The ratio between the areas of equilateral triangles $\triangle BXY$ and $\triangle BAC$ is $1:4.$ If $AC=6,$ what is $XY?$

The trigonometric function for the values in the table is defined as follows:

y = 3sin(π/4(x - π/2)) + 3.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a maximum value of 6 and a minimum value of 0, for a difference of 6 units, hence the amplitude is obtained as follows:

2A = 6

A = 3.

Without vertical shift, a function with amplitude of 3 would oscillate between -3 and 3, while this one oscillates between 0 and 6, hence the vertical shift is given as follows:

D = 3.

The shortest distance between repetitions can be given by 8 - 0, hence the period is of 8 units and the coefficient B is given as follows:

2π/B = 8

B = 2π/8.

B = π/4.

The function is at's minimum value at x = 0, meaning that the sine function has a phase shift of π/2 units right, thus the coefficient C is given as follows:

C = π/2.

Then the function is defined as follows:

y = 3sin(π/4(x - π/2)) + 3.

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The value of k that makes the probability distribution valid is given as follows:

k = 4.

To obtain the value of k, we must consider that the integral assumes a value of 1 over it's entire domain, that is:

[tex]\int_{-1}^{1} F(x) dx = 1[/tex]

The function F(x) is given as follows:

F(x) = (x + 2)/k.

Considering 1/k as a constant, the integral is given as follows:

1/k[0.5x² + 2x].

At x = 1, the integral is given as follows:

0.5 + 2 = 2.5.

At x = -1, the integral is given as follows:

0.5 - 2 = -1.5.

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

1/k[2.5 - (-1.5)] = 4/k.

As the result of the integral must be of one, the value of k is obtained as follows:

4/k = 1

k = 4.

More can be learned about probabilities and integrals at https://brainly.com/question/15937125

#SPJ1

Answer:

y = 125°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540°

y + 86° + 142° + 72° + 115° = 540°

y + 415° = 540° ( subtract 415° from both sides )

y = 125°

Answer:

125°

Step-by-step explanation:

First you find the value of total interior angles

Since it's a Pentagon

[tex](5- 2) \times 180[/tex]

Then you arrive at 540°

When you sum all the angles in the Pentagon together they should be equal to 540

[tex]540 = 86 + 142 + 72 + 115 + y[/tex]

[tex]540 = 415 + y[/tex]

[tex]540 - 415 = y[/tex]

[tex]y = 125[/tex]

The solution is given below.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

the reflection is with respect to y=x line,

so, the transformation will be,

(x,y)⇒(y,x)

so, we get,

X = (-3,8 ) ⇒ X' = (8,-3)

Y(2,5)⇒Y(5,2)

Z(-4,-1)⇒Z'(-1,-4)

To learn more on transformation click:

brainly.com/question/20211457

#SPJ1

The value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.

Rounding to the nearest hundredth, the interval is 1 year.

Using the following formula, we can determine the car's value each year:

value = 20000 * [tex](1 - 0.15)^year[/tex]

We're looking for the years where the value exceeds $10,000.

Let's start by determining the car's value after 1 year:

value = 20000 * [tex](1 - 0.15)^1[/tex] = 20000 * 0.85 = 17000

We need to keep lowering the value since it will eventually exceed $10,000 because the value after one year is less than $10,000.

After 2 years:

value = 20000 * (1 - 0.15)² = 20000 * 0.85² = 14525

Still less than $10,000.

After 3 years:

value = 20000 * (1 - 0.15)³ = 20000 * 0.85³ = 12318.75

Since the value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.

Rounding to the nearest hundredth, the interval is 1 year.

To learn more about year, visit the link below:

https://brainly.com/question/3108928

#SPJ4

Answer:

526.68

To find out how much the price went up, you first want to find what 32% of 399 is.

32% of 399 = 127.68

The price will go up $127.68.

Now, just add that to the original price:

127.68 + 399 = 526.68

The price of the game system will now be $526.68

Step-by-step explanation:

Hope it helps! =D

The values of x and y​ are x = 5 and y = 5.

The subtraction of vectors a and b can be represented as the vector sum of a and the negative of b:

a - b = a + (-b)

To find the negative of b, simply multiply each component by -1:

-b = (-1) × (1, 2) = (-1, -2)

So,

a - b = a + (-b) = (6, 7) + (-1, -2) = (5, 5)

Therefore, the values of x and y are 5 and 5 respectively.

Find out more on vector sum here: https://brainly.com/question/15314185

#SPJ1

Answer:

5.6km

Step-by-step explanation:

1km = 1000 meters

5,600 meters = 5.6km

5600 divided by 1000 = 5.6km

So, Chen walked 5.6km today.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ -2 }{ 1 } \implies - 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=-2x+3 \end{array}}[/tex]

Answer:X[tex]x^{2} +2x-15[/tex]

Step-by-step explanation:   you do it by multiplying  out the brackets and then you  simplify the result expression by collecting the like terms.

