In the early spring, the trout at Big Blue Lake swim at a depth of 30 feet below sea level.
When the lake warms up in the summer, the trout swim 20 feet deeper than that.
At what position relative to sea level do the trout swim in the summer?

Answer:

102

Step-by-step explanation:

Let x be the amount of money John spends.

x/2-5=46

x/2=51

x=102

Answer:3.6 m

Given:10cm=2m

Then, 5cm=1m

Therefore, (18/5)= lenght I'm meters on blueprint scale

(18/5)=3.6m

Answer:

Step-by-step explanation: fg + Gh = fh

8x+1=9

8x=8

X=1

The numerical length of the line segment FG is 7 units.

Given that, FG=5x+2, GH= 3x-1, and FH= 9.

We need to find the numerical length of FG.

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Now, FH=FG+GH

⇒9=5x+2+3x-1

⇒8x+1=9

⇒8x=8

⇒x=1

So, FG=5x+2=7

Therefore, the numerical length of the line segment FG is 7 units.

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Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                     →  A = π - (B + C)

                                                     → B + C = π - A

Use the Pythagorean Identity: cos² A + sin² A = 1   →  sin² A = 1 - cos² A

Use Double Angle Identities: cos 2A = 2 cos² A - 1 → cos² A = (cos 2A + 1)/2

                                             → cos A = 1 - 2 sin² (A/2)    

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]

Use Cofunction Identities:  cos (π/2 - A) = sin (A)

                                             sin (π/2 - A) = cos A

                                             cos (-A) = cos (A)

Proof LHS → RHS:

[tex]\text{LHS:}\qquad \qquad \sin^2\bigg(\dfrac{B}{2}\bigg)+\sin^2 \bigg(\dfrac{C}{2}\bigg)-\sin^2\bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Pythagorean:}\qquad 1-\cos^2 \bigg(\dfrac{B}{2}\bigg)+1-\cos^2 \bigg(\dfrac{C}{2}\bigg)-\bigg[1-\cos^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\cos^2 \bigg(\dfrac{B}{2}\bigg)-\cos^2 \bigg(\dfrac{C}{2}\bigg)+\cos^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Double Angle:}\quad 1-\bigg(\dfrac{\cos(2\cdot \frac{B}{2})+1}{2}\bigg)-\bigg(\dfrac{\cos (2\cdot \frac{C}{2})+1}{2}\bigg)+\bigg(\dfrac{\cos (2\cdot \frac{A}{2})+1}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1-\dfrac{\cos B}{2}-\dfrac{1}{2}-\dfrac{\cos C}{2}-\dfrac{1}{2}+\dfrac{\cos A}{2}+\dfrac{1}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}[1-(\cos B+\cos C)+\cos A][/tex]

[tex]\text{Sum to Product:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Given:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{\pi -A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Cofunction:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]    

[tex]\text{Double Angle:}\qquad \dfrac{1}{2}\bigg[1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)+1-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg[2-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Factor:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{A}{2}\bigg)\bigg][/tex]

[tex]\text{Given:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{\pi -(B+C)}{2}\bigg)\bigg][/tex]

[tex]\text{Cofunction:}\qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)+\cos \bigg(\dfrac{B+C}{2}\bigg)\bigg][/tex]

[tex]\text{Sum to Product:}\ 1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot 2 \cos \bigg(\dfrac{(B-C)+(B-C)}{2\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{(B-C)-(B+C)}{2\cdot 2}\bigg)\\\\\\.\qquad \qquad \qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(-\dfrac{C}{2}\bigg)[/tex][tex]\text{Cofunction:}\qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{LHS = RHS:}\quad \checkmark\\\\\quad 1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)=1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\quad[/tex]

Answer:

72 cats

Step-by-step explanation:

sum the parts of the ratio, 3 + 8 = 11 parts

Divide the total by 11 to find the value of one part of the ratio.

99 ÷ 11 = 9 ← value of 1 part of the ratio, then

8 parts = 8 × 9 = 72 ← number of cats

Answer:

30

Step-by-step explanation:

Answer:

a. Addition & division

Step-by-step explanation:

2x - 4 = 16   (adding 4 to both sides)

2x  = 16 + 4

2x = 20  (dividing both sides by 2)

x = 20/2 = 10

Hence we can see that the two operations are addition and then division

Answer:

23/3

7 7/8

7.9

Step-by-step explanation:

Answer:

if i;m right its 45 degrees

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

alternative angle theorem lets you know that angle acb is equal to cae and you can find acb since you know all angles add up to 180. 180-105-47=28

Answer:

A0.15

Step-by-step explanation:

this is what I found hope its correct!‍♀️

Answer:

3/4

Step-by-step explanation:

3/5(1+p)-21/20

3/5+3/5p=21/20

3/5p=21/20-3/5

3/5p=21/20-12/20

3/5p=9/20

p=9/20÷3/5

p=9/20*5/3

p=45/60

p=3/4

Answer:

Substitute the given value into the function and evaluate is

− 9

Answer: 30x+2, 0<x<10

24x+6, x>10

Step-by-step explanation:

Make sure the x>6 has the line under the >. It would not let me enter it like that.

The piecewise function that models the cost of x pounds of trout is:  [tex]\bold{f(x)=\left \{ {{30x + 2,~~0 < x < 10} \atop {24x + 6,~~~x > 10}} \right. }[/tex],

"It is a function that is defined on a sequence of intervals."

For given question,

'x' represents number of pound of trout.

Each pound of trout costs $30, and the company charges a $2 fee for

shipping the order.

We write this in equation form as,

f(x) = 30x + 2

This is possible if Karen orders less than 10 pounds.

So, the function would be,

f(x) = 30x + 2, 0 < x < 10

If  Karen orders 10 or more pounds, the trout costs only $24 per pound, but the shipping fee is $6.

This means, the function would be,

f(x) = 24x + 6, x > 10

Hence, the piecewise function that models the cost of x pounds of trout is:  [tex]\bold{f(x)=\left \{ {{30x + 2,~~0 < x < 10} \atop {24x + 6,~~~x > 10}} \right. }[/tex]

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Answer:

OC 193 lb is correcte!

The person's weight, in pounds, when rounded to the nearest

the whole number is equal to [tex]1.9\times10^{2} pound[/tex]

We have given that, A pound is approximately 0.45 kilogram.

0.45 kg = 1 pound

Thus if 0.45 kg is equal to= 1 pound

87 kg will be equal to [tex]=\frac{1}{0.45} \times 87=1.9 \times 10^2 pound[/tex]

The number of significant digits in an answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided, etc.

Thus the answer should contain 2 significant digits.

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Step-by-step explanation:

42+90 can be written in many ways.

Fore example, it can be written with double negatives, or even commutative property.

42-(-90) or 90+42

(21x2)+(45x2) or (6x7)+(3x30)

Sorry if it's wrong...

Answer:

The answer should be 5

Step-by-step explanation: cause 3x5=15 which leaves 9 more shots that are equal to 2 2x9= 18 and 18+15= 33 which means the answer is 5

Answer:

B.) 5

Step-by-step explanation:

Edge2021

Answer:   A  C and D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function

To find

Solution

Substitute x with 3 in the equation to find f(3)

Exact Form: t = 8/5

Decimal Form: t = 1.6

Mixed Number Form: t = 1 3/5 (one and three fifths)

Answer:

t = 8/5 or t = 1.6

This will be a fraction buh can be turned into a decimal

Step-by-step explanation:

subtract 1 on both sides 5t + 1 - 1 = 9 - 1

then simplify 5t = 8 after det divide both side 5t/5 = 8/5 and den your answer is t = 8/5...

HOPE DIS HELPS YU OR IS RIGHT!!!!!

Answer:

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

  range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

  increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.