Which of the following represents a function?

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.

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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

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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.

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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.

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First symmetrically cut the octagon to get 8 pieces. (So that you will get the idea that this polygon is divided into 8 triangles)

Then find the area of one of the triangles:

Area of Triangle = [tex]\frac{1}{2} * b* h[/tex]

A = [tex]\frac{1}{2}[/tex] × 12 × 19

A = 114 cm²

To find the area of the whole octagon shape:

A = 114 × 8 = 912 cm²

Hope it helps!

Answer:

Step-by-step explanation:

You cannot do this unless you are certain that P is the center of the octagon. I don't know if that's solvable from the information given. So I will make the assumption that P is the center.

Determine the midpoint of BC. Call it E.  Draw a line from P to E. By symmetry EP = AP. BE = 1/2 * BC = 19/2 = 9.5 by construction

You have a trapezoid witch is 1/4 the area of the octagon. Three more trapezoids can fit into the octagon.

Formula

Area = (AP + BE)*PE / 2

Givens

AP = 12

BE = 9.5

PE = 12

Solution

Put the givens and constructions into the formula

Area = (12 + 9.5)*12/2

Area = 21.5 * 12/2

Area = 21.5 * 6

Area = 129

That's the area of one of the trapezoids. Multiply the area here by 4.

You get 516.

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.

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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:

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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?

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.

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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]

:)

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

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The information given that A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle.

It should be noted that an equilateral triangle simply means the triangle tht had equal shape and angles. Here, since A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.

Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle. On such triangle, two out of the three sides are equal.

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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

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Answer:

3, 4, 27

Step-by-step explanation:

1) Area scale factor = 9

Length scale factor = 3 because √9

2) 12/3 = 4

3) 3³ = 27

(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

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Answer:

  9.08

Step-by-step explanation:

To find the predicted value of y, put the x-value where x is in the equation and do the arithmetic.

  [tex]\hat{y}=134.63-2.79x\qquad\text{given}\\\\\hat{y}=134.63-2.79(45) = 134.63-125.55\qquad\text{use 45 for x}\\\\\boxed{\hat{y}=9.08}\qquad\text{simplify}[/tex]

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]

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)

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The expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].

What is an expression?

To find which expression correctly sets up the quadratic formula to solve the equation:

Theory of quadratic equation - A quadratic equation is defined as any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

An example of a quadratic equation in x is [tex]-4x^{2} +4=9x[/tex].

How to solve any quadratic equation using the Sridharacharya formula?

Let us represent a general quadratic equation in x, [tex]ax^{2} +bx+c=0[/tex] where a, b and c are coefficients of the terms.

According to the Sridharacharya formula, the value of x or the roots of the quadratic equation is -

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

The given equation is [tex]x^{2} -4x+3=0[/tex]

Comparing with the general equation of quadratic equation, we get a = 1, b = -4 , c = 3.

Putting the values of coefficients in the Sridharacharya formula,

[tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex]  which is (A).

Therefore, the expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].

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The complete question is shown below:

Consider this quadratic equation. x^2+3=4x. Which expression correctly sets up the quadratic formula to solve the equation?

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.

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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

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°

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Answer: C

Step-by-step explanation:

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 }

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Answer:

E. >

Because 65 is greater than 56.

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!

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

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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.

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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:

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