Noah, Preston, and Zach work for 26 hours, 24 hours and 44 hours respectively

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

Let N, P and Z represent the number of hours Noah, Preston, and Zach work respectively. Thus, we can write:

N = P + 2  ---- (1)

Z = 2P - 4  ---- (2)

N + P + Z = 94  ---- (3)

Put (1) and (2) in (3):

N + P + Z = 94

P+2 + P + 2P-4 = 94

4P -2 = 94

4P = 94 + 2

4P = 96

P = 96/4

P = 24

Since N = P + 2,

N = 24 + 2 = 26

Since Z = 2P - 4,

Z = 2(24) - 4 = 44

Learn more about word problems on:

brainly.com/question/1781657

#SPJ1

45.0 units is the required perimeter of triangle XYZ

Triangles are known to be similar if the ratio of the similar sides are equal to a constant. The perimeter is the sum of all the sides of the triangle.

From the given diagram , we need to solve for the value of x first as shown:

9/10 = 14/x

9x = 140

x = 140/9

x = 15.6

Find the required perimeter of XYZ
perimeter = ZY + XY + XZ

perimeter = 15.4 + 14 + 15.6

Perimeter = 45.0 units

Hence the perimeter of triangle XYZ is approximately 45.0 units

Learn more on similar triangles here: https://brainly.com/question/14285697

#SPJ1

Answer: $252 for 120 ft

Step-by-step explanation: Divide the money by the feet value in order to find dollars per foot. Since 252/120 = 2.1 $/ft and 285/150 = 1.9 $/ft, it would be better value to go with the 1.9 $/ft option.

A. X is a discrete random variable

B. The conditions are satisfied.

C. The expected value of X is 15.25

A. X is a discrete random variable because it can only take on specific values (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16) and not any value in an interval.

B. To show that the probability distribution is valid, we need to check if the following conditions are satisfied:

1. P(X=x) ≥ 0 for all x in the set of possible values of X

2. The sum of all probabilities equals 1

From the information given, it appears that these conditions are satisfied.

C. The expected value of X can be calculated as the weighted average of all possible values of X, where the weights are their corresponding probabilities.

E(X) = Σ[x * P(X=x)]

E(X) = (14*0.15) + (15*0.55) + (16*0.20) + (17*0.10) = 15.25

The expected value of X, which is 15.25, represents the mean or average number of credits taken by a randomly selected first-year student at the large state university.

D. The standard deviation measures the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the values are close to the mean (expected value), while a high standard deviation indicates that the values are spread out over a wider range. In this context, a standard deviation of 0.829 means that the number of credits taken by first-year students at the university is spread out over a range of approximately 0.829 units on average.

E. The event "taking at least 16 credits" can be expressed as X ≥ 16. To find its probability, we can sum up the probabilities of all the values that are greater than or equal to 16.

P(X ≥ 16) = ΣP(X = x)

P(X ≥ 16) = 0.20 + 0.10 = 0.30

Learn more expected value on:

brainly.com/question/29352440

#SPJ1

The musical frequency of notes is decreasing between beat number 6 and 7.

Beats refer to the periodic variations in the loudness of a sound resulting from the interference between two waves of slightly different frequencies. When two waves of different frequencies overlap, they create an interference pattern that results in a waveform that varies in amplitude (loudness) over time. The resulting pattern of loud and soft sounds is known as beats.

The musical note frequency is in the given question is measured in Hz and it started decreasing from a frequency of 444 Hz to frequency of 392 Hz.

Learn more about beat frequency here: https://brainly.com/question/3086912

#SPJ1

Consecuencia de 5^3 - 3 √(375 ÷ 3) + (7 + 2)^2 - 9^11 ÷ 9^9 es 91.46.

Potencias es una operación matemática para la multiplicación repetida de un número tanto como el rango. El rango de un número es un número que se escribe más pequeño y se ubica ligeramente hacia arriba. Basado en la semántica de escribir letras se llama superíndice, por ejemplo: 2², 3², 4³ y otros. En inglés, el exponencial se llama "potencia" o "exponente".

5³=125

3√(375:3) =3√125=3√5³= 3.5^3/2

(7+2) ²=9²=81

9¹¹÷9^9=9²=81

5³ - 3 √(375 ÷ 3) + (7 + 2)² - 9¹¹ ÷ 9^9= 5³-3.5^3/2+81-81 =125-3√125=125-(3(11.18) = 125- 33.54=91.46

Learn more about exponential number at

https://brainly.com/question/29197125

#SPJ1

Probability that the event can happen = 1/2

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Given,

Total outcomes of event = 14

Outcomes, event can happen = 7

Probability

= Favorable Outcomes/Total Outcomes

= 7/14 = 1/2

Hence, 1/2 is Probability that the event occurs.

