Pythagoream Theorem Escape Room

The rigid motion of the solid line figure is translated to the dotted line figure.

Translation describe a function that moves an object a certain distance.

In a translation, every point of the object must be moved in the same direction and for the same distance.

In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.

Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation

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Answer:

1 is multiplication

2 is simplification

3 is subtraction

4 is simplification

Step-by-step explanation:

The value for the Inequality 13x ≤ 200 is x ≤ 15.384.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

13 times a number x is less than or equal to 200.

Now, Writing the Inequality Mathematically

13x ≤ 200

x ≤ 200 / 13

x ≤ 15.384

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The required polygon whose area is to be calculated is attached below :

Answer:

16 unit²

Step-by-step explanation:

From the graph, the polygon is a triangle with height of 8 units and base of 4 units ;

Area of a triangle is given as :

Area = 1/2 * base * height

Area = 1/2 * 4 * 8

Area = 2 * 8

Area = 16 unit²

Answer:

-12 =x

Step-by-step explanation:

3(x - 2) = 6(5 + x)

Distribute

3x -6 = 30 +6x

Subtract 3x from each side

3x-6-3x = 30 +6x-3x

-6 = 30+3x

Subtract 30 from each side

-6 -30 = 30+3x-30

-36 = 3x

Divide each side by 3

-36/3 = 3x/3

-12 =x

Answer:

Nick

Step-by-step explanation:

Find their rates by dividing the number of meters they biked by 10:

Jason:

30/10

= 3 meters/sec

Nick:

45/10

= 4.5 meters/sec

So, since 4.5 is bigger than 3, Nick was biking at a faster rate.

SOLUTION:

Step 1 :

In this question, we are given that:

Step 2 :

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

Answer:

x = {x: -1, 5}

Step-by-step explanation:

\({ \rm{f(m) = (x + 1)(x - 5)}}\)

- To find the values of function f(m), we consider its zero or its root by letting f(m) = 0

\({ \rm{f(m) = 0 = (x + 1)(x - 5)}} \\ { \rm{(x + 1)(x - 5) = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: }}\)

- Either (x + 1) or (x - 5) is equated to zero

\({ \rm{x + 1 = 0}} \\ { \rm{x = - 1}}\)

\({ \rm{x - 5 = 0}} \\ { \rm{x = 5}}\)

Therefore, x is -1 and 5

\({ \bold{ \boxed{ \red{ \delta}}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}\)

Answer:

1a, 1b, 1c, 1d, 2a, 2b, 2c, 2d, 3a, 3b, 3c, 3d, 4a, 4b, 4c, 4d, 5a, 5b, 5c, 5d

20x2 = 40

Step-by-step explanation:

you half ot do the a1,a2,a3,a4 you get what i mean

The total number of possible outcomes are 20.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given that, choose a number from 1 to 5 and a letter from A to D.

Here, the sample space is

{1A, 1B, 1C, 1D, 2A, 2B, 2C, 2D, 3A, 3B, 3C, 3D, 4A, 4B, 4C, 4D, 5A, 5B, 5C, 5D}

So, possible number of outcomes is 20.

Therefore, the total number of possible outcomes are 20.

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The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.

Given expression y² - 13y + ?

Comparing with the general equation

a = 1

b = -13

For perfect square trinomial

b² = 4ac

(-13)² = 4 * 1 * c

169 = 4c

c = 169/4

So the expression becomes,

y² - 13y + 169/4 = (y - 13/2)²

Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.

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Answer:

  -1

Step-by-step explanation:

You want the average rate of change of the function shown in the graph between x=-1 and x=2.

The y-value at x = -1 is 9.

The y-value at x = 2 is 6.

The graph changes by 6-9 = -3 units as x changes by 2 -(-1) = +3 units.

The average rate of change is ...

  (change in y) / (change in x) = -3/3 = -1

The average rate of change from x = -1 to x = 3 is -1.

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Answer:

$3.20/gallon

Step-by-step explanation:

to fill up your tank at $3.20/gallon only costs $38.40

Answer:

Ordered

Step-by-step explanation:

The ordered pair is the location of a point on the coordinate plane and contains the x coordinate and y coordinate

An ordered pair tells you the location of a point by relating the point's location along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair). In an ordered pair, such as (x, y), the first value is called the x-coordinate and the second value is the y-coordinate.

Answer:

y=4x+4

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

To find the zeros, you want to first factor the expression.

x³+x²-36

(x-3)(x²+4x+12)

Now that we have found the factors, we set each to 0.

x-3=0

x=3

Since x²+4x+12 cannot be factored, we can forget about this part.

Therefore, the zeros are x=3. You can check this by plugging the expression into a graphing calculator to see the zeros.

|0.4552| < 1.96, we fail to reject the null hypothesis that p₁ = p₂.

Therefore, at the 0.05 significance level, there is not enough evidence to conclude that the proportions of success in the two samples are significantly different.

To find the standardized test statistic (z) to test the hypothesis that p₁ = p₂, where p₁ and p₂ are the proportions of success in two independent samples, we can use the following formula:

z = (p₁ - p₂) / √(p * (1 - p) * ((1/n₁) + (1/n₂)))

where:

p₁ and p₂ are the sample proportions of success in the two samples.

p = (x₁ + x₂) / (n₁ + n₂) is the pooled proportion of success in both samples.

n₁ and n₂ are the sample sizes of the two samples.

x₁ and x₂ are the number of successes in the two samples.

Given the sample statistics:

n₁ = 50, x₁ = 35 (sample 1)

n₂= 60, x₂ = 40 (sample 2)

First, calculate the pooled proportion (p):

p = (x₁ + x₂) / (n₁ + n₂)

p = (35 + 40) / (50 + 60)

p = 75 / 110

p ≈ 0.6818

Now, calculate the standardized test statistic (z):

z = (p₁ - p₂) / √(p * (1 - p) * ((1/n₁) + (1/n₂)))

z = (35/50 - 40/60) / √(0.6818 * (1 - 0.6818) * ((1/50) + (1/60)))

z = (0.7 - 0.6667) / √(0.6818 * 0.3182 * (0.02 + 0.0167))

z = 0.0333 / √(0.1456 * 0.0367)

z = 0.0333 / √(0.00534272)

z = 0.0333 / 0.073068

z ≈ 0.4552

Now, compare the standardized test statistic (z) with the critical value at α = 0.05. Since this is a two-tailed test, the critical value is approximately ±1.96 (at a 5% significance level).

Since |0.4552| < 1.96, we fail to reject the null hypothesis that p₁ = p₂.

Therefore, at the 0.05 significance level, there is not enough evidence to conclude that the proportions of success in the two samples are significantly different.

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Answer:

Probability that student will be a girl = 17 / 28

Step-by-step explanation:

Given:

Total number of student = 28 student

Number of boys in the class = 11

Find:

Probability that student will be a girl = ?

Computation:

⇒ Number of girls in class = Total number of student - Number of boys in the class

⇒ Number of girls in class = 28 - 11

⇒ Number of girls in class = 17

⇒ Probability that student will be a girl = Number of girls in class / Total number of student

⇒ Probability that student will be a girl = 17 / 28

Answer:

5 feet

Step-by-step explanation:

\(f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}\)

Answer:

42 minues 5 seconds to do 17 laps.

Step-by-step explanation:

it takes her 2 minuetes and 50 seconds to do 1 lap if you multiply 2.5x17=

42 munites and 5 secondesto do 17 laps

Answer:

It would take 42.5 min

Step-by-step explanation:

4/10 = 2.5(unit rate for every lap it takes 2.5 min)

17 x 2.5 = 42.5

It's asking  would not be a solution soo

(-10, -9) as you can see

You're welcome thank me later

The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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Answer:

The answer is "\(f_{R} (r) =\frac{5}{2r^2}; \frac{10}{12} \leq r \leq \frac{10}{8}\)"

Step-by-step explanation:

They have the distributional likelihood function of T: \(f_{\Gamma } \ (t)= \frac{1}{12-8}= \frac{1}{4}; 8 \leq t \leq 12\)

This is the following PDF of transformation \(R =\frac{10}{T}\)

They know that PDF is the Y=g(X) transformation

\(f_{y} (y)=f_{x} (g^{-1} (y))|\frac{dg^{-1} (y)}{dy}\)

Using theformula, the PDF of  \(R =\frac{10}{T}\) is

\(f_{R} (\Gamma)=f_{(\Gamma)} |\frac{d(\frac{10}{r})}{dr}| \\\\f_{R}(r) =\frac{1}{4}| -\frac{20}{r^2}|\\\\f_{R} (r) =\frac{5}{2r^2}; \frac{10}{12} \leq r \leq \frac{10}{8}\\\\\)  

The python function code is written as follows.

The python function that takes four integer parameters and returns the count of parameters where the value is an even number. is as follows,

def count_even(*args):

   """

   Returns the count of even numbers among the given arguments.

   """

   count = 0

   for num in args:

       if num % 2 == 0:

           count += 1

   return count

# Example usage

result = count_even(2, 5, 6, 7)

print(result)  # Output: 2

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--The complete question is, Write a Python function that takes four integer parameters and returns the count of parameters where the value is an even number.--

Answer:

-5x + 20 = -30

-5x = 10

x = -2

Answer:

-3 and 4

Step-by-step explanation:

since they aren't multiplied a variable

The probability that two cards will be drawn at random, without replacement, is 13/18.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our answer-

P(at least 1 green) = 1 - P(no green)

P(no green) = draw yellow on both draws

= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)

= 5/9 * 4/8 = 20/72 = 5/18

P(at least 1 green) = 1 - 5/18

= 13/18

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Answer:

The number 15/10 is a fraction, specifically a rational number. It can be expressed as the quotient of two integers, where 15 is the numerator and 10 is the denominator. In this case, the fraction is equivalent to 1.5, which is a decimal representation of the rational number.

Step-by-step explanation:

Answer:

Fraction, 15/10 is written out as 15 Over 10