Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:
A. 19 p
B. 20 p
C. 21 p
D. 18 p

The solution to given expression tan(2θ) is 22.615°

For given question,

We have been given an expression tan(2θ)

Given that cos(θ) = 5/13, and θ is in quadrant 1.

We know that the trigonometric identity

sin²θ + cos²θ = 1

⇒ cos²θ = (5/13)²

⇒ sin²θ = 1 - 25/169

⇒ sin²θ = 169 - (25/169)

⇒ sin²θ = 144/169

⇒ sin(θ) = 12/13

We know that the identity cos(2x) = cos²x - sin²x

⇒ cos(2θ) = cos²θ - sin²θ

⇒ cos(2θ) = 25/169 - 144/169

⇒ cos(2θ) = -119/169

And sin(2x) = 2sin(x)cos(x)

⇒ sin(2θ) = 2sin(θ)cos(θ)

⇒ sin(2θ) = 2 × 12/13 × 5/13

⇒ sin(2θ) = 120/169

We know that, tan(x) = sin(x)/cos(x)

⇒ tan(2θ) = sin(2θ)/cos(2θ)

⇒ tan(2θ) = (120/169) / (-119/169)

⇒ tan(2θ) = 120 / (-119)

⇒ tan(2θ) = -1.008

Since θ is in quadrant 1, tan(2θ) = 1.008

⇒ 2θ = arctan(1.008)

⇒ 2θ = 45.23

⇒ θ = 22.615°

Therefore, the solution to given expression tan(2θ) is 22.615°

Learn more about the expression here:

https://brainly.com/question/14961928

#SPJ4

The system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:

To find the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse:

The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k

Where (h, k) is the vertex of the parabola, a is constant.

For the sailboat we have vertex: (h, k) = (2, -6) and one point: (-7, 8) that is f(-7) = 8.

We will find a using f(-7) = 8:

The quadratic function for the sailboat is given by:

The equation for a circle with a radius of 5 and center (1, 2) is:

Therefore, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:

Know more about equations here:
https://brainly.com/question/22688504

#SPJ4

The correct form of the question is given below:
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?

The probability that the outcome is red then yellow is 0.036.

Given that in a jar there are 8 red marbles, 1 yellow marble and 6 green marbles.

We are required to find the probability of obtaining a red then yelow marble if two marbles are drawn and replacement is used.

Probability is the calculation of finding the chance of happening a event among all the events possible. It lies between 0 and 1.

Probability=Number of items/ Total items.

Number of red marbles=8

Number of yellow marble=1

Number of green marbles=6

Total marbles=15

Probability of obtaining red marble=8/15

Probability of obtaining yellow marble=1/15 (Because replacing is there so the number of total marbles do not decrease)

Required probability=8/15*1/15

=8/225

=0.035555

After rounding off we will get 0.036.

Hence the probability that the outcome is red then yellow is 0.036.

Question is incomplete. The following line should be included in question:

A jar contains 8 red marbles , a yellow marble and 6 green marbles.

Learn more about probability at https://brainly.com/question/24756209

#SPJ4

The measure of the side SQ from the given diagram is 19/6

Similar shapes are shapes that has equal length and equal side measures and angles.

From the given diagram, the measure of the sides TSis congruent to SP and the measure of MS is congruent to SQ.

Using the expression below to determine the value of x

MS/ST = SQ/SP

Given the following parameters

MS =30

ST = 10

SQ = 6x-1

SP =  3 - 2x

Substitute the given parameters into the formula to have:

30/10 = 6x-1/3-2x

Cross multiply

10(6x-1) = 30(3-2x)

Expand

60x - 10 = 90 - 60x

60x + 60x = 90 + 10

120x = 100

x = 10/12

x = 5/6

Determine the measure of SQ

SQ = 6x - 1

SQ = 5(5/6) - 1

SQ = 25/6  - 1

SQ = 19/6

Hence the measure of the side SQ from the given diagram is 19/6

Learn more on similar triangles here: https://brainly.com/question/4163594

#SPJ1

Answer:

1st option

Step-by-step explanation:

to find f(g(x)) substitute x = g(x) into f(x) , that is

f(g(x))

= f(4x - 5)

= 2(4x - 5) + 1 ← distribute parenthesis

= 8x - 10 + 1

= 8x - 9

Answer:

[tex]Question 1\\1+i\\-1-i\\Question 2\\\\-1+i\\1-i[/tex]

Step-by-step explanation:

Complex Numbers:

   Complex numbers can generally be expressed in the form: [tex]a+bi[/tex] where a and b are both real numbers, with the a part representing the real part of the complex number, and the bi representing the imaginary part.

