3 parts: List the ratios for using angle A as the angle of reference reduce when necessary

Sin A= Cos A= Tan A=

Answer:

x2-14x+58=0

Two solutions were found :

x =(14-√-36)/2=7-3i= 7.0000-3.0000i

x =(14+√-36)/2=7+3i= 7.0000+3.0000i

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-14x+58

The first term is,  x2  its coefficient is  1 .

The middle term is,  -14x  its coefficient is  -14 .

The last term, "the constant", is  +58

Step-1 : Multiply the coefficient of the first term by the constant   1 • 58 = 58

Step-2 : Find two factors of  58  whose sum equals the coefficient of the middle term, which is   -14 .

     -58    +    -1    =    -59

     -29    +    -2    =    -31

     -2    +    -29    =    -31

     -1    +    -58    =    -59

     1    +    58    =    59

     2    +    29    =    31

     29    +    2    =    31

     58    +    1    =    59

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  1  :

 x2 - 14x + 58  = 0

Step  2  :

Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-14x+58

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   7.0000  

Plugging into the parabola formula   7.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 7.00 * 7.00 - 14.0 * 7.00 + 58.0

or   y = 9.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-14x+58

Axis of Symmetry (dashed)  {x}={ 7.00}

Vertex at  {x,y} = { 7.00, 9.00}

Function has no real roots

Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-14x+58 = 0 by Completing The Square .

Subtract  58  from both side of the equation :

  x2-14x = -58

Now the clever bit: Take the coefficient of  x , which is  14 , divide by two, giving  7 , and finally square it giving  49

Add  49  to both sides of the equation :

 On the right hand side we have :

  -58  +  49    or,  (-58/1)+(49/1)

 The common denominator of the two fractions is  1   Adding  (-58/1)+(49/1)  gives  -9/1

 So adding to both sides we finally get :

  x2-14x+49 = -9

Adding  49  has completed the left hand side into a perfect square :

  x2-14x+49  =

  (x-7) • (x-7)  =

 (x-7)2

Things which are equal to the same thing are also equal to one another. Since

  x2-14x+49 = -9 and

  x2-14x+49 = (x-7)2

then, according to the law of transitivity,

  (x-7)2 = -9

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-7)2   is

  (x-7)2/2 =

 (x-7)1 =

  x-7

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x-7 = √ -9

Add  7  to both sides to obtain:

  x = 7 + √ -9

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1

Since a square root has two values, one positive and the other negative

  x2 - 14x + 58 = 0

  has two solutions:

 x = 7 + √ 9 •  i

  or

 x = 7 - √ 9 •  i

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-14x+58 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =   -14

                     C   =   58

Accordingly,  B2  -  4AC   =

                    196 - 232 =

                    -36

Applying the quadratic formula :

              14 ± √ -36

  x  =    ——————

                     2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -36  =

                   √ 36 • (-1)  =

                   √ 36  • √ -1   =

                   ±  √ 36  • i

Can  √ 36 be simplified ?

Yes!   The prime factorization of  36   is

  2•2•3•3

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 36   =  √ 2•2•3•3   =2•3•√ 1   =

               ±  6 • √ 1   =

               ±  6

So now we are looking at:

          x  =  ( 14 ± 6i ) / 2

Two imaginary solutions :

x =(14+√-36)/2=7+3i= 7.0000+3.0000i

 or:

x =(14-√-36)/2=7-3i= 7.0000-3.0000i

Two solutions were found :

x =(14-√-36)/2=7-3i= 7.0000-3.0000i

x =(14+√-36)/2=7+3i= 7.0000+3.0000i

R

Step-by-step explanation:

The roots of the given quadratic equation are (7+i) and (7-i).

The given quadratic equation is:

[tex]x^{2} -14x=-50[/tex]

Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where a≠0.

We can write the above equation as:

[tex]x^{2} -14x+50=0[/tex]

Using the Shreedharacharya formula to solve a quadratic equation

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(-14)+-\sqrt{(-14)^2-4*1*50} }{2*1}[/tex]

[tex]x=7+i\\x=7-i[/tex]

Where i=√-1

Hence, the roots of the given quadratic equation are (7+i) and (7-i).

