For a standard-position angle determined by the point (x, y), what are the values of the trigonometric functions?

For the point (9, 12), find csc θ and sec θ.

A. csc θ = 5/4, sec θ = 5/3
B. csc θ = 5/4, sec θ = 4/5
C. csc θ = 3/5, sec θ = 4/5
D. csc θ = 3/4, sec θ = 3/5

The matrix expressions are:

The rule for matrix product states that:

If the dimensions of matrix A is m by n, and the dimension of matrix B is n by p.

Then, the dimension of the product matrix is: m by p

Using the above rule, we have:

Expression 1:

[tex]\left[\begin{array}{cc}12&7\\5&3\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right][/tex]

Expand:

[tex]\left[\begin{array}{cc}12a + 7c&12b + 7d\\5a + 3c &5b + 3d\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right][/tex]

By comparison, we have:

12a + 7c = 2

5a + 3c = 3

12b+ 7d = -1

5b + 3d = 2

Using a graphing tool, we have:

a = -15, b = -17, c = 26 and d = 29

Hence, the matrix expression is:

[tex]\left[\begin{array}{cc}12&7\\5&3\end{array}\right] * \left[\begin{array}{cc}-15&-17\\26&29\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right][/tex]

Expression 2:

[tex]\left[\begin{array}{cc}6.75&3\\-9&-4\end{array}\right] * \left[\begin{array}{c}a&b\end{array}\right] = \left[\begin{array}{c}8&5\end{array}\right][/tex]

Expand:

[tex]\left[\begin{array}{c}6.75a +3b\\-9a - 4b\end{array}\right] = \left[\begin{array}{c}8&5\end{array}\right][/tex]

By comparison, we have:

6.75a + 3b = 8

-9a - 4b = 5

Using a graphing tool, the system of equation has no solution

Hence, the matrix expression cannot be solved

Expression 3:

[tex]\left[\begin{array}{cc}-2&3\\-4&5\end{array}\right] * \left[\begin{array}{c}a&b\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right][/tex]

Expand:

[tex]\left[\begin{array}{c}-2a +3b &-4a +5b\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right][/tex]

By comparison, we have:

-2a + 3b = 6

3a + 5b = 8

Using a graphing tool,

a = 3 and b = 4

Hence, the matrix expression is:

[tex]\left[\begin{array}{cc}-2&3\\-4&5\end{array}\right] * \left[\begin{array}{c}3&4\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right][/tex]

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As all sides are equal it's equitorual hexagon

An inscribed hexagon is best fit for construction

Steps

Done ! We created

you can erase the circle later on

Answer:

Attachment 1

Take a compass and adjust it so that it is the width of line r.

Place the point of the compass on the left point of line r and draw a circle going through the right point of line r with radius r.

Attachment 2

Take a ruler, place it so it is against line r and extend the line r across the width of the circle (this is the diameter of the circle).

Attachment 3

Place the point of the compass on the right point of line r and draw a circle (blue circle).

Place the point of the compass on the left of the diameter and draw a circle (orange circle)

Attachment 4

The points of intersection of the 3 circles are the vertices of the hexagon.  

Attachment 5

Join the points of intersection with line segments - this is your hexagon with sides equal to r.

(If necessary, erase the circles to show the hexagon only.)

Answer: Ha

Step-by-step explanation:

The equation for the function g(x) = log₃(x+4) after applying the transformation x → (x+4).

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have equation of the graph:

[tex]\rm f(x) = log_3x[/tex]

Apply transformation in the parent function:

Replace x → (x+4)

The parent function will shift 4 units to the left.

And function becomes:

[tex]\rm g(x) = log_3(x+4)[/tex]

Thus, the equation for the function g(x) = log₃(x+4) after applying the transformation x → (x+4).

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Answer:

use ali result to estimate the probability of him winning the next solitaire game

Answer:

$1.05

Step-by-step explanation:

Find the unit price by dividing $0.75 by 5.

$0.75/5 = $0.15

Now find the price of 7 pencils by multiplying 7 and the unit price of $0.15.

$0.15 x 7 = $1.05

These are functions inside another function. The resulting composite function is given as (5x+9)^2 + 3

These are functions inside another function. Given the following functions

m(x) = x^2 +3

n(x) = 5x +9

We are to solve for the function m(n(x))

m(n(x)) = m(5x+9)

Substitute 5x +9 into m(x) to have:

m(n(x)) = (5x+9)^2 + 3

Hence the resulting composite function is given as (5x+9)^2 + 3

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An exponential function that represents the population is y = 5 (7)ˣ. And the population after 5 days will be 84035.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

The table is shown.