   We can also graph these numbers using the complex plane. The complex plane has the real axis where the x-axis would normally be, and the imaginary axis where the y-axis would normally be. So by this definition the "a" is what determines the horizontal position or the position on the real axis and the "b" is what determines the vertical position or the position on the imaginary axis.

I attached a diagram of the complex plane, and it's essentially the same as a normal graph, with a=x, and b=y.

Question 1:

So when a complex number lies above the real-axis, that means the imaginary part is greater than 0. When a complex numbers lies to the right of the imaginary axis, that means the real part is greater than 0.

This means we have the form: [tex]a+bi \text { where } a > 0 \text{ and } b > 0[/tex]. You can literally plug in any number for a and b, so long as it fits this. For example we can just do: [tex]1+i[/tex]

So when a complex number lies below the real-axis, that means the imaginary part is less than 0. when a complex numbers lies to the left of the imaginary axis, the real part is less than 0.

This means we have the form: [tex]a+bi \text { where } a < 0\text{ and }b < 0[/tex]. You can plug in any real number that lies within this restriction. An example would be:

[tex]-1-i[/tex]

Question 2:

Above real axis and to the left of the imaginary axis means: b>0 and a<0. So we can plug in any number into the standard form that fits this restriction. an example would be: [tex]-1+i[/tex]

Below real axis and to the right of the imaginary axis means: b<0 and a>0. So we can plug in any number into the standard form that fits this restriction. An example would be: [tex]1-i[/tex]

The value of n from the given expression is 5.5

Fractions are expression written as a ratio of two integers. The linear equation on the other hand has a leading degree of 1.

Given the equation below;

n/11 = 3.5/7

Simplify to have

n/11 = 1/2

Cross multiply the given result to have:

11 = 2n

Swap

2n = 11

Divide both sides by 2 to have;

2n/2 = 11/2

n = 5.5

Hence the value of n from the given expression is 5.5

Learn more on linear equation and fraction here: https://brainly.com/question/11955314

#SPJ1

The area of the triangle rounded to the nearest tenth is 33.3 squared inches.

Given the data in the diagram;

First we find the dimension of side b.

From the rule of cosines.

b = √[ a² + c² - 2acCosB ]

We substitute into the formula.

b = √[ 7² + 13² - ( 2 × 7 × 13 × cos( 133° ) ]

b = √[ 49 + 169 - ( 182 × cos( 133° ) ) ]

b = √[ 218 - 182×cos( 133° ) ]

b = √[ 342.1237 ]

b = 18.5

Next, we find angle C.

From rule of cosines.

cosC = [ b² + a² - c² ] / 2ba

cosC = [ 18.5² + 7² - 13² ] / [ 2 × 18.5 × 7 ]

cosC = [ 342.25 + 49 - 169 ] / [ 259 ]

cosC = [ 222.25 ] / [ 259 ]

cosC = [ 0.8581 ]

C = cos⁻¹[ 0.8581 ]

C = 30.9°

Now, we can find the area of the triangle.

Area = [ ab × sinC ] / 2

Area =  [ 7 × 18.5 × sin( 30.9 ) ] / 2

Area =  [ 129.5 × 0.51354 ] / 2

Area =  66.5 / 2

Area = 33.3 in²

The area of the triangle rounded to the nearest tenth is 33.3 squared inches.

Learn about cosine rule here: brainly.com/question/20839703

#SPJ1

The simplest form is 10.

