Show that the lines x2-4xy+y2=0 and x+y=1 form an equilateral triangle

The cost of small sundae = 4 dollars

cost of large sundae = 6 dollars

What is the cost price?

The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

Here, we have

Given: An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. On another day, 15 small sundaes and 35 large sundaes were sold for $270.

let

x = cost of each small sundae

y = cost of each large sundae

30x + 50y = 420...(1)

15x + 35y = 270...(2)

multiply equation(ii) by 2

30x + 50y = 420

30x + 70y = 540

subtract equation(i) from equation(ii)

20y = 120

y = 120 / 20

y = 6

Now, put the value of y in equation(1) and we get

30x + 50(6) = 420

30x + 300 = 420

30x = 420 - 300

30x = 120

x = 120 / 30

x = 4

Hence, the cost of small sundae = 4 dollars

cost of large sundae = 6 dollars

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The expression [tex]x^2 + 28 / (3x)[/tex] can be written in standard form as [tex](3x^2 + 28x) / 3[/tex].

To write the expression in standard form, we need to simplify it and arrange it in a specific order.

First, let's simplify the expression:

[tex]x^2 + 4 / (3x/7)[/tex]

To simplify the expression, we need to multiply the numerator and denominator of the fraction by the reciprocal of the denominator, which is 7/3x. This gives us:

[tex]x^2 + 4 * 7 / (3x)[/tex]

Simplifying the fraction gives:

[tex]x^2 + 28 / (3x)[/tex]

Now, to write the expression in standard form, we need to arrange it in the order [tex]ax^2 + bx + c[/tex], where a, b, and c are constants. To do this, we need to simplify the expression further:

[tex]x^2 + 28 / (3x)[/tex]

= [tex]3x(x^2 / 3x + 28 / (3x^2))[/tex]

= [tex]3x(x + 28/3x)[/tex]

Therefore, the expression in standard form is:

[tex](3x^2 + 28x) / 3[/tex]

Standard form of a linear equation in two variables is represented as Ax + By = C, where A, B, and C are constants, and x and y are variables.

Standard form of a complex number is represented as a + bi, where a and b are real numbers, and i is the imaginary unit, which satisfies the equation [tex]i^2 = -1[/tex].

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After answering the presented question, we can conclude that As a result, the probability is 0.0333. (rounded to four decimal places).

Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how likely an event appears to be to occur. Probability is a mathematical expression for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. the proportion of occurrences among equally likely events

There are six options for the first song, but we want Mariah Carey to be the first song, so there is only one option.

There are 5 songs left after Mariah Carey's, but we want Shania Twain's song to be second, so there is only one option for the second song.

As a result, the likelihood of the first song being Mariah Carey and the second song being Shania Twain is:

1/6 * 1/5 = 1/30

As a result, the probability is 0.0333. (rounded to four decimal places).

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The helicopter is almost 10 feet above the ground.

What is meant by angle of elevation?

An angle of elevation is the angle formed by the horizontal plane and the observer's line of sight to an object above.

Let x be the height at which the helicopter is flying from Bill and John's eye level.

The angles of elevation from Bill and John are 48° and 55° respectively.

The distance between Bill and John is 10 feet.

The height of Bill and John is 4 feet.

From the figure, we can say that,

[tex]tan48=\frac{x}{b}\\ b=\frac{x}{tan48}[/tex]

and

[tex]tan55=\frac{x}{a} \\a=\frac{x}{tan55}[/tex]

We know that a+b=10

[tex]\frac{x}{tan55}+\frac{x}{tan48} =10\\\\x=\frac{10}{cot48+cot55} \\x=\frac{10}{1.6} \\x=6.25[/tex].

Therefore the helicopter is 6.25+4 = 10.25 feet above the ground.

The rounded-off value is equal to 10 feet.

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Answer:

P(X = 10) = (13 choose 10) * 0.35^10 * 0.65^(13-10)

= 286 * 0.35^10 * 0.65^3

= 0.1017

The rate of change between the points (0.2) and (1) is 6.25.

Rate of change is a measure of how quickly the value of a function is increasing or decreasing at a given point. It is calculated by taking the difference between two points on the function and dividing it by the change in the independent variable, usually time. This allows us to measure how quickly the function is changing over time. Rate of change is a key concept in calculus and can help us to understand how different functions behave.

To find the rate of change between the two points (0.2) and (1), we must first find the y-values of each x-value. On the graph, this is done by drawing a vertical line from the x-value to the graph, and then drawing a horizontal line from that point to determine the y-value. Thus, the y-value at x-value 0.2 is 3, while the y-value at x-value 1 is 8.

Now we can use the slope formula to find the rate of change between the two points. The slope formula is given as (y2 - y1) / (x2 - x1). Plugging in the values we got from the graph yields (8 - 3) / (1 - 0.2) = 5 / 0.8 = 6.25.

Therefore, the rate of change between the points (0.2) and (1) is 6.25.

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Answer:

Step-by-step explanation:

The perimeter of a figure be 27.85 ft .

Answer:

27.85

Step-by-step explanation:

I done the test.

After answering the presented question, we can conclude that As a trigonometry result, the distance from the tower's base to its peak is roughly 660 feet to the nearest foot.

Trigonometry is the field of mathematics that explores the relationship amongst triangle side angles. The issue first originated in the Hellenistic era, during the third century BC, as a consequence of the usage of geometry in astrological investigations. The subject of algebra known as exact techniques is concerned with certain trigonometric factors and their practical benefits in computations. Trigonometry has six commonly used trigonometric functions. Their separate names and initials are sine, arc, tangent, coordinate geometry, secant, and cosecant (csc). Basic arithmetic is the study of geometric properties, specifically those of trigonometry. As a result, geometry is the analysis of the properties of all shapes.

tan(84.7°) = h/x (since the tower is leaning at an angle of 84.7°, the opposite side is "h," and the neighbouring side is "x").

tan(47.4°) = h/(185+x) (Since the elevation angle to the top of the tower is 47.4°, the opposing side is "h," and the neighbouring side is 185+x.)

first equation yields h = x*tan(84.7°), which we can substitute for h in the second equation:

x*tan(84.7°)/(185+x) = tan(47.4°)

xtan(84.7°) = (185+x)tan(47.4°).

x(tan(84.7°) - tan(47.4°) = 185tan(47.4°)

x = 185*tan(47.4°)/(tan(84.7°) minus tan(47.4°))

659.5 feet = h*tan(84.7°) (rounded to the nearest tenth).

As a result, the distance from the tower's base to its peak is roughly 660 feet to the nearest foot.

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Answer:

20

Step-by-step explanation:

divide 10 by 1/2

The sum of angles in a triangle is always 180 degrees. Therefore, the angle C measures 60 degrees.

In triangle ABC, we know that angle A measures 75 degrees, and angle B measures 45 degrees.

To find the measure of angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:

Angle A + Angle B + Angle C = 180

Substituting the values we know:

75 + 45 + Angle C = 180

Simplifying:

120 + Angle C = 180

Subtracting 120 from both sides:

Angle C = 60

Therefore, angle C measures 60 degrees.

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When the $2,300 loan is taken out, the simple interests rate will be 8.33%.

Simple Interests (S.I.) is indeed a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 percent per year for two years, their interest for those 2 years would be S.I. loaned money.

Simple interest is often a fixed percentage of a principal amount borrowed or lent, given or received over a certain period of time. Borrowers are required to pay extra on interest in addition to principal since compound interest incurs and therefore is applied to the accrued interest from prior periods.

Formula for interest,

[tex]I = (PRT)/100[/tex]

[tex]2755 = 2300 + I[/tex]

[tex]I = 455[/tex]

[tex]r = I / Pt[/tex]

[tex]r = 455 / (2300 * (3/12))[/tex]

[tex]r = 0.0833[/tex]

Multiplying by [tex]100[/tex] to convert to a percentage,

[tex]r = 8.33[/tex]%

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The probability of someone telling the truth if they pass their polygraph test is 3960/4000, which is 99%.

Polygraph tests are used to detect deception by monitoring physiological responses, such as changes in blood pressure and heart rate, while the subject is asked a series of questions. The accuracy rate of a polygraph test is typically around 90%, meaning that it will detect 90% of people who are lying and 90% of people who are telling the truth. In the given scenario, there is a population of 4000 employees and it is known that 40 of them will lie during their polygraph test. This means that there are 3960 people who will tell the truth. The probability of someone telling the truth if they pass their polygraph test is 3960/4000, which is 99%. This means that if someone passes their polygraph test, there is a 99% probability that they are telling the truth. It is important to note that the accuracy rate of polygraph tests is not 100%, so it is still possible for someone to lie and pass their test. However, the probability of a truthful person passing the test is much higher than the probability of a liar passing the test.

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Answer:

Step-by-step explanation:

You want the solution to triangle TUV, given U=12°, V=148°, v=45.

Solving a triangle generally means finding the measures of all sides and angles. When two angles and one side are given, and that side is opposite the largest angle, there is one solution. It can be found using the Law of Sines.

The Angle Sum theorem tells you the sum of angles in a triangle is 180°. This means ...

  T +U +V = 180°

  T +12° +148° = 180°

  T = 20° . . . . . . . . . . . . subtract 160°

The Law of Sines tells you the side lengths are proportional to the sine of the opposite angle:

  t/sin(T) = u/sin(U) = v/sin(V)

  t = v/sin(V)·sin(T) = 45/sin(148°)·sin(20°) ≈ 29.0 . . . . multiply by sin(T)

  u = v/sin(V)·sin(U) = 45/sin(148°)·sin(12°) ≈ 17.7 . . . . . multiply by sin(U)

__

Additional comment

There may be two solutions if the given side is not opposite the largest angle.

a) Equation is: (3x)° + (x + 14)° = 90° and value of x = 19°

b) ∠1 = 57° and ∠2 = 33°

A right angle triangle is a geometric form with a single angle that is precisely 90 degrees in length. A right angle is another name for this angle. The other two angles are acute, which means that they have a degree value below 90. The hypotenuse, which is the triangle's longest side, is the side that faces the right angle.

Given a right angle of ∠1 and ∠2:

a) So, ∠1 + ∠2 = 90°

(3x)° + (x + 14)° = 90°

4x + 14° = 90°

x = 19°

b) ∠1 = (3x)°

∠1 = (3*19)°

∠1 = 57°

and, ∠2 = (x+14)°  

∠2 = (19+14)°

∠2 = 33°

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The probability for the  random sample are estimated as:

a) P(13 ≤X ≤ 16) = P( 0.158 ≤  X ≤ 0.50)

b) P(X ≤ 13) =  P( X ≤  0.158)

c) P(X >22)  =  P( X > 0.9777 )

The random sample will consist of a sample mean that asymptotically follows the normal distribution regardless of the distribution of both the parent population if a sample of size (n) is obtained from the population and as the sample's number of participants keeps increasing.

Let's say a random variable is divided up with just some parameters (μ,σ).

X~N(16,3³)

Then,

mean μ = 16

standard deviation σ = 3

z score is: z = (x - μ)/σ

The probability are estimated as:

a) P(13 ≤X ≤ 16)

P(13 ≤X ≤ 16) = P( (13 - μ)/σ  ≤  X ≤  (16 - μ)/σ )

                     = P( (13 - 16)/3  ≤  X ≤  (16 - 16)/3 )

                     = P( -1  ≤  X ≤  0 )

                     = P(  0.158 ≤  X ≤ 0.50)

b) P(X ≤ 13)

P(X ≤ 13) = P( X ≤  (13 - μ)/σ )

               =  P( X ≤  (13 - 16)/3 )

               =  P( X ≤  -1 )

               =  P( X ≤  0.158)

c) P(X >22)

P(X >22) = P( X > (22- μ)/σ )

              =  P( X > (22- 16)/3 )

              =  P( X > 2 )

              =  P( X > 0.9777 )

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Answer: 10,000

Step-by-step explanation:

One angle of a triangle measures 75°. The other two angles are in a ratio of 10:11. What are the measures of those two angles?

One angle measures = 75°

Ratio of other 2 angles = 10 : 11

Let the number be x

So, 10x : 11x

Sum of interior angles of a triangle = 180°

Now,

[tex]75 + 10x + 11x = 180[/tex]

[tex]10x + 11x = 180 - 75[/tex]

[tex]10x + 11x = 105[/tex]

[tex]21x = 105[/tex]

[tex]x = 105\div21[/tex]

[tex]x = 5[/tex]

So,

Second angle = 10x = 10 × 5 = 50° ans

Third angle = 11x = 11 × 5 = 55° ans

Answer:

sal-43 mins

elena-45 mins

Step-by-step explanation:

cant be bothered to type explanation

Step-by-step explanation:

16. 2/8 and 12/32

Common denominator is 32

8/32 and 12/32

17. 10/100 and 12/50

Common denominator is 100

10/100 and 24/50

18. 24/16 and 3/4

Common denominator 16

24/16 and 12/ 16

Answer:

a)  x = 90°

b)  The angle between the tangent and the radius at a point on a circle is 90°.

[tex]\hrulefill[/tex]

Step-by-step explanation:

The radius of a circle is the distance from the center of the circle to any point on its circumference.

The tangent of a circle is a straight line that touches the circle at exactly one point, called the "point of tangency".

The given diagram shows circle O along with a tangent line. The radius of the circle intersects the tangent at the point of tangency.

The tangent of a circle is always perpendicular to its radius.

Therefore, the size of angle x is 90°.

Therefore, the circle theorem that allowed us to work out the size of angle x is:

The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we  two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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The truth set of the equation 4^x + 2 = 3^(2x) is:

{x | x ∈ (-∞, 0)}

To find the truth set of the equation 4^x + 2 = 3^(2x), we need to find all values of x that make the equation true.

First, we can simplify the equation by writing 4 as 2^2 and 3^2 as (3^1)^2:

2^(2x) + 2 = (3^1)^(2x)

Simplifying further:

2^(2x) + 2 = 3^(2x)

Now, we can subtract 2^(2x) from both sides:

2 = 3^(2x) - 2^(2x)

Next, we can factor the right-hand side:

2 = (3^x - 2^x)(3^x + 2^x)

We want to find the values of x that make this equation true. Since 2 is a positive constant, we know that both factors on the right-hand side must be positive or both must be negative. If one factor is negative and the other is positive, then their product would be negative, which would contradict the equation.

So, we consider two cases:

Case 1: 3^x - 2^x > 0 and 3^x + 2^x > 0

In this case, both factors are positive, which means their product is positive. Therefore, there are no solutions in this case.

Case 2: 3^x - 2^x < 0 and 3^x + 2^x < 0

In this case, both factors are negative, which means their product is positive. Therefore, we can solve for x as follows:

3^x - 2^x < 0 and 3^x + 2^x < 0

3^x < 2^x and 3^x < -2^x

We can ignore the second inequality because it is always false (since 3^x and 2^x are always positive). So, we only need to solve the first inequality:

3^x < 2^x

Taking the logarithm of both sides with the same base (for example, base 2), we get:

log₂(3^x) < log₂(2^x)

Using the properties of logarithms, we can simplify:

x·log₂(3) < x·log₂(2)

Dividing both sides by x (which is positive because we are only considering the case where both factors are negative), we get:

log₂(3) < log₂(2)

Since log₂(3) is approximately 1.585 and log₂(2) is approximately 1, we can see that the inequality is true. Therefore, the solution set for Case 2 is:

{x | 3^x - 2^x < 0 and 3^x + 2^x < 0}

or, equivalently:

{x | x·log₂(3) < x·log₂(2)}

or, in interval notation:

(-∞, 0)

Hence, the truth set of the equation is {x | x ∈ (-∞, 0)}

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Answer:

6x+2

Step-by-step explanation:

We can use the distributive property.

2(3x+1) is the problem

The distributive property means you distribute what is outside the parenthesis to every term that is in the parenthesis.

So we get this:

3x(2) + 1(2)

Which leads to this

6x+2

6x+2 cannot be simplified, so that is our answer.

The expression 2|2x-4|-5=-3 is the value of x=5/2 or x=3/2.

The act of expressing something involves making your ideas, sentiments, etc. known through voice, writing, or another means. Algebraic expressions fall into three main kinds, including: Numeral Expression. Binary Expression. Expression of a polynomial.

Exponential equations to solve

The standard exponential equation is expressed as  y = ab^x

Given the expression

2|2x-4|-5=-3

Rearrange the terms.

2|2x-4|=-3+5

Reduce.

2|2x-4|=2

Divide the both.

|2x-4|=1

Separate into possible cases.

2x-4=1 or 2x-4=-1

Show more steps.

x=5/2 or x=3/2.

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Answer:

1st: 56, 2nd: 12, 3rd: 112

Step-by-step explanation:

Let's allow "x" to represent the first angle. This would mean:

1st: x

2nd: x-44 [ The second is 44 less than the first(x) ]

3rd: 2x [ The third is double the first(x) ]

Then, we create and equation using each of these expressions, and set it equal to 180. This is because the sum off all the angles in a triangle is equivalent to 180.

x + x - 44 + 2x = 180

4x = 180 + 44 (224)

4x/4 = 224/4

x = 56

Finally, we insert the value of x into the expressions we made in the beginning.

1st: 56

2nd: 12

3rd: 112

To check our work, we simply need to verify whether this equation is true:

56+12+112=180

This equation is valid. Therefore, the answers provided are correct.

The required value of x is 16.1 units.

Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.

We have;

∅ = 49°, Base = 14, perpendicular = x

To find value of x.

Then,

tan∅ = perpendicular/Base

tan(49°) = x/14

Here tan(49°) = 1.15

x = 1.15(14)

x = 16.1 units

Thus, required value of x is 16.1 units.

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Answer:224 SILLAS HAY AHORA

YA QUE ANTES HABIAN 216

Step-by-step explanation:

There are 224 chairs in the theater now.

Given:

9 rows

1 row = 24 chairs

8 extra chairs

9 x 24 = 216 chairs

216 chairs + 8 chairs = 224 chairs in all.

Answer:

7z + 17

Step-by-step explanation:

Like terms

All the numbers without letters are like terms

All the numbers with letters are like terms

Since we have 2 numbers without letters, we'll combine those.

15 + 2 = 17

Since there's only one number with letters, we can keep it the same since there's no others to combine it with

7z + 17