Solve for q in terms of r, s, and t

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Step-by-step explanation:

\(46064yx \times ( \frac{ { > < |x { \frac{( {))(6460 = 464}^{?} }{?} }^{?} | }^{?} }{?} \)

Answer:

(E) < BDE = 2x + y.

Step-by-step explanation:

As  triangle ABC is isosceles the 2 base angles are equal.

Therefore m < BAC = x.

Consider triangle ABD:

m < BDE = m < BAC + m < ABD ( external angle of a triangle theorem)

So < BDE =  x + x + y = 2x + y.

Hope you could understand.

If you have any query, feel free to ask.

Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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The value of f(g(1) from the table of functions is given as 1.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

when x = 1

g(x) = 3

or f(g(1) = f(3) = 1

The value of f(g(1) from the table of functions is given as 1.

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Answer:

here's the answer

Step-by-step explanation:

19/100*x=6.46

x=$34

Answer:

25%

Step-by-step explanation:

multiply it by 100 over 1 then divide the top by the bottom.

Answer:

The point-slope form of the equation of a line is generally given as;

From the question, we're told that the slope, m, is 1/4 and the line passes through -1 and 4, so our x1 = -1 and y1 = 4, let's substitute these values into the above equation to determine the equation of the line;

So the line will have a y-intercept at 17/4. See below the graph of the line;

The computation shows that the total score is 450.

The total points to get an A will be:

= 397 + 8 = 405

Therefore, this is 90% of the total score. Let the total score be x.

The will be:

= 90% × x = 405

0.9x = 405

Divide

x = 405/0.9

x = 450

The total score is 450.

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The exact values of the six trigonometric functions of the angles are: Sinθ = 4/5, Cosθ = 3/5, Tanθ = 4/3, Secθ = 5/3, Cotθ = 3/4.

The the given question, the point (3, 4) is on the terminal side of an angle in standard position, we have to determine the exact values of the six trigonometric functions of the angle.

The given point is (3, 4).

Let x = 3 and y = 4

Let z be the length of the line segment drawn from the origin to the point.

Now using the Pythagorean Theorem to find the value of z.

z^2 = x^2 + y^2

z^2 = (3)^2 + (4)^2

z^2 = 9+16

z^2 = 25

Taking square root on both side, we get

z = 5

Now finding the exact values of the six trigonometric functions of the angle.

As we know that;

Sinθ = y/z

Sinθ = 4/5

Cosθ = x/h

Cosθ = 3/5

Tanθ = y/x

Tanθ = 4/3

Cscθ = 1/Sinθ

Cscθ = 1/(4/5)

Cscθ = 5/4

Secθ = 1/Cosθ

Secθ = 1/(3/5)

Secθ = 5/3

Cotθ = 1/Tanθ

Cotθ = 1/(4/3)

Cotθ = 3/4

Hence, the exact values of the six trigonometric functions of the angles are: Sinθ = 4/5, Cosθ = 3/5, Tanθ = 4/3, Secθ = 5/3, Cotθ = 3/4.

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As per the angle sum property, the interior angles that form the triangle is option

B. 60, 60, 60°

C. 40.50,90°

D. 30.60.90*

Angle sum property

Angle sum property states that the sum of all the interior angles of the triangle is equal to 180 degrees.

Given,

Here we have the list of interior angles

A. 45, 45, 45*

B. 60, 60, 60°

C. 40.50,90°

D. 30.60.90*

E. 90,90°, 45°

F. 90, 90, 90°

Now, we have to find in which for these angle will form the tringle.

As per the definition of the angle sum property, the sum of all the interior angle of the triangle is 180°.

Based on these we have to verify each of the given interior angles,

A) 45 + 45 + 45 = 135

B. 60 + 60 + 60 = 180

C. 40 + 50 + 90 = 180

D. 30 + 60 + 90 = 180

E. 90 + 90 + 45 = 225

F. 90 + 90 + 90 = 270

Therefore, based on these values we have identified that the options (B), (C), and (D) forms the triangle.

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Answer:

Step-by-step explanation:

Remaining fraction:

1/5 of books are encyclopedia

Answer:

Let the total fraction of books be 1, then;

\(1 - ( \frac{1}{10} + \frac{2}{10} + \frac{1}{2} ) \\ 1 - ( \frac{(1 + 2 + 5)}{10} ) \\ (1 - \frac{8}{10}) = \frac{(10 - 8)}{10} \\ \frac{2}{10} = \boxed{ \frac{1}{5} }\)

Notes are commonly issued on discounted value when the issuer needs to raise funds quickly and is willing to accept a lower price for the note in exchange for immediate cash.

Notes can be issued either at their face value or at a discounted value.

A note is issued at its face value, the price of the note is the same as the face value of the note.

This is known as issuing the note at par value or face value.

A note is issued at a discounted value, the price of the note is lower than the face value of the note.

This is known as issuing the note at a discount.

The difference between the face value of the note and the discounted value is called the discount.

The investor who purchases the note at a discounted value will receive the face value of the note when it matures.

Notes may be issued at face value or at a discount from that amount.

The price of a note is equal to its face value when it is issued, or at face value.

The note will then be issued at face value or par value.

A note is sold for less than its face value when it is issued at a reduced price.

This is referred to as discounting the note's issuance.

The discount is the amount that separates the note's face value from its reduced value.

The face value of the note will be paid to the investor who paid the reduced price when the note matures.

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Answer:

Step-by-step explanation:

if he spends x hours = 6x>168

A, the relation is not a function

in order for something to be a function, x (the input) can't repeat itself more than once

Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

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Answer:

Step-by-step explanation:

4x2 - 8x -12 = 0

divide through by 4

x2 - 2x - 3 = 0

x2 - 3x + x - 3 = 0

(x2 - 3x) + (x - 3) = 0

x(x - 3) + 1(x - 3) = 0

(x + 1) (x - 3) = 0

x + 1 = 0 and x - 3 = 0

x = -1 and x = 3

Answer:

B IS THE ANSWER

Step-by-step explanat

(22x2 -  8x) -  12  = 0

  4x2 - 8x - 12  =   4 • (x2 - 2x - 3)

The first term is,  x2  its coefficient is  1 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -2 .

     -3    +    1    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  1  

                    x2 - 3x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-3)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-3)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-3)

            Which is the desired factorization

4 • (x + 1) • (x - 3)  = 0

A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately  

Any solution of term = 0 solves product = 0 as well.

  Solve  :    x+1 = 0

Subtract  1  from both sides of the equation :  

                     x = -1

   Solve  :    x-3 = 0  

Add  3  to both sides of the equation :  

                     x = 3

Step-by-step explanation:

Ok so lets begin with what we know. Each guest is $20.50, 144 guests arrived, and they started with $2,500.

The equation would be 2,500-20.5(144)

20.5(144)=$2,952

Now the issue here is that the payment is more than the account balance and so im guessing either they want the answer as $0, they want the negative value which is -$452, or there was another part before this with the old account info.

Hence the correct option is to translate down 2 unit

Transformations can be non-rigid (when the preimage's size or shape is unaltered) or stiff (where the size is changed but the shape remains the same). These are the fundamental guidelines that this concept abides by. It is a straightforward approach to alter 2D forms.

Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets.

We have the parent function f(X)= x

and transformed function is g(x)= -3f(x+5)-2

the parent function f(x) is translated dawn 2 units and stretched by 5 .

Hence the correct option is to translate down 2 unit

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Answer:

c

Step-by-step explanation:

Answer:

Width = 10ft

Length = 12ft

Step-by-step explanation:

For a rectangle of length L and width W, the area is calculated as:

A = L*W

In this case, we know that:

The area is 120 ft^2.

The length is 2 ft more than the width.

Then we can write:

L = W + 2ft.

If we use these two equations and replace them in the equation for the area of a rectangle, we get:

A = 120ft^2 = W*L = W*(W + 2ft)

120ft^2 = W*(W + 2ft)

Now we can solve this for W

120 ft^2 = W^2 + 2ft*W

Now we can rewrite this as:

W^2 + 2ft*W - 120ft^2 = 0

The solutions of this equation can be found by the Bhaskara's formula.

We know that for an equation of the form:

a*x^2 + b*x + c = 0

The two solutions are given by:

\(x = \frac{-b +\sqrt{b^2 - 4*a*c} }{2*a}\)

in our case, we have:

a = 1

b = 2ft

c = -120ft^2

Then the solutions for the equation W^2 + 2ft*W - 120ft^2 = 0 are:

\(W = \frac{-2ft + -\sqrt{(2ft)^2 - 4*1*(-120ft^2)} }{2*1} = \frac{-2ft +- 22ft}{2}\)

Then the two solutions are:

W = (-2ft - 22ft)/2 = -12ft  (this is a negative measure, does not have a real meaning in this case, so this solution can be discarded)

The other solution is:

W = (-2ft + 22ft)/2 = 10ft  (this is the correct solution)

Then the width is 10ft, and we know that the length is 2 ft longer than the width, then the length is:

L  = W + 2ft = 10ft + 2ft = 12ft

Answer:

2.4*18 = $43.2

stock price is $43.2

Step-by-step explanation:

The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

Now, For the greatest distance that can be filmed by a drone with a maximum altitude of 0.12 km, we can use the Pythagorean theorem.

Let's a right triangle with one leg being the radius of the Earth 6378 km and the other leg being the maximum altitude of the drone 0.12 km.

Hence, The hypotenuse of this triangle represents the line of sight from the drone's camera to the horizon.

Hence, By Using the Pythagorean theorem, we can solve for the length of the hypotenuse:

h² = 6378² + 0.12²

h = √40684000.145

h = 6374.5 km

Therefore, The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

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