Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for $35, then took 5 hours of group snowboarding lessons. Victor paid $175 in all.

Side AC is computed s by applying similar triangles to give 12

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

From the description, pair of equivalent sides are

AB and BD, AC and CE

The solution is worked out using sides AB and BD, AC and CE

AB / BD = AC / CE

where

AB = 8

BD = 10

CE = 15

AC = ?

8 / 10 = AC / 15

cross multiplying

8 * 15 = 10 * AC

AC = 8 * 15 / 10

AC = 12

hence  AC is 12

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The Fourier series is a summation of sine waves with different amplitudes and frequencies that, when combined, approximate the original function. The coefficients of the sine waves are determined by the values of the function at certain points.

The Fourier series for the given function f(x) can be derived as follows:

Step 1: Calculate the average value of f(x) over one period.

Average value = (1 + 0)/2 = 0.5

Step 2: Calculate the Fourier coefficients for the given function.

Fourier coefficients =[tex](1/2L) + (1/π)∑_(n=1)^∞▒(sin(nπx/L) - sin(nπx/2L))/n[/tex]

Step 3: Construct the Fourier series by combining the Fourier coefficients and the sine waves of different frequencies.

Fourier series = [tex]0.5 + (1/π)∑_(n=1)^∞▒(sin(nπx/L) - sin(nπx/2L))/n[/tex]

The Fourier series is a way of expressing a function as a sum of sine and cosine waves, each of which has a specific amplitude and frequency. This can be used to approximate the original function. To find the Fourier series of a given function, the average value of the function over one period must first be determined. Then, the Fourier coefficients of the function can be calculated, which are determined by the values of the function at certain points. Finally, the Fourier series can be constructed by combining the Fourier coefficients and the sine waves of different frequencies.

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x > 1200 and x < 1600; Patrice needs to consume more than 1200 calories, but less than 1600 calories.

The 1st option is the answer

Given that: Patrice is trying a low-calorie diet. She would like to keep her calories consumed between the levels shown in the following compound inequality: 2450 < 2x + 50 and 2x + 50 < 3250.

Solve the two inequalities separately:

2450 < 2x + 50

2450 - 50 < 2x

2400 < 2x

1200 < x

x > 1200

2x + 50 < 3250

2x < 3250 - 50

2x < 3200

x < 1600

Therefore, Patrice needs to consume more than 1200 calories (i.e. x > 1200), but less than 1600 calories  (i.e. x < 1600).

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Depends on the specific values of x, y, and the step size h used in the approximation.

What is differentiation ?

Differentiation is a concept in calculus that involves finding the rate of change of a function with respect to one of its variables. It is represented by the symbol ∂/∂x or ∂/∂y or ∂/∂t (where x, y and t are the variables of the function). The process of differentiation allows us to find the slope of a curve, the instantaneous rate of change, and the maximum or minimum points of a function.

The difference between dy and δy can be determined by subtracting dy from δy. The accuracy of dy in approximating δy depends on the specific values of x, y, and the step size h used in the approximation.

For example, if we consider dy = (f(x+h, y+k)-f(x,y))/h, and δy= f'(x)*δx.

Where f(x,y) is the given function for the system of differential equations and f'(x) is the derivative of the function f(x,y) with respect to x.

so the difference between dy and δy is δy-dy= f'(x)*δx - (f(x+h, y+k)-f(x,y))/h.

The accuracy of dy in approximating δy can be determined by taking the limit of the difference as h approaches 0.

In the end, it all depends on the specific problem and desired level of accuracy.

Depends on the specific values of x, y, and the step size h used in the approximation.

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The governments are possible 90 different student body if there are 6 seniors, 5 juniors and 3 sophomores.

We need to fill three positions. There are six options for the senior position. There are five options for the junior position.There are three options for the sophomore position.

Whoever is elected senior president has no bearing on who is elected junior or sophomore president, and vice versa, i.e. the three events are completely separate.