We can find simplest as form:

Given, fractions are [tex]9\frac{1}{6}[/tex] and [tex]1\frac{1}{11}[/tex]

[tex]9\frac{1}{6}\times 1\frac{1}{11}[/tex]

[tex]\frac{55}{6}\times \frac{12}{11}[/tex]

[tex]=\frac{55\times 12}{6\times 11}[/tex]

=10

Hence, simplest form of given fraction is 10.

Learn more about fractions here:

https://brainly.com/question/78672

#SPJ1

The type of model that best fits the given situation is; A linear equation  Model

Right inside the local reservoir we will have an initial amount of water A.

Now, for every hour that passes by, the amount of water in the reservoir decreases by 500 gals.

Thus, after t hours, the amount of water in the reservoir is expressed as:

W = A - 500gal * t

This is clearly a linear equation model and so we can conclude that the model that fits best in the given situation is a linear model.

The domain of this model is restricted because we can't have a negative amount of water in the reservoir,  and as such the maximum value of t accepted is: W = 0 = A - 500gal*t

t = A/500 hours

Therefore, the domain of this linear relation is: t ∈ {0h, A/500 }

Read more about Equation model at; https://brainly.com/question/25896797

#SPJ1

The answer is tenths

Step-by-step explanation:

According to the place value chart of decimals,the first number after the decimal point starts from tenths and continues.so the answer is tenths

Hi :)

Remember Place value in decimal numbers

[tex]\large\boldsymbol{\hfill\stackrel{hundreds}{9}~\hfill\stackrel{tenths}0~\hfill\stackrel{ones}6.\hfill\stackrel{tenths}{7}}[/tex]

Then

The place-value of [tex]\boldsymbol{7}[/tex] is [tex]\boldsymbol{tenths}[/tex].

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

The area of the region is: 63.585 square inches.

If we have a circle of radius R, the area of said circle is:

A = pi*R^2

Particularly, if we have a section of the circle defined by an angle θ, the area of that region is:

A = (θ/2pi)*pi*R^2 = (θ/2)*R^2

In this case we have:

θ = 90° = pi/2

R = 9in

Replacing that we get:

A = (pi/4)*(9in)^2 = (3.14/4)*(9in)^2 = 63.585 in^2

If you want to learn more about circles:

https://brainly.com/question/1559324

#SPJ1

Answer:

y = - 2x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - 2x - 1 ← equation of line

The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.

The correct option is D.

A quadratic equation is an algebraic equation of the second degree in x.. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

Total area  = 7 square feet

and,

Total area = Length x Width

So,

7 = (2x + 3)(2x + 2)

7 = 4x2 + 4x + 6x + 6

7 = 4x2 + 10x + 6

4x2 + 10x + 6 - 7 = 0

4x2 + 10x - 1 = 0

Hence,

The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.

To know more about quadratic equation visit:

https://brainly.com/question/1863222

#SPJ4

I understand that the question you are looking for is:

Mary wants to hang a mirror in her room. the mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long.  Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. Which quadratic equation can be used to determine the thickness of the frame, x?

A. x² + 14x - 2 = 0

B. 2x² + 10x - 7 = 0

C. 3x² + 12x - 7 = 0

D. 4x² + 10x - 1 = 0

Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]

d₁ = 16 yd

Area = 72 yd²

Rhombus Area =>

[tex]\frac{16 * d2}{2} = 72[/tex]

16*d₂ = 144

d₂ = 9

AC = 9 yd

Hope it helps!

[tex](\frac{3}{2},\frac{5}{2})[/tex]

The first equation can be rearranged by subtracting y from both sides. This gives you x = 4 - y.

The second equation is x = y - 1

Therefore, as both equations are equal to x, you can say that they are equal to each other, so 4 - y = y - 1.

If you add 1 to each side, you get 5 - y = y

If you add y to each side, you get 5 = 2y

Divide both sides by 2 to get y = 5/2

Now you can substitute 5/2 for y. For example, the second equation becomes x = 5/2 - 1

x is therefore 3/2

This can  be written as [tex](\frac{3}{2},\frac{5}{2})[/tex], which is the final answer.

After reflected over  the triangle the point a become A = (-1,-6). The option c is correct.

