2}[/tex]

Step-by-step explanation:

We can see certain points plotted which are  (-1, 2) (1,-1) and (3, -4)

We use the slope formula to find slope with any two points that were given

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

The derivative of [tex]f(x) = 2\cdot x^{2}-9[/tex] is [tex]f'(x) = 4\cdot x[/tex].

In this exercise we must apply the definition of derivative, which is described below:

[tex]f'(x) = \lim_{x \to 0} a_n \frac{f(x+h)-f(x)}{h}[/tex] (1)

If we know that [tex]f(x) = 2\cdot x^{2}-9[/tex], then the derivative of the expression is:

[tex]f'(x) = \lim_{h \to 0} \frac{2\cdot (x+h)^{2}-9-2\cdot x^{2}+9}{h}[/tex]

[tex]f'(x) = 2\cdot \lim_{h \to 0} \frac{x^{2}+2\cdot h\cdot x + h^{2}-2\cdot x^{2}}{h}[/tex]

[tex]f'(x) = 2\cdot \lim_{h \to 0} 2\cdot x + h[/tex]

[tex]f'(x) = 4\cdot x[/tex]

The derivative of [tex]f(x) = 2\cdot x^{2}-9[/tex] is [tex]f'(x) = 4\cdot x[/tex].

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Answer:

a₁ = 10

Step-by-step explanation:

The common difference d is calculated as

d = a₃ - a₂ = - 20 - (- 5) = - 20 + 5 = - 15

Then

a₂ - a₁ = d , that is

- 5 - a₁ = - 15 ( add 5 to both sides )

- a₁ = - 10 ( multiply both sides by - 1 )

a₁ = 10

Answer:

No of student can be found using x+y=total

X+y=total

Concept

Step-by-step explanation:

Let vans be x

Let bas be y

14x+6y=564

4x+6y=414

With that you can get the answer am sorry I couldn't give the appropriate answer I only showed the way am in a trip that's why

Answer:

y=6x-1

Step-by-step explanation:

6x - y = -1

-y = -1 -6x

y = 6x+1

Answer:

y = 6x + 1

Step-by-step explanation:

hope it helps

should I show steps?

Answer:

B 13/2

Step-by-step explanation:

2x² + 7x - 15 = 0

First we want to find the two solutions

We can do this by using the quadratic formula

Quadratic formula:

[tex] \frac{- b + or - \sqrt{b {}^{2} - 4(a)(c)} }{2(a)} [/tex]

Where the values of a,b and c are derived from the equation.

The equation is put in ax² + bx + c = 0 form

2x² + 7x - 15 = 0

so a = 2, b = 7 and c = - 15

We now plug these values into the quadratic formula

(-(7) + or - √7² - 4(2)(-15) ) / 2(2)

first solution: -(7) + √7² - 4(2)(-15) ) / 2(2)

remove parenthesis on 7

(-7 + √7² - 4(2)(-15) ) /2(2)

Apply exponents 7²

(-7 + √49 - 4(2)(-15) ) /2(2)

Multiply -4,2 and -15

(-7 + √49 + 120 ) / 2(2)

add 49 and 120

(-7 + √ 169 ) / 2(2)

Take square root of 169

(-7 + 13 ) / 2(2)

add 13 and -7

6/2(2)

multiply 2 and 2

= 6/4

The first solution is 6/4 or 1.5

Now the second solution: -(7) - √7² - 4(2)(-15) ) / 2(2)

For the second solution we basically go through the same steps as for finding the first solution, the only difference is instead of adding -b and √b² - 4(a)(c) we are subtracting.

So we would have ( -7 - 13 ) / 2(2) instead of (-7+13)/2(2)

So second solution: ( -7 - 13 ) / 2(2)

subtract 13 from -7

-20/2(2)

multiply 2 and 2

-20/4

divide

The second solution is -5

Now that we have found the solutions we want to find r - s if r and s are the solutions to the equation and that r > s

The two solutions are 6/4 and -5.

6/4 > -5 so we know that r must equal 6/4 and s must equal -5 because r has to be greater than s

So if r = 6/4 and s = -5

Then r - s = 6/4 - (-5) = 6/4 + 5 = 13/2

So the answer is B. 13/2

Answer:

∠ B = 126°

Step-by-step explanation:

∠ A and ∠ B are alternate angles and are congruent , then

8x + 78 = 2x + 114 ( subtract 2x from both sides )

6x + 78 = 114 ( subtract 78 from both sides )

6x = 36 ( divide both sides by 6 )

x = 6

Then

∠ B = 2x + 114 = 2(6) + 114 = 12 + 114 = 126°

Answer:

angel b is 70 because all the degrees in a triangle must add up to 180

Answer:4 1/3

Step-by-step explanation:

Answer:

R.I.P

Step-by-step explanation:

goodluck doing that

[tex]y = 9x + \dfrac 94 \\\\\text{The above equation is in a form of y=mx + b, where b is the y - intercept}\\\\\\\text{Hence the y-intercept is }~ \dfrac 94[/tex]