Keegan was asked to graph (R90•D2)(Triangle ABC). Explain Keegan’s error.

The function which represent the distance and time is y=6x-17.5.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here according to the given data, let us take to points to find linear function then,

[tex](x_1,y_1)=(0.5,3)[/tex] and [tex](x_2,y_2)=(1,6)[/tex].

Now using slope formula, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slope m = [tex]\frac{6-3}{1-0.5} = \frac{3}{0.5}[/tex] = 6

Now using equation formula , [tex]y-y_1=m(x-x_1)[/tex] then,

=> y-0.5=6(x-3)

=> y-0.5=6x-18

=> y=6x-18+0.5

=> y=6x-17.5

Hence the function which represent the distance and time is y=6x-17.5.

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Answer:

1011.00

Step-by-step explanation:

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The points M, N, P, and Q have been plotted in the coordinate plane below.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;

Midpoint MP = [(2 + 1)/2, (-1 + 2)/2]

Midpoint MP = [3/2, 1/2]

Midpoint MP = (1.5, 0.5).

For the fourth vertex Q, we have:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(1.5, 0.5) = [(4 + x₂)/2, (0 + y₂)/2]

4 + x₂ = 2(1.5)

x₂ = -4 + 3

x₂ = -1.

0 + y₂ = 2(0.5)

y₂ = 1.

Therefore, vertex Q = (-1, 1).

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Equation of straight line parallel to y = 3x - 2 and passing through (1, 9) is

y = 3x + 6

A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity. A straight line is a figure formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them, and the line ends are extended to infinity.

Given,

Line y = 3x - 2

Comparing with y = mx + c

slope = 3

Line parallel to y = 3x - 2 and passing through (1, 9)

Slope of the parallel line = slope of line y = 3x - 2

slope m = 3

Equation of the line,

y - y' = m(x - x')

y - 9 = 3(x - 1)

y - 9 = 3x - 3

y = 3x + 6

Hence y = 3x + 6 is equation of line parallel to y = 3x - 2 and passing through (1, 9)

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The functions involved in g(x) are multiply by 2 and subtract the value of 5.

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted on the line y = x. This graph's line traverses the origin and has a slope value of 1.

Given that, f(x) involves the following functions:

Divide by 2

Add 5

Also, g(x) is the inverse of the function of f(x) hence, the function involved are inverse of the original function.

Hence, the functions involved in g(x) are multiply by 2 and subtract the value of 5.

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1 divided by 2/6 is equal to 3.

Division is a mathematical operation used to divide one number (the dividend) by another number (the divisor) to find out how many times the divisor is contained within the dividend

To divide 1 by 2/6, we need to find out how many times the denominator (2/6) fits into the numerator (1).

One way to approach this is to convert the fraction 2/6 to an equivalent fraction with a denominator of 1. To do this, we can multiply both the numerator and denominator of 2/6 by the same number, in this case 3:

2/6 = (23)/(63) = 6/18

Now, we can divide 1 by 6/18:

1 ÷ 6/18

= 1 x 18/6 (reciprocal of 6/18 is 18/6, which is equivalent to 3)

= 3

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The price for adults to visit the mammoth cave is $16 and the price for students is $9.

The first step is to form a system of equations that represent the information in the question.

2a + 5s = 77 equation 1

2a + 7s = 95 equation 2

Where:

a = price of one adult

s = price of one student

The elimination method would be used to solve the equations.