The exponential equation is given as

y = abˣ

Then at x = 1, y will be 35. Then we have

35 = ab ...1

Then at x = 2, y will be 245. Then we have

245 = ab² ...2

On solving equations 1 and 2. Then we have

a = 5 and b = 7

Then the exponential function will be

y = 5 (7)ˣ

Then the population after 5 days will be

y = 5 (7)⁵

y = 5 x 16807

y = 84035

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Answer:

3x×2c+1

Step-by-step explanation:

6x+15 =4c-12

[tex] \frac{6x + 15}{4c - 12} = \frac{4c - 12}{4c - 12} [/tex]

[tex] \frac{6x + 15}{4c - 12} [/tex]

[tex] \frac{3x + 5}{2c - 4} [/tex]

[tex]3x + 5 \div 2c - 4[/tex]

[tex]3x \times 2c + 5 - 4[/tex]

[tex]3x \times 2c + 1[/tex]

Answer: 25 in.

Step-by-step explanation:

A = bh

A = 5 x 5

A = 25

Answer:

6/63

Step-by-step explanation:

To find the probability in fraction form you must first add all the evidence together and then use that number as the denominator

Answer:

2/21

Step-by-step explanation:

There were a total of 7+6+12+19+19=63 spins, 6 of which blue.

So, you can make the fraction 6/63=2/21 to represent the probability of the spinner landing on blue the next spin

Answer:

Dependent

Step-by-step explanation:

Since the marble is not returned, the result of the second probability is dependent upon which marble was 1st drawn.

Answer:

134:346 Add the 33 to 101 to get first number, then total number of parks 346 is the second number, they may end up wanting you to to reduce the fraction.67:143

Answer:

2ft 2ft

Step-by-step explanation:

2ft,2ft,2ft,2ft

Answer:

A=

[tex]3(3m + 1)(3m - 1)[/tex]

Step-by-step explanation:

[tex] {27m}^{2} - 3[/tex]

Factorise

[tex]3( {9m}^{2} - 1)[/tex]

Rewrite it

[tex]3(( {3m)}^{2} - {1}^{2} )[/tex]

[tex]3(3m + 1)(3m - 1)[/tex]

Answer:

length= 5+ 12= 17

Step-by-step explanation:

will take width as x

then the length is x+12

perimeter = x+ x+12+x+x+12= 44

=4x= 44-24= 36

x= 20/4

x= 5

Answer:

pls that's the answer to the question. thanks.

The equation of the given circle with points  P(-10,10) and Q(6,-2) gives the diameter of a circle will be (x-2)² +(y-4)² = 100.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

Area of circle = πr²  and the perimeter of circle = 2πr where r is the radius of the circle.

Given that diameter of the circle is bounded by points P(-10,10) and Q(6,-2).

Centre coordinate = midpoint of P(-10,10) and Q(6,-2).

Midpoint of P(-10,10) and Q(6,-2)  

[(-10 + 6)/2 , (10-2)/2 ] = (-2,4 )

Diameter of circle = length between P(-10,10) and Q(6,-2).

lenth between P(-10,10) and Q(6,-2) = 10 units can be calculated by length formula.

The equation of a circle with a center (-2,4 ) and diameter of 10 is given by

(x-2)² +(y-4)² = 10² hence it will be correct.

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Answer:4.2

Step-by-step explanation:

14 times 70% subtracted from 4.2

The original price or cost price of a board game is 20.

The cost price is the price at which "goods are bought by merchant or retailer".

According to the question,

Joe paid 14.00 for a board game which is 70% of the original price or cost price.

In order to find cost price or original price. Let 'x' be the original price or cost price

70%  =  14

100% = x

x = [tex]\frac{1400}{70}[/tex]           [cross multiplication]

=20

Hence, the original price or cost price of a board game is 20.

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Answer:

  3° < x < 32.538°

Step-by-step explanation:

The possible values of the angle marked with an x-expression may not be as obvious as they first seem. There is a somewhat complicated interaction between the angle value and the length of the side(s) marked 'a'.

__

We can label the vertices of the figure A through D, clockwise from the bottom.

The minimum value of angle ACB (marked 3x-9°) is 0°. That will be its measure when AB +BC = AC, or B lies on line AC. In this case, the value of x is ...