According to the statement

we have given that the a triangle ABC at the points A=(1,6) B=(-3,5) C=(7,1), and we have to find the points of a when the triangle is first reflected over the y axis.

So, For this purpose

we know that the when the triangle is at the x axis then the point A is A=(1,6).

But when the triangles reflected over the y - axis then the point A goes to the negative side of the graph. In other  words whole of the triangle shift to the negative side of the graph. That's why the point become negative.

So, The option c is correct. After reflected over  the triangle the point a become A = (-1,-6)

Learn more about Triangle here

https://brainly.com/question/1675117

#SPJ1

On a number line, an absolute value equation that has the given solution set is |m - 4| = 2.

By critically observing the given question, we can infer and logically deduce that the solution sets for this absolute value equation is given by:

m = {2, 6}

Next, we would calculate the mean of the solution sets as follows:

m₁ = (2 + 6)/2

m₁ = 8/2

m₁ = 4.

Also, we would calculate the difference in the solution sets as follows:

m₂ = (6 - 2)/2

m₂ = 4/2

m₂ = 2.

Mathematically, the absolute value equation is given by:

|m - m₁| - m₂ = 0

|m - 4| - 2 = 0

|m - 4| = 2.

Read more on absolute value equation here: https://brainly.com/question/27197258

#SPJ1

Answer: C

Step-by-step explanation:

The time spent practicing and the number of free throws made has a positive correlation. The number of items bought and the checking account balance has a negative correlation. The height of baseball player and the

number of hits made has no correlation.

About positive correlation:

Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation.

About negative correlation:

A negative or inverse relationship between two variables in statistics exists when higher values of one variable tend to be correlated with lower values of the other. Such scenarios have negative correlation.

About no correlation:

When two events or variables are unaffected by each other or are not inter-related, they are said to possess no correlation.

Learn more about correlation here:

https://brainly.com/question/27886995

#SPJ1

Answer:

option 1 is positive option 2 is negative option 3 is none

Step-by-step explanation:

Enginuity said so

The sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt

The given parameters are

Stuffed toys, n = 3

Toys to arrange, r = 3 i.e. teddy bear (t), a kitten (k), and an elephant (e).

The number of arrangement is calculated as;

Ways = nPr

Substitute the known values in the above equation

Ways = 3Pr

Apply the permutation formula

Ways = 3!/0!

0! =1

So, we have

Ways = 3!/1

This gives

Ways = 3!

Expand

Ways = 3 * 2 * 1

Evaluate

Ways = 6

This means that the sample size is 6

Hence, the sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt

Read more about sample space at

https://brainly.com/question/3119162

#SPJ1

In words (6 + q) - xy is six added to a number subtracted from the product of two numbers

The problem is a algebraic expression

A algebraic expression  a mathematical expression containing one or more variables used to express a word problem

We want to convert the algebraic expression (6 + q) - xy into a word problem.

So, (6 + q) - xy in words is six added to a number subtracted from the product of two numbers

Learn more about algebraic expression here:

https://brainly.com/question/4758002

#SPJ1

(a) The velocity when the particle reaches B is 8 m/s.

(b) The distance between point A and B is 5.33 m.

(c) The value of t when the particle reaches C is 1.63 seconds.

(d) The distance AC​ is 8.7 m.

The velocity when the particle reaches B is calculated as follows;

v = ∫a. dt

where;

v =  ∫(4t . dt)

v = 4t²/2

v = 2t²

v(2) = 2(2)²

v(2) = 8 m/s

Thus, the velocity when the particle reaches B is 8 m/s.

x = ∫v

where;

x = ∫2t². dx

x = ²/₃t³

x(2) = ²/₃(2)³

x(2) = 5.33 m

Thus, the distance between point A and B is 5.33 m.

when the particle reaches point C, final velocity, vf = 0

vf = v + at

where;

0 = 8 - 3t(t)

0 = 8 - 3t²

3t² = 8

t² = 8/3

t² = 2.67

t = √(2.67)

t = 1.63 seconds

x = ∫vf

x = ∫(8 - 3t²)

x = 8t  - t³

x(1.63) = 8(1.63) - (1.63)³

x(1.63) = 8.7 m

Learn more about velocity here: https://brainly.com/question/24681896

#SPJ1

The equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.