Learn more about Probability here:

https://brainly.com/question/30034780

#SPJ1

Answer:

y = -2.5x + 6.5

Step-by-step explanation:

The equation of the line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

With a slope of -2.5 and a point (2,1.5) on the line, we can use the point-slope formula to find the equation of the line:

y - 1.5 = -2.5 (x - 2)

Expanding the right-hand side, we get:

y - 1.5 = -2.5x + 5

Adding 1.5 to both sides, we get:

y = -2.5x + 6.5

So the equation of the line in slope-intercept form is y = -2.5x + 6.5.

Answer:

B

Step-by-step explanation:

[tex]1. \: 5.1 \div - 2 \\ 2. \: - 2.55[/tex]

let's say we have two points A(a , b) and B(c , d) partitioned by a point C, since we're dealing with the MidPoint, C is partitioning AB into two equal halves, so in the ratio of 1 : 1.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(a,b)\qquad B(c,d)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:1} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{1}\implies \cfrac{A}{B} = \cfrac{1}{1}\implies 1A=1B \\\\\\ 1(a,b)=1(c,d) \implies (a~~,~~ b)=(c~~,~~ d) \\\\\\ C=\left( \cfrac{a+c}{1+1}~~,~~\cfrac{b+d}{1+1} \right)\implies \stackrel{ \textit{MidPoint Formula} }{C=\left( \cfrac{a+c}{2}~~,~~\cfrac{b+d}{2} \right)}[/tex]

Answer:

y = -2x + 7

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals.

That means that their product is -1.

If the slope of a line is m, then a perpendicular line has slope -1/m.

Given line slope: 1/2

Perpendicular slope: -2

Perpendicular line:

y = -2x + b

Point on new line: (0, 7)

7 = -2(0) + b

b = 7

Perpendicular line:

y = -2x + 7

Perpendicular lines have slopes that are negative reciprocals of each other.

We're given:

First, we must find the slope.

The y-intercept occurs when x=0. Therefore, given the point (0,7), we know that the y-intercept is 7:

[tex]y=-2x+7[/tex]

Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

Use the simple formula "a / b" to create a group of linked variables "a" and "b," where "b" may also be higher than zero. One ratio is created by combining two equation ratios. If there were only one man and three ladies, the ratio would be 1:1. There are 1/4 males and 3/4 girls in the group. A division between two or more objects, a number, or even a portion of a component's volume are all examples of parts.

Here,

Ratio 1: AB:BC = 2:1

Let's use the midpoint formula to find the coordinates of point C, which is the midpoint of line segment AB:

C = ((5+x)/2, (0+y)/2) = ((5+x)/2, y/2)

Since AB:BC = 2:1, we know that the distance from A to B is twice the distance from B to C. Using the distance formula, we can write:

2 * BC = AB

2 * √((x+1)² + y²) = √((x-5)^2 + y^2)

Simplifying this equation, we get:

4 * (x+1)² + 4y² = x² - 10x + 25 + y²

Simplifying further, we get:

3x²+ 8x - 16y² - 75 = 0

Ratio 2: CD:DE = 1:2

Let's use the midpoint formula to find the coordinates of point E, which is the midpoint of line segment CD:

E = ((p-1)/2, (q-4)/2)

Since CD:DE = 1:2.

Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

To know more about ratio visit:

brainly.com/question/13419413

#SPJ1

Answer:

(-4, 6) (-1, 0)

Source:

Took test. ✌

Answer:

Ecuación: 59.53 - 6.49 = 53.04

53.04 / 8 = X

X = 6.63

Respuesta: X=6.63

The values in the parallelogram figure are as follows

angle B = 74 degrees

x = 4

angle BCA = 49 degrees

Remembering that opposite angels of a parallelogram are equal will help us know that angel B is equal to angel D which is 74 degrees

The property that the two opposite sides of parallelogram is used to find x

4x = 16

x = 4

Applying alternate interior angles postulate, we can see that

angle BCA = angle DAC = 49 degrees

Learn more about alternate interior angles at:

https://brainly.com/question/20344743

#SPJ1

Answer: Young gentleman. Here are some things you can use.

Step-by-step explanation: Calculator, Desmos (this was a website) ruler, protractor, math dictionary.

Answer:

3404.9(1dp)

Step-by-step explanation:

The linear graph represents a proportional relationship, a graph of a line that passes through the points (0, 0) and (0.5, -3).

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the coordinates to find the  linear graph represents a proportional relationship,

we know the equation of a line given by,

y = mx + c

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

to prove the graph the proportional value of the y-intercept should be zero, (0, 0)

when c = 0, y = mx

the equation will proportional,

When the line passes from the origin the equation will be proportional.

Hence option A is correct.

Learn more about linear equations;

https://brainly.com/question/11897796

#SPJ1

Its A because if the line passes through the middle of the square is a proportional relationship.

Answer: 104

Step-by-step explanation:

To put it simply, let's say 100% is 160 dollars. When Christmas arrived, it was sold with a discount of 35%. This means we deduct 35% from 100% which is 65%. We then find 65% of 160 dollars, which is 104.

Hope that helps, if not, then please reply back :)