The number of possibilities for separate events is simply the product of the individual number of possibilities, i.e.                    

As a result, the total number of ways to assign the student body is
(ways to choose senior president) * (ways to choose junior president) * (ways to choose sophomore president) = 6*5*3= 90          

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The required maximum and minimum x-values are 4 and 1 respectively and maximum and minimum y-values are 4 and 0 respectively.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
Graph of the inequalities 4x - 2y ≤8, x ≥ 1 and 0 ≤ y ≤ 4 has been shown, the red dotted quadrilateral shows the solutions of the given inequalities, From the graph maximum and minimum x-values are 4 and 1 respectively and maximum and minimum y-values are 4 and 0 respectively.

Thus, the required maximum and minimum of the given inequalities exist.

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Answer: A)

FCE and CAB are congruent angles they are formed by the same line FA and two parallel lines between them

FEC and EDB are congruent angles for the same reason

B)we will write the measure of each angle based on the statement

The line AD contains the angles ABC,CBE and EBD if we sum all angles we make the line and the measure of a line is 180 degrees so

the CBE is 72°

C)

congruent triangles are those that have all their angles equal,Since all the triangles are copies of triangle ABC, they are all congruent since they all measure the same but are located in different ways

so a triangle congruent to triangle CBE can be any for example :ABC,BED or FCE

Answer:

1

Step-by-step explanation:

y = −2x+3 is Neither parallel nor perpendicular to line a.

y = −2x+5 is Parallel to line a.

y = (1/2)x+7 is  Perpendicular to line a

The slope-intercept form of the equation a straight line is:

y = mx + c,

where m is the slope and c is the y-intercept

When two lines are perpendicular, the product of their slope is -1 i.e.

m₁ × m₂ = -1

where m₁ and m₂ represent the slope of the lines

But when two lines are parallel, they have the same slope i.e.

m₁ = m₂

Let's examine the equations:

Line a, y = −2x+3

y = 2x-1

y = −2x+5

y = (1/2)x+7

For Line a and  y = 2x-1:

Comparing their slopes. So y = −2x+3 is Neither parallel nor perpendicular to line a

For Line a and y = −2x+5:

They have the same slope (-2). So y = −2x+5 is Parallel to line a

For Line a and y = (1/2)x+7:

(1/2) × −2 = -1.  The product of their slope is -1 (i.e. 1/2 × −2 = -1 ). So  y = (1/2)x+7 is  Perpendicular to line a

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The value of x is = -0.5, for the equation [tex]$$ e^x \times e^{x+1}[/tex], after converting it to logarithm form.

The inverse function to exponentiation in mathematics is called the logarithm. In other words, to produce a number x, b must be raised to an exponent equal to the logarithm of x to the base b. Assuming that 1000 = 10³, for instance, the logarithm of 1000 in base 10 is 3, or log10 (1000) = 3.

When there is no possibility of confusion or when the base is irrelevant, such as in big O notation, the logarithm of x to base b is written as logb (x), logb x, or even without the explicit base, log x.

When multiplying two powers of the same base, the exponents are added.

= [tex]$$ e^x \times e^{x+1}[/tex]

= [tex]$$ e^{x + x+1}[/tex]

= [tex]$ \text e^{2x+1}[/tex]

=  [tex]$ \text e^{2x+1}[/tex] = 1

Convert to logarithm form

[tex]\log_e(1) = 2x+1[/tex]

Solve the equation

Isolate the variable by dividing each side by factors that don't contain the variable.

[tex]$\text x = -\frac{1}{2}[/tex]

x = -0.5

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Population A and B are in geometric sequence.

A geometric sequence is one where each phrase is obtained by multiplying the term before it by the same number.

Formula to find nth term of geometric sequence is aₙ = a₁ rⁿ⁻¹. The common ratio is expressed as the value r.

In the given table,

The population A of the table changing with respect to time,

0 hours =  12 millions

1 hour = 6 millions

2 hours = 3 millions

3 hours = 1.5 millions

The population B of the table changing with respect to time,

0 hours =  64 millions

1 hour = 48 millions

2 hours = 36 millions

3 hours = 27 millions

Since, the population A changes in geometric sequence.

And the common factor is 1/2.

Also, population B changes in geometric sequence.

and the common factor is 3/4.

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Each fraction must first be transformed into its simplest form.Hence, The  problem can be solved in this way.

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The slope of a line in the form "y = mx + b" is given by the coefficient "m" of the x term.

For the first equation, x - 2y = -1/2, we can rearrange the terms to get y = (1/2)x - 1/2. The coefficient of the x term is 1/2, so the slope of the line is 1/2.

For the second equation, -4x - 8y = 2, we can rearrange the terms to get y = -(1/2)x - 1/4. The coefficient of the x term is -1/2, so the slope of the line is -1/2.

The value of x after the statements execute is 46, as the value at the memory address of x was changed to 46.

Step 1: int x = 25;

Step 2: int *p;

Step 3: p = &x;

Step 4: *p = 46;

Step 5: x = 46;

The value of x after the statements execute is 46. This is because the statement int x = 25 sets the variable x to the value of 25. The statement int *p; creates a pointer variable p, which is a variable that stores the memory address of another variable. The statement p = &x; sets the pointer variable p to the memory address of x, so that it points to x. The statement *p = 46; changes the value of the variable that p points to, which is x, to 46. So, the value at the memory address of x was changed to 46, and thus the value of x is now 46.

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Answer: the slant height of the cone is 7ft

Step-by-step explanation:

Answer: $18,000.

Step-by-step explanation:

Let X be the number of adult tickets sold and Y be the number of youth tickets sold.

We can set up the following system of equations to represent this situation:

X * 25 + Y * 12.50 = 15000

X + Y <= 1000

The first equation represents the total ticket sales, and the second equation represents the maximum capacity of the theater.

To solve this system of equations, we can use a method such as graphing, substitution, or elimination.

Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for X:

X = (15000 - Y * 12.50) / 25

Then, we can substitute this expression for X into the second equation:

(15000 - Y * 12.50) / 25 + Y <= 1000

Solving this equation for Y gives us the number of youth tickets that can be sold:

Y <= 600

This means that the theater can sell a maximum of 600 youth tickets. We can then use this value to find the maximum number of adult tickets that can be sold by substituting it into the expression for X that we derived earlier:

X = (15000 - 600 * 12.50) / 25

Solving this equation gives us a maximum of 240 adult tickets that can be sold.

Therefore, the theater can sell a maximum of 600 youth tickets and 240 adult tickets for a total of 840 tickets. The total ticket sales for this scenario would be 600 * $12.50 + 240 * $25 = $18,000.

The equation y - 1 = 2 · (x - 2)² is the vertex form of the parabola y = 2 · x² - 4 · x + 9.

Parabolae are represented by quadratic equations of the form:

y = A · x² + B · x + C

Where A, B, C are real coefficients. This form is known as standard form and whose equivalent vertex form can be found by completing the square, that is, an application of algebra properties to modify part of the polynomial. Vertex form is described below:

y - k = C · (x - h)²

Where:

Now we proceed to modify the expression:

y = 2 · x² - 4 · x + 9

y = 2 · (x² - 2 · x + 9 / 2)

y = 2 · (x² - 2 · x + 4) + 1

y - 1 = 2 · (x - 2)²

The vertex form of the parabola is y - 1 = 2 · (x - 2)².

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A system of linear equations that represents this situation include the following:

y = 0.5x + 2.5

y = 0.5x + 5.5

In order to write the required system of linear equations, we would have to determine the slope for your friend and cousin respectively as follows;

y - y₁ = m(x - x₁)

Where:

Substituting the given parameters into the point-slope formula, the equation for your friend's hair is given by;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (6.5 - 4)/(8 - 3)(x - 3)

y - 4 = 2.5/5(x - 3)

y - 4 = 0.5x - 1.5

y = 0.5x - 1.5 + 4

y = 0.5x + 2.5

Also, the equation for your cousin's hair is given by;

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 7 = (9 - 7)/(8 - 3)(x - 3)

y - 7 = 2/5(x - 3)

y - 7 = 0.5x - 1.5

y = 0.5x - 1.5 + 7

y = 0.5x + 5.5

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Descartes' number is 30.453 while mine is 45.3 times higher than 3,000 when multiplied by 100.

When m and p are coprime numbers and 2n = (m) (p + 1), where p is regarded as a "spoof" prime, the result is an odd number, which is known as a Descartes number. The provided example is the sole one that is currently known. A number that comes very near to becoming the ideal number is known as a Descartes number in mathematics. They are called after René Descartes, who noted that the number D, which is 32, 72, 112, 132, 22021 (which equals 198585576189), would be an odd perfect number if only 22021 were a prime number, because the sum-of-divisors function for D is satisfied.

given

n = (3000+45.3)/100

=     n = 3045.3/100

=     n = 30.453

Descartes' number is 30.453 while mine is 45.3 times higher than 3,000 when multiplied by 100.

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0.2% of 3500 is equal to 7

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, 7 is what percent of 3500

Let 7 be the x% of 3500,

Therefore,

x% of 3500 = 7

x/100 × 3500 = 7

x = 1/5

1/5 = 0.2

Hence, 7 is 0.2% of 3500

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The height of a player at 18 points average is 78 and the points per game a player averages if he is 70 inches tall is 7

From the question, we have the following parameters that can be used in our computation:

height (in) 84 80 79 82 74 72 86 76

points per game 22 21 21 26 12 8 28 15

Using a graphing calculator, we have the following calculation summary

The regression equation is represented as

p = bh + a

Where

b = SP/SSX = 224.88/166.88 = 1.35

a = MY - bMX = 19.13 - (1.35*79.13) = -87.5

So, we have

p = 1.35h - 87.5

At a point of 18, we have

1.35h - 87.5 = 18

So, we have

1.35h = 105.5

Divide by 1.35

h = 78

This means that

h = 70

So, we have

p = 1.35 * 70 - 87.5

Evaluate

p = 7

Hence, the point is 7

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The value of expression  (√3+1)(1-2√3)​ is -5-√3

An expression is combination of variables, numbers and operators.

The given expression is (√3+1)(1-2√3)​

Square root three plus one times of one minus two root three.

(√3+1)(1-2√3)​

Now distribute each terms

√3-2√3√3+1-2√3

√3-2(3)+1-2√3

Add the like terms

√3-6+1-2√3

√3-5-2√3

-5-√3

Hence, the value of expression  (√3+1)(1-2√3)​ is -5-√3

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

4[tex]\sqrt{\frac{1}{15} }[/tex]

Step-by-step explanation:

In triangle ADC and CD = 10 in triangle ABC, this means that the length of DB in triangle ABC is 10 - 4 = 6. Therefore, DB = 6.

In right triangle ABC, if CD is an altitude drawn to the hypotenuse and AD is also an altitude drawn to the hypotenuse, then triangles ADC and BDC are both right triangles. This means that triangles ADC and BDC are similar to triangle ABC.

We can use this similarity to find the length of DB. If AD = 4 and CD = 10, then we know that the ratio of AD to CD in triangle ABC is 4/10. This means that the ratio of AD to CD in triangle ADC is also 4/10. Since AD = 4 in triangle ADC, this means that CD = 10 * (AD/CD) = 10 * (4/10) = 4 in triangle ADC.

Since CD = 4 in triangle ADC and CD = 10 in triangle ABC, this means that the length of DB in triangle ABC is 10 - 4 = 6. Therefore, DB = 6.

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In right triangle ABC, where altitude CD is drawn to the hypotenuse AB with CD = 10 and AD = 4, then DB equals 25.

Therefore the answer is 25.