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Answer:

The maximum profit of $  10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) -C(x)

       = -31.72x^2 + 2,030x -( -126.96x + 26,391)

Distribute the minus sign

       = -31.72x^2 + 2,030x+126.96x - 26,391

 Combine like terms

      =   -31.72 x^2 + 2156.96 x - 26391

This is a parabola.  It is facing downwards.  The maximum profits is at the vertex ( where the max is)

vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34

Evaluate P(x) at x=34 to determine the profit

P(34) =  -31.72 (34)^2 + 2156.96 (34) - 26391

          -36668.32+73336.64-26391

          10277.32

The maximum profit of $10,243.32 can be made when the selling price of the dog food is set to $947.17. per bag.

1. Define the profit function: Profit [tex](\( P(x) \))[/tex] is calculated by subtracting the cost function [tex](\( C(x) \))[/tex] from the revenue function [tex](\( R(x) \)):[/tex]

[tex]\[ P(x) = R(x) - C(x) \][/tex]

2. Substitute the given revenue and cost functions:

[tex]\[ R(x) = -31.72x^2 + 2,030x \][/tex]

[tex]\[ C(x) = -126.96x + 26,391 \][/tex]

3. Plug in the revenue and cost functions into the profit function:

[tex]\[ P(x) = (-31.72x^2 + 2,030x) - (-126.96x + 26,391) \][/tex]

[tex]\[ P(x) = -31.72x^2 + 2,156.96x - 26,391 \][/tex]

4. Find the x-coordinate of the vertex of the profit function:

  The x-coordinate of the vertex is given by:

[tex]\[ x = \frac{-b}{2a} \][/tex]

  where [tex]\( a = -31.72 \) and \( b = 2,156.96 \).[/tex]

[tex]\[ x = \frac{-2,156.96}{2*(-31.72)} \][/tex]

  x ≈ 34

5. Calculate the maximum profit:

  Substitute x ≈ 34  into the profit function:

P(34) ≈ [tex]-31.72(34)^2 + 2,156.96(34) - 26,391[/tex]

P(34) ≈ 10,243.32

6. Determine the selling price per bag that maximizes profit:

  Plug x ≈ 34 into the revenue function to find the corresponding revenue:

[tex]\[ R(34)[/tex] ≈ [tex]-31.72(34)^2 + 2,030(34)[/tex]

[tex]\[ R(34)[/tex] ≈ [tex]32,183.68[/tex]

  Divide the revenue by the quantity x ≈ 34  to find the selling price per bag:

[tex]\[ \text{Selling price per bag}[/tex] ≈ [tex]\frac{32,183.68}{34}[/tex] ≈ [tex]947.17[/tex]

So, the maximum profit is approximately $10,243.32, and the selling price per bag that maximizes profit is approximately $947.17.

The expression that can be used to find the volume of the rectangular prism is 20825 cm³.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The formula for the volume of a rectangular prism is given by:

V = A x h

where A is the area of the base and h is the height of the prism.

In this case,

The area of the base is given as 245 cm^2 and the height is given as 85 cm.

Therefore, we can substitute these values into the formula to get:

V = 245 x 85

Multiplying these values together, we get:

V = 20825 cm³

Therefore,

The expression that can be used to find the volume of the rectangular prism is 20825 cm³.

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Answer:

x=4

Step-by-step explanation:

f(x) = 3x- 1 and g(x)=2x-3

f(2) means x=2

f(2) = 3(2)-1

f(2) = 6-1 =5

We want g(x) =5

5 = 2x-3

Add 3 to each side

5+3 = 2x-3+3

8 = 2x

Divide by 2

8/2 =2x/2

4=x

g(x) = f(2)  when x=4

Let x represent number of redwood trees and y represent number of spruce trees.

We have been given that a park ranger bought 12 trees. We can represent this information in an equation as:

[tex]x+y=12...(1)[/tex]

[tex]y=12-x...(1)[/tex]

We are also told that redwood trees cost $24 each, so cost of x redwood trees would be [tex]24x[/tex].

Each spruce tree costs $16, so cost of y spruce trees would be [tex]16y[/tex].

Since the park ranger spent $208 on trees, so we can represent this information in an equation as:

[tex]24x+16y=208...(2)[/tex]

Upon substituting equation (1) in equation (2), we will get:

[tex]24x+16(12-x)=208[/tex]

[tex]24x+192-16x=208[/tex]

[tex]8x+192=208[/tex]

[tex]8x+192-192=208-192[/tex]

[tex]8x=16[/tex]

[tex]\frac{8x}{8}=\frac{16}{8}[/tex]

[tex]x=2[/tex]

Therefore, the park ranger bought 2 redwood trees.

Upon substituting [tex]x=2[/tex] in equation (1), we will get:

[tex]y=12-x\Rightarrow 12-2=10[/tex]

Therefore, the park ranger bought 10 spruce trees.

The park ranger bought 2 redwood trees and 10 spruce trees.

To solve this problem, we can set up a system of equations based on the given information:

We have two pieces of key information:

This gives us two equations:

We can solve this system using substitution or elimination. Let's use substitution:

Therefore, the park ranger bought 2 redwood trees and 10 spruce trees.

Answer:

-2.4

Step-by-step explanation:

The solution to the given expression is -2.4.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

[tex]\frac{16.8 - 1.2^2}{-4.3+3(-0.7)} =\frac{16.8 - 1.44}{-4.3 +(-2.1)}\\\\\frac{15.36}{-4.3-2.1} =\frac{15.36}{-4.3-2.1}\\\\\frac{15.36}{-6.4} =\frac{15.36}{-6.4}[/tex]

-2.4 = -2.4

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Complete Question:

Evaluate the expression.

[tex]\frac{16.8 - 1.2^2}{-4.3+3(-0.7)} =\frac{16.8 - 1.44}{-4.3 +(-2.1)}[/tex]

The x-coordinate of the solution is -2 .

Answer:

V≈302ft^3

Step-by-step explanation:

The equation for finding volume of a cone with slant height and radius is 1/3πr^2√l^2-r^2 input the values and solve, then round to the nearest cubic foot and you get 302

Please mark as brainliest :)

Answer:

D

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

The hypotenuse is always the longest side of your right triangle and so the answer would be 26 since it is the largest number.

Answer:

24.39262183530094+33.33166662499792 is the answer

Step-by-step explanation:

57.72428846029885

therefore the first digit is 5

I want Brainliest

Answer:

57.7242884603 its 5

Step-by-step explanation:

Option C, [tex]y = 3x^2[/tex], is the equation that could represent the parabola with a vertex at (0, 0).

To determine which of the given equations could represent the parabola with a vertex at (0, 0), we need to consider the standard form of a parabolic equation: [tex]y = ax^2[/tex]

In this standard form, 'a' is a constant that determines the shape and orientation of the parabola. For a parabola with a vertex at (0, 0), the equation will be of the form [tex]y = ax^2[/tex].

Let's examine each option:

A. [tex]x = 3y^2[/tex]: This equation is not in the standard form [tex]y = ax^2.[/tex] It is a different type of equation and does not represent a parabola with a vertex at (0, 0).

B. x = -3y: Similarly, this equation is not in the standard form [tex]y = ax^2[/tex]. It represents a linear relationship between x and y, not a parabola.

C. [tex]y = 3x^2[/tex]: This equation is in the standard form [tex]y = ax^2[/tex], where a = 3. It represents a parabola with a vertex at (0, 0), so it could be the equation of the parabola in question.

D. y = -3: This equation is not in the standard form [tex]y = ax^2[/tex]. It represents a horizontal line with a constant value of -3, not a parabola.

Based on the analysis, Option C, [tex]y = 3x^2[/tex], is the equation that could represent the parabola with a vertex at (0, 0) in the standard form.

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1. outcome

2. probability

3. equally likely

4. likely

5. certain

6. unlikely

7. impossible

Hope this helps! If you have any more questions or need further clarification then please comment down below or message me! Good luck!

Answer:

A

Step-by-step explanation:

Focus on what the question is telling you, as it's given to you in the question. It's saying five times, which means "×5" the number of person B, so it'll always be 5 times quicker, since they're breathing more times in a certain period of time than person B.

Hopefully this helped!

Person A is breathing five times as fast as person B. Therefore, the period of the graph for person A is 5 times shorter than the period of the graph for person B.

In this scenario, person A is breathing five times as fast as person B. The period of a graph represents the time it takes for one complete cycle. Since person A is breathing faster, the period of their graph will be shorter than the period of person B's graph. So, the correct statement is:

The period of the graph for person A is 5 times shorter than the period of the graph for person B.

7+2+5=????? will mark brainest 14

Answer:

I think it is b but let me check my answer

Step-by-step explanation:

Answer:

A. (-6,0) I got it right

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

2.18 x 7.31 = 15.9358

15.9 + 4.92 = 20.85

20.85 = 4.5

4.5 , hope this helps! and have a great day

-Dhruva;)

The fraction 3/2 and square root of 2 are not equivalent because their decimal approximations (1.5 and about 1.41 respectively) are not the same.

To determine if a fraction like 3/2 is equal to the square root of 2, we would need to compare their decimal values.

First, divide 3 by 2 to get the decimal value for the fraction, which is 1.5.

For the square root of 2, we can use a calculator and find that its approximate decimal value is 1.41.

Therefore, since 1.5 is not equal to 1.41, the fraction 3/2 is not equivalent to the square root of 2.

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The fraction 3/2 is not equal to the square root of 2. By comparing the values directly or using fractional exponents, we can see that squaring 3/2 gives us 9/4, which is not equal to 2, and numerically the square root of 2 is approximately 1.414.

To determine if the fraction 3/2 is equal to the square root of 2, we can compare them directly or convert them into the same format. Recall that fractional exponents serve as another way to represent roots. Specifically, an exponent of 1/2 equates to taking the square root of a number. Thus, [tex](3/2)^{2}[/tex] would equal 3/2 multiplied by itself, which is 9/4, and that is not equal to 2. Therefore, 3/2 is not the square root of 2. We can also numerically evaluate the square root of 2, which is approximately 1.414, and see that it does not equal 3/2, which is 1.5.

Another consideration is that the square root of any number x can be expressed as [tex]x^{1/2}[/tex]. For instance, [tex](\sqrt{2})^2[/tex] = 2 because [tex](2^{1/2})^2[/tex] equals [tex]2^{1/2 * 2}[/tex] = 2. When we do this with 3/2, we would have [tex](3/2)^{1/2} * (3/2)^{1/2}[/tex] = 3/2, which does not satisfy the equation for the square root of 2. Therefore, 3/2 is not equal to the square root of 2.

Answer:

C= 72

Step-by-step explanation:

Because if AB=3 and AC= 9 and you solve and find all the side lengths you will get 71.565 for m<B and you round to the nearest degree its 72. Hopefully this helps you and you get it right. But I'm 100% it is 72.

Answer:

∠ B ≈ 72°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan B = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{9}{3}[/tex] = 3 , thus

B = [tex]tan^{-1}[/tex](3) ≈ 72° ( to the nearest degree )

Answer:

4

Step-by-step explanation:

First you would need to look at the line at the right. It has 2 parts, 3 and 2. When added you get 5.

As when you look at the other side it only has 2 and x.

To make it simple 5 - 1 = 4.

That is your final answer.

Hope this helps!

Answer:

x = 4

Step-by-step explanation:

In triangle BAC, DE || AC.

Therefore, by basic proportionality theorem:

[tex] \frac{x + 2}{x} = \frac{3}{2} \\ 2(x + 2) = 3x \\ 2x + 4 = 3x \\ 4 = 3x - 2x \\ 4 = x \\ x = 4[/tex]

Answer:

y= 2x + 1

Step-by-step explanation:

We are asked to write an equation of that line that passes through points (3, 7) and (5, 11).

First of all, we will find slope of our given line using the coordinates of given points as:

Now, we will write our given equation in slope-intercept form , where m represents slope and b represents y-intercept.

Let us find the y-intercept using coordinates of point (3,7) and slope as:

Therefore, our required equation in slope-intercept form would be.

Answer:

Its 25.

Step-by-step explanation:

Answer: +25

Step-by-step-Explanation: Absolute value means distance from zero on a number line.

So for the absolute value of -25, it's important to understand

that -25 is 25 units from zero on a number line.

So the absolute value of -25 is +25.

Whenever you are asked to find the absolute value of a negative number, just think about finding the positive version of that number.

Answer:

BACD the third one I hope that this is right

The correct quadrilateral which is a trapezoid is shown in image 3.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are three figures are shown.

Now, We know that;

A trapezoid, which is also known as a trapezium, is a closed shape which having 4 straight sides, with one pair of parallel sides.

Hence, By given figures.,

The correct quadrilateral which is a trapezoid is shown in image 3.

Because it has one pair of parallel sides.

Thus, The correct quadrilateral which is a trapezoid is shown in image 3.

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Answer:

120 minutes

Step-by-step explanation:

15 x 8 = 120

40 x 3 = 120

The Number of hours passed for both buses to arrive at the same time is the value of the least common multiple of the stop made by each bus. Hence, 120 minutes will pass before the buses arrive at the same time.

Bus route A = 15 minutes

Bus route B = 40 minutes

Multiples of :

The least multiple common to both 15 and 40 is 120.

Therefore, 120 minutes will pass before both buses arrive at the same time.

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Answer:

Point R

Step-by-step explanation:

Go back 12 points

Answer:

Point R

Step-by-step explanation:

Count back in points and you will figure it out