edmentum question:
-post test: similarity and proof
in the diagram, the ratios __ and ___ are equal

The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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Answer:

  all are "yes"

Step-by-step explanation:

A polynomial is defined for all values of x. None are excluded. Every value listed is in the domain of f(x) = (x +1)².

Answer:

Step-by-step explanation:

Answer:

17 hours

Step-by-step explanation:

156/12 = 13

221/13 = 17

Hope this helped :)

Answer:

17 hours

Step-by-step explanation:

156 / 12 = 13 ( 13 dolars per hour)

221 / 13 = 17 ( 17 hours of work to earn $221)

Answer:

perimeter = 12

Step-by-step explanation:

In a right-angled triangle, a² + b² = c²

where c is the hypotenuse, and a and b are opposite and adjacent, either way.

have a look at attached documents for answer and explanation

Answer:

7:4 that would be the ratio

this is the sample answer if you're doing PLATO

Answer: PLATO/Edmentum

Step-by-step explanation:

Given the function

Vertical asymptote of the function:

The vertical asymptote of a function is obtained by equating its denominator to zero.

Thus,

Horizontal asymptote of the function

In the function, since the degree of the numerator is same as the degree of the denominator, the horizontal asymptote is evaluated as

For the numerator, the leading coefficient is 9 while for the denominator, the leading coefficient is -6.

Thus, the horizontal asymptote of the function is evaluated to be

Hence,

Vertical asymptote:

Horizontal asymptote:

The first option is the correct answer.

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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Answer:

2x = 26, x = 13

Step-by-step explanation:

Write and solve an equation twice a number is 26

x = unknown number

Equation: 2x = 26

Solve:

2x = 26

/2    /2 <== divide both sides by 2

x = 13

Check your answer:

2x = 26

2(13) = 26

26 = 26

This stament is correct

Hope this helps!

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

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

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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Answer:

6x^2-3x-2

Step-by-step explanation:

6x^2 + 2x - 20 / 4 x x - 2

6x^2 + 2x - 5x - 2

6x^2 -3x - 2

Answer:

112 yards

Step-by-step explanation:

quarter is 1/4 right¿

28 × 4 = 112

Answer:

144? or 126 sorry

Step-by-step explanation:

Answer:

the 3rd one is the true one

The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

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The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d)  .

In the question ,

four set of sides is given ,

we need to find the set of side that forms a right triangle ,

we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .

Option(a)

the sides are 4 , 8 , 11.

4 + 8 = 11

16 + 64 = 121

80 = 121

we know that 80 121 ,

So , the sides do not form a right triangle

Option(b)

the sides are 6 , 8 , 13

6 + 8 = 13

36 + 64 = 169

100  169

we know that 100 169 ,

So , the sides do not form a right triangle .

Option(c)

the sides are √3, √5 , 8

√3 + √5 = 8

3 + 5 = 64

8 = 64

we know that 8  64 ,

So , the sides do not form a right triangle .

Option(d)

the sides are √3, √13 , 4

√3 + √13 = 4

3 + 13 = 16

16 = 16

Yes , the sides form a right triangle .

Therefore , The sides {√3 , √13 , 4} forms a right triangle  .

The given question is incomplete , the complete question is

Determine which set of side measurements could be used to form a right triangle ?

(a) 4, 8, 11

(b) 6, 8, 13

(c)√3, √5,8

(d)√3, √13, 4

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Answer:

The answer is 2 ¾

Step-by-step explanation:

11/4 = 2 ¾

4 - 2 ¾ = 2¾

The exponential function corresponding to the data is:

f(x) = 32.4(1.31)ˣ

We can use the formula for geometric sequences to solve this problem. Let the initial population be a, and let r be the common ratio. Then:

a = initial population in 2002

ar = population in 2004 (2 years later)

ar² = population in 2005 (3 years later)

ar³ = population in 2006 (4 years later)

We can set up a system of equations using the given information:

ar = 42

ar² = 55

ar³ = 72

We can also solve for r using the first and second equations:

ar = 42

ar² = 55

Dividing the second equation by the first equation, we get:

r = (ar²)/(ar) = 55/42

This is consistent with our previous result, so we can use this value of r to solve for a:

ar = 42

a(55/42) = 42

a = 42(42/55)

a ≈ 32.4

Therefore, the initial invasive plant population in 2002 was approximately 32.4 plants.

The common ratio is approximately 1.31 to the nearest tenth.

The exponential function corresponding to the data is:

f(x) = 32.4(1.31)ˣ

where x represents the number of years after 2002.