By Pythagoras theorem in ΔACD right angled at ∠CDA

AC² = CD² + AD², that is

[tex]AC^{2} = CD^{2} + AD^{2}[/tex]

AC² = 10² + 4²

AC² = 116

By Pythagoras theorem in ΔBCD right angled at ∠CDB

BC² = CD² + DB², that is

[tex]BC^{2} = CD^{2} + DB^{2}[/tex]

BC² = 10² + DB²

BC² = 100 + DB²

By Pythagoras theorem in ΔABC right angled at ∠BCA

BC² + AC ² = AB², that is

[tex]BC^{2} + AC^{2} = AB^{2}[/tex]

As AB = AD + DB

BC² + AC ² = (AD + DB)²

BC² + AC ² = AD² + 2×AD×DB + DB²

Substituting for AD, BC² and AC²

100 + DB² + 116 = 4² + 2×4×DB + DB²

8DB = 216 - 4²

DB = 200/ 8

DB = 25

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Triangles that do not have the same angles or side lengths as triangle ABC cannot be similar to triangle ABC.

Similar triangles are triangles that have the same angles and side lengths. Therefore, any triangle that does not have the same angles and side lengths as triangle ABC cannot be similar to triangle ABC.

Similar triangles are triangles that have the same angles and side lengths. Therefore, any triangle that does not have the same angles or side lengths as triangle ABC cannot be similar to triangle ABC. For example, if triangle ABC has an angle of B which is a right angle and sides of length 15 cm, 8 cm, and 17 cm respectively, then a triangle with an angle of B which is not a right angle, or with side lengths that are not the same as triangle ABC's, cannot be similar to triangle ABC. This is because the angles and side lengths of both triangles must match in order for them to be similar. Therefore, any triangle that does not have the same angles and side lengths as triangle ABC cannot be similar to triangle ABC.

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Triangles which are not right angled triangles are not similar to triangle ABC.

As given in the question,

Triangle ABC is right angled triangle.

Angle B of triangle ABC is right angle.

Side length of AB = 15 cm

Side length of BC = 8 cm

Side length of AC = 17 cm

If the other triangles apart from ABC , is not a right angled triangle and its side are not in proportion .

Then the triangles are not similar to the given triangle ABC .

Therefore, triangles which are not right angled triangle are not similar to the given triangle ABC.

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The value of the annual premium is $2609.9

From the question, we have the following parameters that can be used in our computation:

Policy value = $89,657

Plan = 20-Payment Life insurance policy

From the given table:

The annual premium for a 20-Payment Life insurance policy for a 26-year-old male is $29.11

This means that

Total cost = 20 * $29.11

Total cost = $582.2

The annual premium is then calculated as

Annual premium = Total cost * 4.4829

This gives

Annual premium = $582.2 * 4.4829

Evaluate

Annual premium = $2609.9

Hence, the annual premium is $2609.9

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The measure of missing angle is 65°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

From the given triangle 68°, 47° and the missing angle is x.

By angle sum property of triangle, we get

68°+47°+x=180°

115°+x=180°

x=65°

Therefore, the measure of missing angle is 65°.

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The required trasformation vector is given as,
[tex]\vec z = z\hat i + z\hat j\\\vec u = u \hat i + u\hat j\\\vec x = x\hat i + x\hat j\\\vec y = y\hat i+ y\hat j[/tex]

Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.  

Here,
From the figure,
A component for of trasformation vector is given as,
[tex]\vec V= v\hat i + v\hat j[/tex]

where v is the magnitude of the vector and [tex]\hat i[/tex], [tex]\hat j\\[/tex] is the unit vector which shows the direction of the vector.
So vector trasformation equation is given as,
[tex]\vec z = z\hat i + z\hat j\\\vec u = u \hat i + u\hat j\\\vec x = x\hat i + x\hat j\\\vec y = y\hat i+ y\hat j[/tex]

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The question for the rational expressions 5x/2x+3 divided by x+1/3x is "What is the result of 5x/2x+3 divided by x+1/3x?"