question attached, it's trig

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em} \textit{we know that} \begin{cases} y=0.1\\ x=0.2 \end{cases} \\\\\\ 0.1=k(0.2)\implies \cfrac{0.1}{0.2}=k\implies 0.5=k\hspace{5em}\boxed{y=0.5x}[/tex]

The value of the exponential function (-1) will be equal to f(-1) = -0.02.

The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects.

Given that f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55. The value of the exponential function will be calculated as,

[tex]y=ax^b[/tex]

[tex]11=a(-3)^b\\55=a(4)^b[/tex]

Calculate the value of constants,

log5 = blog(4 / 3)

b = 0.7 / 0.125

b = 5.6

The value of 'a' will be,

11 = a(-3)⁵°⁶

a = -0.02

The exponential function f(-1) will be calculated as,

f(-1) = -0.02(-1)⁵°⁶

f(-1) = -0.02

Therefore, the value of the exponential function (-1) will be equal to f(-1) = -0.02.

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Answer:

Inequality:

Graph choice:

Step-by-step explanation:

Inequality

It says at least 90, which means we have to use the greater than or equal to sign

Our inequality so far: 90≥______

Now it says you earn 7 dollars per hour, which means 7 times the number of hours you work or 7h. Our inequality now looks like this:

90≥7h

The answer choice that matches is A (90≥7h = 7h≤90)

For the second question on the bottom, I added an image.

(Answer is B)

Of the part, the whole, and the percent, an information which is still unknown to Ms. Morgan is the number of non-athletes and it is equal to 84 students.

Of the part, the whole, and the percent, an information which is still unknown to Mr. Gregory is the total number of students and it is equal to 180 students.

Since the Ms. Morgan found that​ 30% of her 120 students are athletes, the known and unknown values include the following:

Known value (whole) = 120 students.

Known value (percent) = 30%

Unknown value (part) = ?

Next, we would determine the unknown value as follows:

Number of athletes = 30/100 × 120

Number of athletes = 30 × 1.2

Number of athletes = 36 students.

Unknown value (non-athletes) = 120 students - 36 students

Unknown value (non-athletes) = 84 students.

Since Mr. Gregory found that​ 27, or​ 15%, of his student are athletes, the known and unknown values include the following:

Known value (part) = 27 students.

Known value (percent) = 15%

Unknown value (whole) = ?

For the unknown value, we have:

Let the variable T represent the total number of students.

15/100 × T = 27

0.15T = 27

Total number of students, T = 27/0.15

Total number of students, T = 180 students.

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Complete Question:

Ms. Morgan is a science teacher. She found that​ 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that​ 27, or​ 15%, of his student are athletes. Complete parts a and b below.

a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value.  

b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.​

The statement which is true about the y-values of the graph of the function as required is; Choice B; The y-values are all greater than or equal to 2.

It follows from the task content that the statement which is true regarding the y-values of the graph defined by; f(x) = lx-5l +2 is to be determined.

Therefore, we must recall that expressions enclosed in the absolute value sign upon evaluation are always greater than or equal to zero.

Hence, it can be concluded that we the y-values of the resulting graph to be greater than or equal to 2 (on the occasion that; lx-5l = 0).

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For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.

As given in the question,

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( -9, 5 )

( -9 , 5 ) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = -9

Altitude = 5

Using Pythagoras theorem,

Hypotenuse² = (-9)² + (5)²

⇒ Hypotenuse = √106

cos ∅ = -9 / √106

sec ∅ = 1/ cos ∅

         = - √106/9 ( simplest radical form )

Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of

sec∅= ( - √106/ 9 )  in simplest radical form.

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By using percentage, it can be calculated that

1) Percentage increase in area = 25 %

2) Percentage increase in area = 60 %

3) Percentage decrease in area = 25 %

4) Percentage decrease in area = 40 %

What is percentage?

Sometimes there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100

1) Original area = 12 sq. yard

   New area = 15 sq. yard

   Increase in area = 15 - 12 = 3 sq. yard

   Percentage increase = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 15 sq. yard

   New area = 24 sq. yard

   Increase in area = 24 - 15 = 9 sq. yard

   Percentage increase = [tex]\frac{9}{15}\times 100 \\[/tex]

                                       = 60 %

1) Original area = 12 sq. yard

   New area = 9 sq. yard

   Increase in area = 12 - 9 = 3 sq. yard

  Percentage decrease = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 10 sq. yard

   New area = 6 sq. yard

   Increase in area = 10 - 6 = 4 sq. yard

   Percentage increase = [tex]\frac{4}{10}\times 100 \\[/tex]

                                       = 40 %

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Rearranging the equation, making h the subject of the formula, h =  v² / 2g

we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.

In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.

In our case the the formula needs to be rearrange to make h the subject of the formula.

Therefore,

v = √2gh

square both sides of the equation

v² = (√2gh)²

v² = 2gh

divide both sides by 2g

v² / 2g = 2gh / 2g

h = v² / 2g

Therefore,

h = v² / 2g

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Answer: 2-i

Step-by-step explanation:

multiply the fraction by 3-i/3-i

The equation to illustrate the information when the football team travels to an away game is 5c + 9v = 47.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let cars = c

Let van = v

The equation will be 5c + 9v = 47.

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Answer:

P(x) = 0.7 [tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

Step-by-step explanation:

given a polynomial with roots x = a and x = b , then the factors are

(x - a) and (x - b)

If x = a is of multiplicity 2 then factor is (x - a)²

the polynomial is then the product of the factors

p(x) = a(x - a)(x - b) ← a is a multiplier

give x = 4 is a root with multiplicity 2 then (x - 4)² is the factor

x = 0 has factor (x - 0) , that is x

x = - 1 has factor (x - (- 1)) , that is (x + 1)

the polynomial is then the product of the factors

P(x) = ax(x + 1)(x - 4)² ← expand squared factor using FOIL

       = ax(x + 1)(x² - 8x + 16)

       = a(x² + x)(x² - 8x + 16) ← distribute

       = a([tex]x^{4}[/tex] - 8x³ + 16x² + x³ - 8x² + 16x)

      = a([tex]x^{4}[/tex] - 7x³ + 8x² + 16x)

to find a substitute (5, 21 ) into P(x)

21 = a([tex]5^{4}[/tex] - 7(5)³ + 8(5)² + 16(5))

21 = a(625 - 875 + 200 + 80)

21 = 30a ( divide both sides by 30 )

0.7 = a

then

P(x) = 0.7([tex]x^{4}[/tex] - 7x³ + 8x² + 16x) ← distribute parenthesis

P(x) = 0.7[tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x

In the given circle, the values of required angles are as follow:

a = 51°, b = 28° , c = 31°, and d = 70°.

As given in the question,

In the given circle,

As we know by theorem , angles formed in the same arc are congruent.

Angle a° and angle 51° is formed in the same arc XY .

⇒ Value of a = 51°

Angle b° and angle 28° is formed in the same arc ZY .

⇒ Value of b = 28°

Angle c° and angle 31° is formed in the same arc WX .

⇒ Value of c = 31°

Angle d° and angle 70° is formed in the same arc WZ .

⇒ Value of d = 70°

Therefore, in the given circle the values of required angles are as follow:  a = 51°, b = 28° , c = 31°, and d = 70°.

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The way that zeros of a polynomial function is related to the equation and graph of a function because they act as solutions to the equation and also x-intercepts of a graph.

When the quadratic equation's graph crosses the x-axis, those points are known as the zeros of the equation.

The graph's x-intercepts and a function's zeros are the same thing. If the zero of f has an odd multiplicity, the graph of f will cross the x-axis at that x value. The x-axis will be touched by the graph of f if it has an even multiplicity zero.

Hence, A polynomial's zeros are the answers to any equation such as p(x) = 0, where p(x) stands for the polynomial. Since the values of x where y = 0 if we graph this polynomial as y = p(x). In other words, these are the graph's x-intercepts.

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The measure of each angle of a regular 22-gon is 163.6 degrees.

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

Polygon can be named base on the number of sides they possess. For example pentagon has 5 sides, hexagon has 6 sides, heptagon has 7 sides, octagon has 8 sides, nonagon has 9 sides and decagon has 10 sides.

Therefore, a regular polygon is one which sides and angles are congruent.

A regular  22-gon has 22 sides.

The measure of each angle of 22-gon can be found as follows;

angle= 180(n - 2) / n

where

n = number of sides

angle = 180 (22 - 2) / 22

each angle = 180(20) / 22

each angle = 3600 / 22

Therefore,

each angle =  163.636363636

each angle = 163.6 degrees.

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The equation of lines are (a) x - 2y + 6 = 0

                                          (b) 2x - y - 4 = 0

                                          (c) x - y + 1 = 0

                                          (d) 4x + 3y + 4 = 0

Slope-intercept form of the equation -> y = mx + c

Slope = m = [tex]\frac{y2-y1}{x2-x1}[/tex]

(a) A(0,3) and B(6,6)

    m = [tex]\frac{6-3}{6-0}[/tex]

        = 3/6

        = 1/2

    Putting the value in equation,

     3 = (1/2)*0 + c

     c = 3

   Equation -> y = (1/2)x + 3

                     2y = x + 6

          x - 2y + 6 = 0  

(b) A(0,-4) and B(5,6)

    m = [tex]\frac{6+4}{5-0}[/tex]

        = 10/5

        = 2

    Putting the value in equation,

     -4 = (2)*0 + c

     c = -4

   Equation -> y = (2)x - 4

          2x - y - 4 = 0  

(c) A(-4,-3) and B(2,3)

    m = [tex]\frac{3+3}{2+4}[/tex]

        = 6/6

        = 1

    Putting the value in equation,

     3 = (1)*2 + c

      3 = 2 + c

      c = 3 - 2

      c = 1

   Equation -> y = (1)x + 1

                       y = x + 1

             x - y + 1 = 0  

(d) A(-6,4) and B(3,-8)

    m = [tex]\frac{-8-4}{3+6}[/tex]

        = -12/9

        = -4/3

    Putting the value in equation,

     -8 = (-4/3)*3 + c

     -8 = -4 + c

      c = -8 + 4

      c = -4

   Equation -> y = (-4/3)x - 4

                     3y = -4x - 4

       4x + 3y + 4 = 0  

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Answer:

Step 1: Simplify both sides of the equation.

1/3(6y+3)−24 = 3(1/3y−6)

1/3(6y) + 1/3(3) -24 = 3(1/3y) + 3(-6)

2y +1 −24 = y−18

2y −23 = y −18

Subtract y from both sides.

2y−23−y=y−18−y

y−23=−18

Step 3: Add 23 to both sides.

y−23+23 = −18+23

y = 5

Step-by-step explanation:

The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).

The first and the second differences are:

x            y              first differences                second differences

4            18                      ----

5            28                      10                                        ------

6            35                      7                                        -3

7            39                      4                                        -3

8            40                      1                                         -3

9            38                      -2                                        -3

The values of second differences are constant, therefore, the relation is linear.

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By solving a linear equation, it can be calculated that

The space station is at a distance of 144000 miles from NASA headquarters

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let the space station be d miles from NASA headquarters

Speed of the first rocket = 19200 miles/hour

Speed of the second rocket = 18000 miles /hour

Time taken by the first rocket to reach the space station = [tex]\frac{d}{19200}[/tex]

Time taken by the second rocket to reach the space station = [tex]\frac{d}{18000}[/tex]

By the problem,

[tex]\frac{d}{18000} - \frac{d}{19200} = 0.5\\\\\frac{16d - 15d}{288000} = 0.5\\\\\frac{d}{288000} = 0.5\\\\d = 288000 \times 0.5\\\\d = 144000 \ miles[/tex]

The space station is at a distance of 144000 miles from NASA headquarters

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Answer:

x ≥ 4

Step-by-step explanation:

-4 ( 8 - 3x ) ≥ 6x - 8

First, solve the brackets.

- 32 + 12x ≥ 6x - 8

Subtract 6x from both sides.

- 32 + 12x - 6x ≥ - 8

- 32 + 6x ≥ - 8

Add 32 to both sides.

6x ≥ - 8 + 32

6x ≥ 24

Divide 6 by both sides.

x ≥ 4

The number of ways to fill the tic-tac-toe grid, with at least 4 of each symbol in the grid, using the arrangements formula, is of:

252.

The number of possible arrangements that can be chosen from a set of n elements is given by the factorial of n, as follows:

[tex]A_n = n![/tex]

When the elements arranged can be repeated, the number of arrangements is presented as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1! \times n_2! \cdots n_3!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] represent the number of repetitions of each element.

For the tic-tac-toe grid, we have that the possible ways to organize the nine positions with at least four instances of each symbol is given as follows:

Hence the number of ways to fill up the grid is given as follows:

[tex]\frac{9!}{5!4!} + \frac{9!}{4!5!} = 2 \times 156 = 252[/tex]

Thus 252 ways to fill up the grid.

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The simple interest that Nike will receive after 2 years is $500.

The principal amount =$5000

Rate = 5% = 0.05

Time = 2 years

Now simple interest = PRT = 5000 × 0.05 × 2 = 500

Hence the simple interest earned by Nike is $500

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.

Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.

A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.

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Answer:

2:20

Step-by-step explanation:

The movie started at 3:00 PM they got there at 2:45. and it took them 25 mins to get there meaning they left at 2:20.

Answer: 0

Step-by-step explanation:

If the dividend and the divisor are the same, the quotient is always 1. If the dividend is the, then the quotient would always be 0. A division equation with 0 dividend and 0 divisor is not valid.

Answer: All real numbers

Step-by-step explanation: Anything that's being divided by 0, is always going to be 0. For example, 0/7 is always 0.

Answer:

94.1224489796

this is the answer

The number that is closest to the mean of the distribution is 4 (option C)/

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.  

Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.

Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)

Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16

Mean = 64 / 16

Mean = 4

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The lines p and q are parallel.

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines, but on opposite sides of the transversal.

Given a figure,

Since, ∠ 1 ≅ ∠ 5 and they are alternate exterior angles, then we can conclude that p║q by alternate exterior angles theorem.

Hence, The lines p and q are parallel.

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The partial fraction is proved.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=3x²+8x+4/(x²-4)(3x-2)

=3x2+8x+4/(x2-4)(3x-2)

= 3x2+6x+2x+4/(x2-4)(3x-2)

=3x(x+2)+2(x+2)/(x2-4)(3x-2)

Hence proved, l.h.s = r.h.s

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