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Answer:  vertical -->  x = 3 ;  horizontal -->  y = 15

Step-by-step explanation:

A vertical line is one that goes straight up and down, without moving side-to-side. Thus, its x-coordinate is always the same, a constant.

So, vertical lines all have the form x = k, some constant.

In this case, x = 3 for the vertical line to go through point (3, 15).

A horizontal line is one that goes straight left and right, without moving up or down. Thus, its y-coordinate is always the same, a constant.

So, horizontal lines all have the form y = k, some constant.

In this case, y = 15 for the horizontal line to go through point (3, 15).

I hope this helps.

Answer:

the right half

Step-by-step explanation:

We know that cosine is a pair function.

This means that:

Cos(a) = Cos( -a)

We also know that:

Cos(pi) = 0

then:

Cos(-pi) = 0

pi and -pi are located in the y-axis, so from this we can know that the cosine function will be always positive on the right side, or in the left side, we can discard the other two options.

Now, we also know that cos(0) = 1.

And:

-pi < 0 < pi

So the two zeros are at the y-axis, and we know that cos(0) is positive (the angle 0 would be on the positive side of the x-axis, at the right), then all the right side must be positive.

Then the correct option is:

the right half

Answer:

C - The right half

Step-by-step explanation:

Just took the quiz on edge

The values of the trigonometric functions are

1. sin A = 12/13

2. cos A = 5/13

3. Tan A = 12/5

4. cot A = 5/12

5. cosec A = 13/12

6. sec A = 13/5

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Examples of these functions are; sin, cos , tan cot, cosec , sec e.t.c

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

here the opposite side to angle A is 12 and the adjascent is 5 while the hypotenuse is 13.

Therefore,

1. sin A = 12/13

2. cos A = 5/13

3. Tan A = 12/5

4. cot A =1/tan A = 5/12

5. cosec A = 1/sin = 13/12

6. sec A = 1/cos = 13/5

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Answer:

1,080,000 if invested

Step-by-step explanation:

The fair price to be paid today for the assignment of this $20,000,000 lottery prize, assuming it pays out as an ordinary annuity and can be invested at 8%, is approximately $9,818,181.82.

To calculate the fair price to be paid today for the assignment of the $20,000,000 lottery prize, determine the present value of the 20 annual installments at an 8% interest rate.

Given:

Lottery prize: $20,000,000

Number of installments: 20

Interest rate: 8%

To find the present value (PV) of the lottery prize, use the formula for the present value of an ordinary annuity:

PV = P × [(1 - (1 + r)⁻ⁿ) / r]

Where:

PV = Present value of the lottery prize

P = Annual payment (in this case, the annual installment amount)

r = Interest rate per period (expressed as a decimal)

n = Total number of periods (in this case, the number of installments)

First, find the annual payment (P) using the information provided:

Annual payment (P) = Total prize amount / Number of installments

P = $20,000,000 / 20

P = $1,000,000

Now, calculate the present value (PV):

PV = $1,000,000 × [(1 - (1 + 0.08)⁻²⁰) / 0.08]

Using a calculator or spreadsheet, the present value (PV) is approximately $9,818,181.82.

So, the fair price to be paid today for the assignment of this $20,000,000 lottery prize, assuming it pays out as an ordinary annuity and can be invested at 8%, is approximately $9,818,181.82.

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Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)

Answer:

b < 3

Step-by-step explanation:

3 ( b - 5 ) < - 2b

3 ( b ) - 3 ( 5 ) < - 2b

3b - 15 < - 2b

3b + 2b < 15

5b < 15

b < 15/5

b < 3

Answer:

A square pyramid has 5 faces: 1 square base and 4 triangular faces.

The area of the base is:

A = s^2

where s is the length of the base edge.

In this case, s = 1 m, so:

A = 1^2 = 1 m^2

The area of each triangular face is:

A = 1/2 * b * h

where b is the base of the triangle (which is equal to the length of one side of the square base) and h is the height of the triangle (which is given as 1 m).

In this case, b = 1 m and h = 1 m, so:

A = 1/2 * 1 * 1 = 0.5 m^2

The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces:

SA = A_base + 4 * A_triangles

SA = 1 + 4(0.5)

SA = 1 + 2

SA = 3 m^2

Therefore, the surface area of the pyramid is 3 square meters.

Answer:

sin( 3pi/4 ) = -√2/2

So, B.

Answer:

(x, y) --> (2/3x, 2/3y)

Step-by-step explanation: