Need help with Geometry proof--thank u

Answer:

The answer is C

Step-by-step explanation:

The limit lim x → n − ⌊ x ⌋ is equal to n because the floor function ⌊ x ⌋ approaches n from values less than n as x approaches n from the left.

To evaluate the limit lim x → n − ⌊ x ⌋, we need to understand the concept of the floor function ⌊ x ⌋. The floor function returns the largest integer that is less than or equal to x. For example, ⌊3.7⌋ = 3 and ⌊-2.5⌋ = -3.

When we take the limit as x approaches n from the left (denoted by the minus sign in x → n − ⌊ x ⌋), we are essentially asking what happens to the function as x gets closer and closer to n from values less than n. Since n is an integer, the floor function ⌊ x ⌋ will always be equal to n when x is between n and n+1. Therefore, as x approaches n from the left, ⌊ x ⌋ will approach n.

So the limit lim x → n − ⌊ x ⌋ is equal to n. This makes sense intuitively, as we are essentially taking the integer part of a number that is very close to n from values less than n, so it would make sense for the integer part to be equal to n itself.

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distanceSolution:

Given that a toy car placed on the floor travels at a constant acceleration for 3 seconds reaching a velocity of 4v m/s, we have

It slows down with a constant deceleration of 0.5 m/s² for 4 seconds before hitting a wall and stopping. This is as shown below:

Thus, the velocity-time graph for the toy car is as shown below:

The total distance traveled by the toy car is evaluated by calculating the area of the triangle ABC. Thus,

Hence, the

Answer: D: Quadratic Equation.

Step-by-step explanation:

y = a*x^2 + b*x + c is a polynomial of degree = 2, this is also called a quadratic equation (because the largest exponent is 2)

Then the correct option is D: Quadratic Equation​

The other options are used for:

A: Subtraction:

This is for the difference between two numbers, a subtraction is X - Y.

B: Quotient:

This is for a division between two numbers, the quotient between X and Y is:

X/Y.

C: Scientific Notation:

This is used to simplify the notation of numbers with a lot of digits. Instead of write numbers like:

13,000,000

We can just write this as:

1.3*10^7

Answer: No real solutions

Step-by-step explanation: to solve for x and find a solution you need to take the square root of -144

This is not possible as this a negative number . There is a solution if we use complex numbers, but this not included in the question

Diinineinnneeeeeeeeeeeeeeeeeeeee

The value of a = 1/3 and b = 2.

We can expand the given expression using the binomial theorem:

Binomial theorem statement that for any positive integer n the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form in the sequence of terms, the index r takes on the successive values 0, 1, 2,…, n.

Equation.

(2-x)(1+ax)⁶ = (2-x) × [1 + 6a x + 15a² x² + ...]

Multiplying this out gives:

(2-x)(1+ax)⁶ = 2 + (6a-2x) x + (15a² - 12ax + x²) x² + ...

Comparing the coefficient of x and x² with the given expansion we get:

6a - 2 = 0 (coefficient of x)

15a² - 12a + 1 = b (coefficient of x²)

From the first equation, we get:

6a = 2

a = 1/3

Substituting this value of a into the second equation, we get:

15(1/3)² - 12(1/3) + 1 = b

5 - 4 + 1 = b

b = 2

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When matched with examples, the words would be:

The goal of visiting all fifty states during one's lifespan is clearly a great undertaking. Furthermore, the amusement park ride that attempts to realistically reproduce each person's experience of skydiving is an astonishing feat.

Moreover, it is readily apparent the school buses remain stationary and without activity in their parking lot throughout the weekend-- displaying their ordinary idleness. Likewise, electric cars are known to require fewer repairs than those powered by gas engines, offering a tremendous advantage above traditional cars.

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Answer: 14%

Step-by-step explanation:

Complete question is provided in the attachment below:

Probability that members of the junior varsity swim team wear glasses = 55%=0.55

Given: P(wear glasses) = 0.55

P(not wear glasses) = 1-0.55 = 0.45

P(member in 10th grade | not wear glasses) = 30%

Using conditional probability formula:

\(P(B|A)=\dfrac{P(A\text{ and } B)}{P(A)}\)

\(\Rightarrow\ 0.30=\dfrac{P(\text{not wear glasses and in 10th grade})}{0.45}\\\\\Rightarrow\ P(\text{not wear glasses and in 10th grade})=0.45\times0.30\\\\0.135=13.5\%\approx14\%\)

Hence, the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade = 14%.

So, the correct option is "14%".

Answer:

16 days

Step-by-step explanation:

This is a tricky question.

If you think of it quickly, you may want to say that it goes up 3 ft each day and down 2 ft each day, so it goes up a net 1 ft per day. Since it must climb 18 ft, it will take 18 days. That is incorrect.

Look at the following table.

          Begin           Amt             Pos. after         Amt of         Pos. at

Day     Pos.           of climb             climb             slide        end of night

1              0                   3                      3                    2                1

2             1                    3                      4                    2                2

3             2                   3                      5                    2                3

4             3                   3                      6                    2                4

5             4                   3                      7                    2                5

6             5                   3                      8                    2                6

7             6                   3                      9                    2                7

8             7                   3                     10                    2               8

9             8                   3                     11                     2               9

10            9                   3                    12                     2              10

11             10                  3                    13                    2              11

12            11                   3                    14                   2               12

13             12                 3                    15                   2               13

14             13                 3                    16                   2               14

15             14                 3                    17                   2                15

16              15                3                    18  

Once it reaches 18 ft high on day 16, it is out of the well.

Answer: Let's start by finding out how much distance the cat climbs each day:

Distance climbed during the day = 3 feet

Distance slid back during the night = 2 feet

So, the net distance climbed each day = 3 - 2 = 1 foot

To climb out of the well, the cat needs to climb a total of 18 feet.

Since the cat climbs 1 foot per day, it will take the cat 18 days to climb out of the well.

Step-by-step explanation:

Answer:

Adult ticket is $60

Child ticket is $32

Step-by-step explanation:

Let x = price of adult ticket

     y = price of child ticket

(1)    175x + 103y = 13796               (2)    2x + 2y = 184

                                                                 x + y = 92

                                                                       y = 92 - x

      175x + 103(92 - x) = 13796

      175x + 9476 - 103x = 13796

       72x = 4320

           x = 60                                                  y = 92 - 60

                                                                        y = 32

Answer:

a

Step-by-step explanation:

Cylinders:

Ratio of radii = 1 : 4

Radius of two cylinders are: r , 4r

Ratio of height = 3 :1

Height of two cylinders are: 3h , h

Lateral surface area of cylinder =  2πrh

Ratio of lateral surface area= 2π* r * 3h   : 2π* 4r * h

                                             = 3 : 4

At the zero point the curve can either cross the x-axis or just touch it. The root of the function is the number c with f(c) = 0.

If the graph intersects the x-axis and looks nearly linear at the intersection, it is a single root. Even multiplicity zero if the graph touches the x-axis and bounces off the axis.

Different graphs with different x-intercepts. The graph may intersect the x-axis at the intersection. Otherwise, the graph touches the x-axis and bounces.

For example, suppose you plot a function.

f (x) = (x + 1) (x - 2)²

See the figure above to see how the function behaves differently for different x intercepts.

x intercept at x = -1 is the solution of the equation

x + 1 = 0 , graph goes straight through the x intercept at x= −1 . We call it a single zero because zero corresponds to a single factor in the function.

x intercept at x = 2 is the iterative solution of the equation ( x - 2 )= 0

The graph touches the axis at the intercept and changes direction. The coefficients are quadratic (order 2), so, (x-2)²= (x - 2 )(x - 2)

coefficients are repeated and appears twice. The number of times a given factor appears in the factored form of a polynomial equation is called its multiplicity. Zero associated with this factor, the factor is (x-2), occurs twice, and has a multiplicity of 2 .

thus, the behaviour of graph shows that any point of f(x) which touch or intersect x-axis is call zero of f(x).

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Standard trigonometry texts typically do not include formulas for the cotangent, secant, and cosecant of the sum and difference of two numbers or angles due to several reasons.

Firstly, these functions can be easily derived from the well-known trigonometric identities involving sine, cosine, and tangent. Including separate formulas for the cotangent, secant, and cosecant would result in redundancy and unnecessary complexity.

Secondly, the cotangent, secant, and cosecant are not as commonly used as sine, cosine, and tangent in practical applications, so their inclusion may not be prioritized.

Moreover, space limitations in textbooks also play a role, as providing comprehensive formulas for all trigonometric functions could make the texts excessively lengthy.

Therefore, students are encouraged to understand the relationships between trigonometric functions and employ the existing identities to derive the values they need.

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Triangle XYZ is congruent to triangle ABC using the SAS. To verify the construction using measurement, you can use a protractor to measure the angles of triangle XYZ and compare them to the corresponding angles of triangle ABC.

To construct triangle XYZ congruent to triangle ABC using either SSS or SAS, follow the steps below:

1. Use a straightedge to draw an obtuse triangle ABC on a piece of paper. Ensure that one of the angles of triangle ABC is obtuse (greater than 90 degrees).

2. Select a point X on one side of triangle ABC. This will be one vertex of triangle XYZ.

3. Use a compass to measure the length of side AB. Transfer this length from point X to create side XY.

4. Using the same compass setting, place the compass on point Y and draw an arc that intersects side AC of triangle ABC. Label the point of intersection as Z.

5. Connect points X, Y, and Z to complete triangle XYZ.

Now, let's justify the construction mathematically:

To show that triangle XYZ is congruent to triangle ABC using the SAS (Side-Angle-Side) criterion, we need to demonstrate that the corresponding sides and the included angles are congruent.

1. Side XY is congruent to side AB since they were constructed to have the same length.

2. Side YZ is congruent to side AC because both were constructed using the same compass setting and intersected the same arc.

3. Angle XYZ is congruent to angle ABC because they are corresponding angles formed by the same pair of intersecting lines XY and AC.

Therefore, we have established that triangle XYZ is congruent to triangle ABC by the SAS criterion.

To verify the construction using measurement, you can use a protractor to measure the angles of triangle XYZ and compare them to the corresponding angles of triangle ABC. Additionally, you can use a ruler to measure the lengths of the sides and compare them to ensure they are congruent.

By following the construction steps and verifying the congruence using measurement, you can confirm the accuracy of the constructed triangle XYZ, which is congruent to triangle ABC.

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The java program has been written and the program is implemented to get desired results

Here's a Java program that uses recursion to compute the factorial of a given nonnegative integer:

public class Factorial {

   public static void main(String[] args) {

       int n = 5; // example input

       int result = factorial(n);

       System.out.println(n + ""! = "" + result);

   }

   public static int factorial(int n) {

       if (n == 0) {

           return 1;

       } else {

           return n * factorial(n - 1);

       }

   }

}

Here, the factorial method is defined to take an integer n as input and return the factorial of n. The base case of the recursion is when n equals 0, in which case the method returns 1. Otherwise, the method multiplies n by the factorial of n-1, which is computed by a recursive call to the factorial method with n-1 as the argument.

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Using mathematical induction, prove that for all n ≥ 1, \(k=1nk(k+1)=3n(n+1)(n+2\)) We will utilize induction to prove the given statement. Let P(n) be the given statement i.e., ∑ \(k=1nk(k+1) = 3n(n+1)(n+2)\)

Step 1: Base Case Let’s check P(1).∑ \(k=1nk(k+1) = 1(1+1)(1+2)/3 = 2 = 3(1)(1+1)(1+2)/3\) Thus P(1) is true.

Step 2: Induction Hypothesis Let's assume that P(n) is true for some natural number k, i.e.,∑ \(k=1nk(k+1)\) = \(3n(n+1)(n+2)\)

Step 3: Inductive Step We will now demonstrate that P(n) is true for n+1.

As we know that,∑ \(k=1nk(k+1) + (n+1)(n+2)(n+1+1)=\) ∑ \(k=1n+1k(k+1)=\) ∑\(k=1nk(k+1) + (n+1)(n+2)(n+1+1)\)

From our assumption (induction hypothesis) for P(n) we can state,∑ k=1nk(k+1) = 3n(n+1)(n+2)

And substituting it in the above equation, we get,

∑\(k=1nk(k+1) + (n+1)(n+2)(n+1+1)\)

= \(3n(n+1)(n+2) + (n+1)(n+2)(n+1+1)\)

= \((n+1)(n+2)[3n + (n+1)]\)

=\((n+1)(n+2)(n+3)\)

P(n+1) is true .We can conclude that the given statement is true for all n≥1 by using mathematical induction and we are done.

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The probability of rolling an even number and then an odd number is 1/4.

The probability of rolling an even number on a fair number cube is 1/2, since there are three even numbers (2, 4, 6) and six possible outcomes (1, 2, 3, 4, 5, 6).

Similarly, the probability of rolling an odd number is also 1/2.

To find the probability of rolling an even number and then an odd number, we need to multiply the probabilities of each event. So:

P(even and odd) = P(even) × P(odd)

P(even and odd) = (1/2) × (1/2)

P(even and odd) = 1/4

So the probability of rolling an even number and then an odd number is 1/4.

The number of desired outcomes for rolling an even number and then an odd number is 9

Since there are three even numbers and three odd numbers, and therefore 3 × 3 = 9 possible outcomes.

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The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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Answer:

\(x \leq \frac{1}{3}\) or \(x \geq \frac{1}{2}\)

Answer:

Below

Step-by-step explanation:

From the graph below you can see that

x < = .33 3   and   x >= .5

combined

  .333  ≥  x  ≥  .5

The general equation of the straight line passing through point A perpendicularly to vector AB is y - 2 = 5(x - 3), and the general equation of the straight line passing through point B parallel to vector AC is y - 3 = -1/2(x - (-2)).

To find the equation of a straight line passing through point A perpendicularly to vector AB, we first need to determine the slope of vector AB. The slope is given by (change in y)/(change in x). So, slope of AB = (3 - 2)/(-2 - 3) = 1/(-5) = -1/5. The negative reciprocal of -1/5 is 5, which is the slope of a line perpendicular to AB. Using point-slope form, the equation of the line passing through A can be written as y - y₁ = m(x - x₁), where (x₁, y₁) is point A and m is the slope. Plugging in the values, we get the equation of the line passing through A perpendicular to AB as y - 2 = 5(x - 3).

To find the equation of a straight line passing through point B parallel to vector AC, we can directly use point-slope form. The equation will have the same slope as AC, which is (1 - 3)/(2 - (-2)) = -2/4 = -1/2. Using point-slope form, the equation of the line passing through B can be written as y - y₁ = m(x - x₁), where (x₁, y₁) is point B and m is the slope. Plugging in the values, we get the equation of the line passing through B parallel to AC as y - 3 = -1/2(x - (-2)).

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The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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Answer:-1/2

Step-by-step explanation:

-3/7 x 1-1/14

Multiply first

-3/7-1/14

-7/14=-1/2

Answer:

-1/2

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

Hello There!

(Let x = angle T)

if you didn't know an exterior angle of a triangle is equal to its two opposite interior angles

So basically

155 (being the exterior angle) is equal to 50 + x (being the opposite interior angles)

so x = 155 - 50

155 - 50 = 105

so we can conclude that x (angle T) equals 105

Answer:

105 degrees

Step-by-step explanation:

The angle measure of the exterior angle is equal to the sum of the two nonadjacent interior angles (angle V and angle T).

155 - 50 = 105

Answer:

x = 80

Step-by-step explanation:

750 - 70 = 680

680 / 8.5 = x

Answer:

There are 192 employees in the company.

Step-by-step explanation:

Let x be the total number of employees

Use ratio and proportion

\(\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192\)

x = 192

√ x/4 + 4 is the inverse of the function f(x)=4x^2-16

What is inverse function?

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f

Given  f(x)=4x²-16

Let f(x) = y

So we can say y =4x²-16

We will then make x the subject:

Since y = 4x²-16

4x² = y + 16

x² = y + 16/4

x = √ y/4 + 4

since x = f⁻¹(y)  = √ y/4 + 4

Thus  f⁻¹(x)  = √ x/4 + 4

Therefore, the inverse of f(x)=4x^2-16 is √ x/4 + 4

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Answer:

15840

Step-by-step explanation:

The parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

For this question,

The curve is given as

x(t)=e^-t cos(t),

y(t) =e^-t sin(t),

z(t)=e^-t

The point is at (1,0,1)

The vector equation for the curve is

r(t) = { x(t), y(t), z(t) }

Differentiate r(t) with respect to t,

x'(t) = -e^-t cos(t) + e^-t (-sin(t))

⇒ x'(t) = -e^-t cos(t) - e^-t sin(t)

⇒ x'(t) = -e^-t (cos(t) + sin(t))

y'(t) = - e^-t sin(t) + e^-t cos(t)

⇒ y'(t) = e^-t ((cos(t) - sin(t))

z'(t) = -e^-t

Then, r'(t) = { -e^-t (cos(t) + sin(t)), e^-t ((cos(t) - sin(t)), -e^-t }

The parameter value corresponding to (1,0,1) is t = 0. Putting in t=0 into r'(t) to solve for r'(t), we get

⇒  r'(t) = { -e^-0 (cos(0) + sin(0)), e^-0 ((cos(0) - sin(0)), -e^-0 }

⇒  r'(t) = { -1(1+0), 1(1-0), -1 }

⇒  r'(t) = { -1, 1, -1 }

The parametric equation for line through the point (x₀, y₀, z₀) and parallel to the direction vector <a, b, c > are

x = x₀+at

y = y₀+bt

z = z₀+ct

Now substituting the (x₀, y₀, z₀) as (1,0,1) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get

x = 1 + (-1)t

⇒ x = 1 - t

y = 0 + (1)t

⇒ y = t

z = 1 + (-1)t

⇒ z = 1 - t

Hence we can conclude that the parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

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Answer:

Im so sorry but I have no idea

Step-by-step explanation:

Answer:

$163.5 is the answer.....