The equation of a circle, with the center at the origin and the radius r units, is given as x² + y² = r².

In the question, we are asked to write the equation for a circle centered at the origin with x-intercepts of (-9, 0) and (9, 0).

We can find the radius of the circle using the distance formula,

D = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) are the endpoints of a line segment.

Radius is the distance between the center and any point on the circle.

Thus, taking (x₁, y₁) as (0, 0), the origin, for the center, and (x₂, y₂) as (9, 0), for any point on the circle, we get the radius as:

r = √((9 - 0)² + (0 - 0)²),

or, r = √(9² + 0²),

or, r = √9² = 9.

Thus, the radius of the circle is r = 9 units.

Thus, the equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.

Learn more about the equation of the circle at

https://brainly.com/question/3453918

#SPJ1

The ball will take 1.15 seconds to hit the floor.

It is given that,

A juggler is performing her act using several balls. The height as a function of time is given by :

[tex]h(t) =-16t^{2} + vt +s[/tex].............(1)

where,

v is the speed of the ball

s is initial height

t is time taken

Putting h(t) = 0 and solving equation (1)

[tex]-16t^{2} + vt +s = 0[/tex]

[tex]-16t^{2} + 15t +4 = 0[/tex]

On solving above equation using graphing calculator and solving for t we get, t = 1.154 second.

Hence, the correct option is (b) " 1.15 seconds ".

to learn more about parabolic equation go to - https://brainly.com/question/12703381

#SPJ4

When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

Know more about variables here:

https://brainly.com/question/25223322

#SPJ4

So, 22, 23 are the two numbers.

There are two distinct but related ideas that are referred to as linear functions: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

Consecutive numbers are preceding and following, hence we need two numbers so that

X+1=Y

or

X- Y = -1

In addition, we are aware of

4x + 3y = 157

Let's increase the top equation by 3 times.

We get

3x - 3y = -3

Then we combine that with the bottom equation.

4x + 3y = 157

      7x= 154

       x = 22

Afterward, we substitute x into the initial equation,

22+1 = 23

So, 22, 23 are the two numbers.

To know more about linear function or polynomial function visit:

https://brainly.com/question/11536910

#SPJ4

Answer:

70 inches

Step-by-step explanation:

the width of the original rectangle:

48/2 - 13 = 24 - 13 = 11

the new rectangle:

length: 13

width: 2(11) = 22

perimeter: 2(13+22) = 2(35) = 70

The perimeter of the new rectangle is 70 inches.

The area of Rectangle is length times of width.

The perimeter of a rectangle is given by the formula P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

The first rectangle has a perimeter of 48 inches and a length of 13 inches.

48 = 2(13 + w)

24 = 13 + w

w = 11

So the first rectangle has a length of 13 inches and a width of 11 inches.

The second rectangle has the same length of 13 inches and twice the width of the first rectangle, which means it has a width of 22 inches.

P = 2(13 + 22)

= 2(35)

= 70

Therefore, the perimeter of the new rectangle is 70 inches.

To learn more on Rectangles click:

https://brainly.com/question/20693059

#SPJ2

Answer:

49,2

Step-by-step explanation:

i dont practice math in english so the variables might be a little different!! The little L with the squiggly is supposed to represent length

The length of the painting is 77 cm if the area of the painting is 4081 sq cm and the width is 53 cm.

The area of a rectangle is the product of the length and width of the same rectangle.

Given that:

The area of the painting, A = 4081 cm².

The width of the painting, b = 53 cm.

To find the length of the painting, use the following formula to obtain the area of the rectangle:

Area = length × breadth

Let the length of the painting is l, then

A = l × b

4081 = l × 53

l = [tex]\frac{4081}{53}[/tex]

l = 77

Thus, the length of the painting is 77 cm.

Learn more about Area here:

https://brainly.com/question/1631786

SPJ3