Subtract equation 1 from equation 2:

2s = 18

Divide both sides of the equation by 2

s = 18/2

s = $9

Substitute for s in equation 1:

2a + 5(9) = 77

2a + 45 = 77

2a = 77 - 45

2a = 32

a = 32 / 2

a = 16

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The solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:

X = π/2, 11π/6

To solve the equation 2 sin^2 (x) – sin(x) – 1=0 for all solutions 0 < x < 2π, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -1, and c = -1. Plugging these values into the quadratic formula gives us:

x = (-(-1) ± √((-1)^2 - 4(2)(-1))) / (2(2))

Simplifying the expression inside the square root gives us:

x = (1 ± √(1 + 8)) / 4

x = (1 ± √9) / 4

x = (1 ± 3) / 4

This gives us two possible values for x:

x = (1 + 3) / 4 = 1

x = (1 - 3) / 4 = -0.5

Now we need to find the values of x that satisfy the original equation and are within the given range of 0 < x < 2π. To do this, we can use the inverse sine function:

x = sin^-1(1) = π/2

x = sin^-1(-0.5) = -π/6

Since we are looking for solutions within the range of 0 < x < 2π, we need to add 2π to the nagetive solution to get a positive value:

x = -π/6 + 2π = 11π/6

Therefore, the solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:

X = π/2, 11π/6

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answer = c

its not a or b because the range starts at y = 2

Answer: ∠ABC = 29.745°

Step-by-step explanation:

I believe this is the answer , you should be golden.

Answer:

no se     y ademas me aparece en ingles :(

Step-by-step explanation:

The equation that has no real solution is 12x + 12 = 3(4x + 5), the correct option is (d).

To determine whether an equation has real solutions, we need to solve it and check whether the solutions are real numbers or not.

-5x - 25 - 5x + 25 = 0 simplifies to -10x = 0, which has the solution x = 0. This is a real number solution.

7x + 21 = 21 simplifies to 7x = 0, which has the solution x = 0. This is a real number solution.

12x + 15 = 12x - 15 simplifies to 15 = -15, which is false. This equation has no solution, but it doesn't have any variables left to solve for, so it's not an option for our answer.

12x + 12 = 3(4x + 5) simplifies to 12x + 12 = 12x + 15, which simplifies further to 12 = 15. This is false, which means the equation has no solutions. Therefore, this is the equation that has no real solution, the correct option is (d).

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The complete question is:

Select each equation that has no real solution

a. -5x- 25 - 5x + 25

b. 7x + 21 = 21

c. 12x + 15 = 12x - 15

d. 12x + 12 = 3(4x + 5)

Two functions as cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9)

We can rewrite the product using a sum or difference of two functions as follows:2 sin (2x/3) sin (5x/6)In order to rewrite the product using a sum or difference of two functions, we can use the following formula:2 sin A sin B = cos (A - B) - cos (A + B)Where A and B are two angles or expressions that contain an angle.So, 2 sin (2x/3) sin (5x/6) can be written as follows:2 sin (2x/3) sin (5x/6) = cos [(5x/6) - (2x/3)] - cos [(5x/6) + (2x/3)]On simplifying the above expression, we get2 sin (2x/3) sin (5x/6) = cos [(5x/6 - 4x/9)] - cos [(5x/6 + 4x/9)]= cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9)Therefore, 2 sin (2x/3) sin (5x/6) can be rewritten using a sum or difference of two functions as cos (5x/6 - 4x/9) - cos (5x/6 + 4x/9).

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The irrational number between 5,25 and 5,26 is 2.5135145:

The irrational number between 5,25 and 5,26

2.5135145...

The number is non-terminating and non-recurring. Hence, it is an irrational number.

A real number that cannot be expressed as a simple fraction is called an irrational number.

It is impossible to express in terms of a ratio.

If N is irrational, it is not equal to p/q, where p and q are integers and q is not equal to 0.

Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.

An irrational number is a real number that cannot be expressed as a fraction of two integers. In other words, it is a number that cannot be written as a simple fraction or a ratio of integers. Irrational numbers are decimal numbers that go on forever without repeating. Some famous examples of irrational numbers include pi (3.14159265...) and the square root of 2 (1.41421356...).

Irrational numbers have some interesting properties. For example, they are non-repeating and non-terminating, which means that their decimal expansions never repeat and never come to an end. This makes them difficult to work with, but also makes them important in mathematics and science. Irrational numbers are used in a variety of mathematical and scientific applications, including geometry, physics, and cryptography.

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The value of x is 7

The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°

Therefore ;

50+28+15x-3 = 180

78-3 +15x = 180

75 +15x = 180

collect like terms

15x = 180-75

15x = 105

divide both sides by 15

x = 105/15

x = 7

therefore the value of the missing variable (x) is 7

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The answer is g(-2) = 15.

To find g(-2) using synthetic division, we need to follow these steps:

Write down the coefficients of the polynomial in descending order. The coefficients are 11, 29, 19, 22, and 39.

Write down the value of the divisor in the leftmost column. In this case, the divisor is -2.

Bring down the first coefficient (11) to the bottom row.

Multiply the bottom row value (11) by the divisor (-2) and write the result (-22) in the next column.

Add the coefficient in that column (29) to the result (-22) and write the sum (7) in the bottom row.

Repeat steps 4 and 5 until you reach the last column. The final result in the bottom row is the remainder.

The synthetic division should look like this:

-2 | 11  29  19  22  39
   | -22 -14 -10 -24
   -------------------
     11   7   9  12  15

Therefore, g(-2) = 15.

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Step-by-step explanation:

Refer to pic............

The tabs can be completed in the following way:

1. Fraction for 25% = 25/100 = 5/20 = 1/4

2. 90 percent: Decimal 0.90: Fraction: 90/100 =9/10

3. 60 percent: Decimal 0.60: Fraction: 60/100 = 6/10 = 3/5

4. 35 percent: Decimal 0.35: Fraction: 35/100 = 7/20

5. 33 percent: Decimal 0.33: Fraction: 33/100

6. 65 percent: Decimal 0.65: Fraction: 65/100 = 13/20

A percentage is a value that is obtained as a fraction of the number 100. In the above question, we are given a list of values in percentages and told to convert them to decimal and fraction forms.

To do this, we need to divide the number 90 by 100 for the second expression and express this as a decimal. The resultant figure is 0.9. When converted to a fraction, the value now has a denominator and numerator.

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The median, Q₁, Q₃, lower fence and upper fence of the given data set are 82, 75, 83, 63 and 95.

What is Inter quartile range?

In a range of values, from lowest to highest, the IQR denotes the median 50% of values. Find the median (middle value) of the lower and higher half of the data first, then use that number to calculate the interquartile range (IQR). The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.

Given data set : 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83

Firstly, we will arrange the data into ascending order.

we get, 54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100.

Here, no. of terms is 11

So, Median = (n+1)/2 th = (11+1)/2 = 6th term

So, Median = 82.

Q₁ = (n+1)/4 th term = (11+1)4 th = 3rd term

                                                 = 75

Q₃ = 3(n+1)/4 th term = 9th term = 83

Inter-quartile range = Q₃ - Q₁

                                  = 83 - 75 = 8.

Now, Lower fence = Q₁ - 1.5*IQR

                              = 75 - 1.5× 8

                              = 75 - 12 = 63

       Upper fence = Q₃ + 1.5*IQR

                              = 83 + 1.5×8

                              = 83 + 12

                              = 95.

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No, these two matrices are not equal.

The first matrix is a 3x3 matrix with the elements [[3,-1,7],[2,6,-9],[-5,4,-2]] and the second matrix is also a 3x3 matrix with the elements [[-2,-9,7],[4,6,-1],[-5,2,3]]. In order for two matrices to be equal, they must have the same dimensions and the corresponding elements must be equal. In this case, the dimensions are the same, but the corresponding elements are not equal. For example, the first element in the first matrix is 3, but the first element in the second matrix is -2. Therefore, these two matrices are not equal.

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Phil spent 18.26% of his pocket money on eating out for one meal.

The following is the formula for calculating the percentage difference between two values:

100% of ((new value - old value) old value)

In order to describe the change as a percentage, this formula calculates the difference between the new and old values, divides that difference by the old value, and multiplies the result by 100.

Given that, Phil spent $21 of his $115 pocket money.

Thus,

$21 ÷ $115 × 100% = 18.26%

Hence, Phil spent 18.26% of his pocket money on eating out for one meal.

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Answer:

x = -4 + √15 and x = -4 - √15.

Step-by-step explanation:

To solve for x in the equation (x + 4)^2 = 15 using square roots, we can take the square root of both sides of the equation, remembering to include both the positive and negative square root:

(x + 4)^2 = 15

Taking the square root of both sides:

±(x + 4) = √15

Now we can isolate x by subtracting 4 from both sides of the equation:

x + 4 = ±√15

x = -4 ±√15

Therefore, the solutions to the equation (x + 4)^2 = 15 are x = -4 + √15 and x = -4 - √15.

Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.

A figure can be expressed as a fraction of 100 using a percentage. It is frequently utilised to compare two values or to convey a portion of a whole. "%," which stands for "per hundred," is the symbol used to indicate percentages. 50%, for instance, is 50/100, or 50 out of 100. Calculating percentages involves dividing a portion by a whole and multiplying the result by 100. For instance, if a bag contains 75 blue spheres and 25 red balls, the proportion of red balls is as follows:

(Number of red balls / Total Number of Balls) times 100% equals the percentage of red balls.

Red ball percentage equals (25/100) times 100%

25% of the balls are crimson.

given

You can compute the cost as follows:

Loss is calculated as Initial Price - Selling Price ($210 - $139).

Loss = $71

We must divide the loss by the initial price and multiply by 100 to determine the percentage loss:

(Loss / Original price) times 100 equals the percentage of loss.

($71 / $210) times 100 equals the percentage loss.

Loss as a percentage: 33.81%

Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.

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To create a graph and write an equation to represent the list of ordered pairs given, we need to plot each point on a coordinate system.

x | y

--|--

2 |-3

1 |-1

-1| 3

3 |-5

Plotting these points on a coordinate plane, we get:

![Graph of ordered pairs]

To write an equation to represent these ordered pairs in the form y = mx + b, we need to find the slope of the line and the y-intercept.

To find the slope:

m = (y2 - y1) / (x2 - x1)

Let's use the points (1, -1) and (3, -5) to find the slope:

m = (-5 - (-1)) / (3 - 1)

m = -4 / 2

m = -2

Now that we know the slope, we can use any point and the slope to find the y-intercept (b).

Using the point (1, -1):

y = mx + b

-1 = (-2)(1) + b

b = 1

So the equation that represents these ordered pairs in the form y = mx + b is:

y = -2x + 1

And the graph of this equation looks like:

![Graph of equation y = -2x + 1]

Yes, the algebraic expression [tex]3x^(2)+3x^(-3)-2[/tex] is a polynomial.

A polynomial is an algebraic expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, as well as non-negative integer exponents. The given algebraic expression satisfies these conditions, so it is a polynomial.

To write the polynomial in standard form, we need to rearrange the terms in descending order of exponents. In this case, the term with the highest exponent is [tex]3x^(2)[/tex], followed by the term with the lowest exponent, [tex]3x^(-3)[/tex], and finally the constant term, -2.

Therefore, the polynomial in standard form is:[tex]3x^(2)+3x^(-3)-2 = 3x^(2)-2+3x^(-3)[/tex] So, the polynomial in standard form is  [tex]3x^(2)-2+3x^(-3)[/tex].

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The value of 'x' and 'y' in x + 1 : 3y = 1 : 7 and 2x : y + 3 = 2 : 5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know, We can write a : b as, a/b.

Therefore, The given equations can be formed as,

(x + 1)/3y = 1/7 and 2x/(y + 3) = 2/5.

7x + 7 = 3y.

7x - 3y = - 7...(i)

And,

10x = 2y + 6.

10x - 2y = 6...(ii)

Now, Multiplying eqn(i) by 10 and (ii) by 7 we have,

70x - 30y = - 70...(iii) and 70x - 14y = 42...(iv)

Now, By Subtracting (iii) and (iv) we have,

- 16y = - 112

y = 7 and hence x = 2

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In the given triangle, using congruency, ∠JHI is congruent to ∠SJT.

What is Triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

In the given figure, we can see that there are two pairs of vertically opposite angles, which are opposite to each other at the intersection of two straight lines. These angles are:

According to the ASA Rule, triangles are congruent to one another if any two angles and the side between them are comparable to the corresponding angles and side. According to the AAS Rule, the triangle's angles and excluded side are equal in the same way.

In the given triangle, using congruency, ∠JHI is congruent to ∠SJT

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The chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.

The chain rule is a formula for calculating the derivative of a composite function. It states that the derivative of a composite function f(g(x)) is equal to the derivative of f with respect to g times the derivative of g with respect to x. In mathematical notation, this is expressed as (f(g(x)))' = f'(g(x)) * g'(x).

In the case of the first equation, we can use the chain rule to reduce it to the second equation by applying the formula mentioned above. First, we need to identify the composite function and its components. In this case, the composite function is f(g(x)) and the components are f and g.

Next, we need to find the derivative of f with respect to g and the derivative of g with respect to x. Once we have these derivatives, we can multiply them together to get the derivative of the composite function.

Finally, we can reduce the first equation to the second equation by substituting the derivative of the composite function for the original composite function. This will give us the second equation, which is a simplified version of the first equation.

In conclusion, the chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.

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The series n=1∑[infinity]​(−1)n−13n+4ln(5n+2)​ is conditionally convergent.

To determine the convergence of a series, we can use the Alternating Series Test. This test states that if the absolute value of the terms in the series decrease to zero, then the series is convergent.

First, we need to find the absolute value of the terms in the series:

| (−1)n−13n+4ln(5n+2)​ | = | 3n+4ln(5n+2)​ |

Next, we need to determine if the absolute value of the terms decrease to zero. To do this, we can use the Limit Comparison Test. We will compare the series to the series 1/n:

lim n→∞ | 3n+4ln(5n+2)​ | / (1/n) = lim n→∞ | 3n^2+4nln(5n+2)​ |

Since the limit of the series is infinity, the series is divergent. However, since the series alternates between positive and negative terms, it is conditionally convergent.

Therefore, the series n=1∑[infinity]​(−1)n−13n+4ln(5n+2)​ is conditionally convergent.

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The probability of at most one price hike in one year is 0 + 0 = 0.

No price hikes in a randomly selected one and a half year:

The probability of no price hikes in one year is 0, since the average is 4. Therefore, the probability of no price hikes in one and a half years is also 0.

Four price hikes in 2 years:

The average number of price hikes in one year is 4, so the average number of price hikes in 2 years is 8. The probability of exactly 4 price hikes in 2 years is therefore 0, since it is less than the average.

At most one price hike in one year:

The probability of at most one price hike in one year is the sum of the probabilities of 0 and 1 price hikes. The probability of 0 price hikes is 0, as mentioned before. The probability of 1 price hike is also 0, since it is less than the average of 4. Therefore, the probability of at most one price hike in one year is 0 + 0 = 0.

Overall, the probability of no price hikes in a randomly selected one and a half year, four price hikes in 2 years, and at most one price hike in one year are all 0, since they are all less than the average number of price hikes.

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Answer: (-35, 30)

Step-by-step explanation:

Since the scale factor is four, it denotes that it’s a positive dilation. The question is asking for 5 times the point. In other words, where would the point be if it was stretched out 5 times.

If you draw a line from the given to the QED, (-7, 6) to (-35, 30), then you’ll realize that the image is 5 times the original point.

K= (-7*5, 6*5)

Any number less than one means the point or shape is being compressed or made smaller.