  3x -9° = 0°

  3x = 9° . . . . add 9°

  x = 3° . . . . . divide by 3

value of 'a'

The maximum value of angle ACB will be found where both triangles are isosceles: AC ≅ BC ≅ DC. The length of 'a' can be found for that case using the Law of Sines:

  27/sin(93°) = a/sin(43.5°) . . . where (180° -93°)/2 = 43.5° is the base angle

  a = 27×sin(43.5°)/sin(93°) ≈ 18.611

value of 3x -9°

Angle ACB will obey the same Law of Sines requirement. If z represents the base angle in isosceles triangle ABC, then we have ...

  sin(z)/18.611 = sin(180-2z)/26

Recognizing that sin(180-2z) = sin(2z) and using the double-angle formula, we find ...

  sin(z)/18.611 = 2sin(z)cos(z)/26

  sin(z)(1/18.611 -cos(z)/13) = 0 . . . . . subtract the right side, factor

This has solutions that make the factors zero:

  sin(z) = 0   ⇒   z = 0 . . . . . . an extraneous solution in this case

  cos(z) = 13/18.611 ≈ 45.6925°

Then the value of x can be found from ...

  3x -9° = 180° -2z ≈ 88.615°

  x ≈ 3° +(88.615°/3) = 32.538°

_____

Additional comment

In the above, we have shown numerical values for the side lengths and angles in the maximum-x case. The various expressions can be combined to give ...

  3(x -3°) = 180° -2(arccos(13/27×sin(93°)/sin(43.5°)))

  x = 63° -2/3·arccos(13/27·sin(93°)/sin(43.5°))

Answer:

It will become 64 times larger

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

C is 17.

Use Pythagorean theorem to find c (hypotenuse)

[We can use this theorem because it is a right triangle]

a^2 + b^2 = c^2

8^2 + 15^2 = c^2

c^2 = 289

c = sqrt(289) = 17

Answer: c = 17 cm

Step-by-step explanation:

     Since this is a right triangle, we will use the Pythagorean theorem to solve. The a and b variables are legs, the c variable is the hypotenuse. Here, we are solving for the hypotenuse.

a² + b² = c²

8² + 15² = c²

64 + 225 = c²

64 + 225 = c²

289 = c²

c = [tex]\sqrt{289}[/tex]

c = 17

           Side c has a length of 17 cm.

Answer:

a. (-6, -3)

Step-by-step explanation:

A triangle has been dilated with a factor of 3.

New coordinates will be :

Therefore, A' will be :

Answer:5

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

y=x^2+6

Step-by-step explanation: Look at the vertex (0,6). We know the equation is quadratic so we know x^2. We know in the slope-interpect form equation the y-intercept is the term after the slope. The same applies in this equation. So that means the y intercept is 6 because y is 6 in the coordinate (0,6). We know the slope x^2. We need to plug that into the slope-intercept form equation.

The equation will be y=x^2+6.

Answer:

[tex]y = x^2 + 6[/tex]

Step-by-step explanation:

Vertex form for a parabola is [tex]y = a(x-h)^2 + k[/tex] where the vertex is [tex](h,k)[/tex]. Now for a vertex of (0,6), we can simply plug those values in for h and k: [tex]y = x^2 + 6[/tex].

Hope this helps!! :)

Answer:

p - 14.5 = 53

Step-by-step explanation:

The original price is p.

The discounted price is $14.50 less than p, or $14.50 subtracted from p. The discounted price is p - 14.5.

The discounted price is $53

Equation:

p - 14.5 = 53

The sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2

From the complete question, we have the following expressions:

(-x²+2x+3) and (-x²-2x-1)

Add both expressions

(-x²+2x+3) + (-x²-2x-1)

Expand

-x²+2x+3 -x²-2x-1

Collect the like terms

-x² -x² + 2x - 2x + 3 -1

Evaluate the like terms

-2x²+2

Hence, the sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2

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Answer:

  8 feet

Step-by-step explanation:

The length can be found using the volume formula with the known values. The resulting equation can be solved for the unknown value.

__

  V = LWH . . . . . volume of a prism is the product of its dimensions

  108 ft³ = l×(3 ft)×(4.5 ft) . . . . . known values filled in

  l = 108 ft³/(13.5 ft²) = 8 ft . . . . . . divide by the coefficient of length

The length of the prism is 8 feet.

Answer:

8ft

Step-by-step explanation: