Using Pythagoras' theorem, calculate the length of PR. Give your answer in centimetres (cm) and give any decimal answers to 1 d.p. 50 cm 48 cm​

The pattern with matches is formed by systematically manipulating the arrangement of matches, adding or removing them in each step according to a defined rule.

The pattern with matches can be formed by following a specific arrangement or sequence. Each step in the formation of the pattern involves adding or removing matches in a deliberate manner. Let's examine the steps involved in creating the pattern:

Start with a base shape: The pattern typically begins with a basic shape or arrangement of matches. This could be a square, triangle, or any other simple form. For example, let's consider a square shape.

Manipulate the arrangement: To create the pattern, matches are added or removed from the base shape in each step. The exact manipulation depends on the desired pattern. For instance, let's say we want to create a pattern where each subsequent shape has one less match along one side.

Repeat the process: The manipulation is repeated in a systematic way to create a sequence of shapes. Each new shape is derived from the previous one by adding or removing matches according to the defined pattern rule. This repetition generates a series of shapes that form the complete pattern.

Observe the resulting pattern: By following the defined rules for adding or removing matches, a visually appealing and consistent pattern emerges. The pattern can exhibit various characteristics such as symmetry, repetition, or gradual change.

The specific details of the pattern formation may vary depending on the desired design. Different patterns can be created by altering the rules for adding or removing matches, changing the starting shape, or modifying the manipulation process.

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Answer:

[tex]C = 11.3 \text{ cm}[/tex]

Step-by-step explanation:

We can find the circumference of the circle by using the formula:

[tex]C = 2\pi r[/tex]

↓ plugging in the given radius

[tex]C = 2\pi (1.8 \text{ cm})[/tex]

[tex]C = 3.6\pi \text{ cm}[/tex]

↓ rounding to the nearest tenth

[tex]\boxed{C = 11.3 \text{ cm}}[/tex]

The solution set, using properties of exponents is { 3/4 }.

The solution set to ( 2 ³ˣ . 2 ˣ ) ˣ ⁻ ¹ = 8  can be found by using the properties of exponents in the following manner :

( 2 ^ ( 3 x  + x ) ) ^ ( x ^ ( - 1 ) ) = 8

( 2 ^ ( 4 x ) ) ^ ( x ^ ( - 1 ) ) = 8

2 ^ ( 4 x   * x ^ ( - 1 ) ) = 8

2 ^ ( 4 x * x ^ ( - 1 ) ) = 2^3

4 x  *  x ^ ( - 1 ) = 3

4 * x ^ ( 0)  = 3

4 x = 3

x = 3/4

The solution set is { 3 / 4 }.

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The function is decreasing for the interval of (5, 9). The function is constant for the interval (9, 12). The function is positive for the interval of (-2, 8). The function is increasing for the interval (3, 5). The function is negative for the interval (8, 12.5).

For any given function, y = f(x), if the output value is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

For any given function, y = f(x), if the output value is increasing when the input value is increased, then, the function is generally referred to as an increasing function.

By critically observing the graph shown above, we can reasonably infer and logically deduce the following key features;

In conclusion, a function is positive when the output value is greater than zero [f(x) > 0] while it is negative when the output value is less than zero [f(x) < 0].

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Answer:

7 7/8.

Step-by-step explanation:

o add mixed numbers like these, we first need to convert them to improper fractions, and then add them. Here are the steps to add 5 3/8 and 2 1/2:

Convert the mixed numbers to improper fractions:

5 3/8 = (5 x 8 + 3)/8 = 43/8

2 1/2 = (2 x 2 + 1)/2 = 5/2

Find a common denominator for the two fractions. The least common multiple of 8 and 2 is 8, so we can convert both fractions to have a denominator of 8:

43/8 + 5/2 = (43/8) + (5/2 x 4/4) = 43/8 + 20/8

Add the two fractions with the same denominator:

43/8 + 20/8 = 63/8

Convert the result back to a mixed number:

63/8 = 7 7/8

The length of the golden rectangle is 49 cm.

A rectangle is a quadrilateral (a polygon with four sides) in which each angle is a right angle (90 degrees). It is a type of parallelogram in which opposite sides are parallel and congruent (equal in length). Rectangles have four sides and four vertices (corners).

The length of a rectangle is the distance between its two longer sides, while the width is the distance between its two shorter sides. The perimeter of a rectangle is the sum of the lengths of all its sides, while the area is the product of its length and width.

A golden rectangle has sides in the proportion of the golden ratio, which is approximately 1:1.618. Therefore, if the width is 30cm, the length can be found by multiplying 30 by 1.618.

Length ≈ 48.54 cm

The length of the rectangle is 49 cm.

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The location of Z after the transformations is given as follows:

(-2,-1).

The original coordinates of Z are given as follows:

Z(1, 3).

The translation rule is given as follows:

(x,y) -> (x + 1, y - 4).

Hence the coordinates of Z after the translation are given as follows:

(2, -1).

The rule for a reflection over the y-axis is given as follows:

(x, y) -> (-x, y).

Hence, exchanging the sign of the y-coordinate, the location of Z is given as follows:

(-2,-1).

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Answer:

(-2, -1)

Step-by-step explanation:

Hope this helps :)

The correct option that shows the associative property is D:

[tex](\left[\begin{array}{ccc}4\\2\end{array}\right] + \left[\begin{array}{ccc}3\\5\end{array}\right]) + \left[\begin{array}{ccc}1\\3\end{array}\right] = \left[\begin{array}{ccc}4\\2\end{array}\right] + (\left[\begin{array}{ccc}3\\5\end{array}\right] + \left[\begin{array}{ccc}1\\3\end{array}\right] )[/tex]

The associative property of addition says that we can perform sums in any order we want:

A + (B + C) = (A + B) + C

The option that shows this property is the one at D, where we have 3 vectors and we can select any order in which we add them, such that the sum is written as:

[tex](\left[\begin{array}{ccc}4\\2\end{array}\right] + \left[\begin{array}{ccc}3\\5\end{array}\right]) + \left[\begin{array}{ccc}1\\3\end{array}\right] = \left[\begin{array}{ccc}4\\2\end{array}\right] + (\left[\begin{array}{ccc}3\\5\end{array}\right] + \left[\begin{array}{ccc}1\\3\end{array}\right] )[/tex]

That expression shows the associative property of the addition with matrices.

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Answer:

A list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.

Step-by-step explanation:

The graph could be the graph of exponential function of option b)

[tex]F(x) = 2 • (0.5)^{x} [/tex]

The general form of an exponential function is

[tex]f(x) = {ab}^{x} [/tex]

Here, a is the function's starting value and b is its growth factor.

F(x) is an increasing function if b > 1, and if b<1, then f(x) is a decreasing function

The function's initial value is 2 as can be seen from the provided graph. Therefore, a has a value of 2.

Given that the graph indicates that the function is decreasing, b must be less than 1.

It indicates that the necessary function is in the form of

[tex]f(x) = 2(b)^{x} [/tex]

Where it is b<1

By checking option B, b=0.5<1. Hence, option B is the correct answer

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Note that the full question is:

(check the attached image)

The probability that Jannette in Mr. Alsup's sixth-period English class has not chosen a topic for her writing assignment is approximately c.12%. Therefore, option c.12%.  is correct.

To find the probability that Jannette in Mr. Alsup's sixth-period English class has not chosen a topic for her writing assignment, we need to calculate the proportion of students in that class who have not chosen a topic.

From the table, we can see that in the sixth period, there are a total of 25 students. Out of those, 22 students have chosen a topic, and 3 students have not chosen a topic.

The probability can be calculated by dividing the number of students who have not chosen a topic (3) by the total number of students in the sixth period (25), and then multiplying by 100 to get the percentage:

Probability = (Number of students who have not chosen a topic / Total number of students in the sixth period) × 100

Probability = (3 / 25) × 100

Probability ≈ 12%

Therefore, the probability that Jannette in Mr. Alsup's sixth-period English class has not chosen a topic for her writing assignment is approximately 12%.

The correct answer is c- 12%.

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Answer:

Q6.  x = 8.1 ***

Q7   x = 27.87

***For question 6:  Your picture of question 6 is so blurred I could not really make out the angle; I took it as 36° . If it is something else, use the formula given below with the correct angle and compute **

Step-by-step explanation:

In right triangle, with one of the angles = θ , the following relationships hold

[tex]\cos \theta = \dfrac{adjacent}{hypotenuse}\\\\\sin\theta = \dfrac{opposite}{hypotenuse}\\\\\tan\theta = \dfrac{opposite}{adjacent}\\[/tex]

where

adjacent means side adjacent to θ
opposite means side opposite to θ

In the given figure in Q6,

θ = 36°  (I had difficulty making out the picture)

adjacent = x

hypotenuse = 10

so

[tex]\cos 36^\circ = \dfrac{x}{10}\\\\x = 10 \cdot \cos 36^\circ\\\\x = 10 \cdot 0.809\\\\x = 809\\\\\text{x = 8.1 rounded to the nearest tenth}[/tex]

I have answered question 7 also since it is very similar:

[tex]\sin 35^\circ = \dfrac{16}{x}\\\\x = \dfrac{16}{\sin 35^\circ}\\\\\\= \dfrac{16}{0.574}\\\\\\= 27.8745\\\\= 27.87 \text{ to the nearest hundredth\\}[/tex]

The term (x - 1) is a factor of both of the given polynomials as;

x² + x - 2

2x² - 5x + 3

Given that (x - a) is a factor of a polynomial p(x), then x = a is a zero of the polynomial, which means that:

p(a) =0.

When x - 1 is a factor of any of the given polynomials, then we need to evaluate them in x = 1 and check if we get zero.

a) x² + x - 2

Evaluate it in x = 1;

1² + 1 - 2 = 0

so (x - 1) is a factor.

b) 2x² - 5x + 3

Evaluating this in x = 1;

2*1² - 5*1 + 3

2 - 5 + 3 = 0

(x - 1) is a factor.

Therefore, the correct option is the last one, it is a factor of both polynomials.

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The zero of f is equal to -12.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (1, -9) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-9) = 3(x - 1)

y = 3x - 12

When x = 0, the y-value is given by;

f(0) = 3(0) - 12

f(0) = -12

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Answer:

To determine which bank is more cost-effective, we need to consider how many transactions we will make per month. Let's call the number of transactions "t".

Bank A charges a flat fee of $45 per month, regardless of how many transactions we make. So the total cost of using Bank A for one month is:

Total cost for Bank A = $45

Bank B charges a monthly fee of $20, plus $0.70 for each transaction. So the total cost of using Bank B for one month is:

Total cost for Bank B = $20 + ($0.70 x t)

To determine which bank is more cost-effective, we need to find the value of "t" that makes the total cost of Bank B equal to the total cost of Bank A.

$45 = $20 + ($0.70 x t)

$25 = $0.70 x t

t = $25 / $0.70

t ≈ 36

So if we make 36 or more transactions per month, Bank A is more cost-effective. If we make fewer than 36 transactions per month, Bank B is more cost-effective.

Answer: (the 2s I added are for square 2)

5sq(5g2s2 - 16qs + 9)

Step-by-step explanation:

Answer:

please see explanation and attachment

Step-by-step explanation:

√16 = 4.

√14 = ?

how do we get from 16 to 14? we subtract 2. r = remainder. denominator is twice √16, ie 8.

so we have 4 r -2 r 8

= 4 r -1 r 4

= 3 r 3 r 4

= 3.75

= 3.8 to nearest tenth

The difference of two positive integers is never negative.

Through definition, a positive integer is any whole number greater than zero, and subtraction is the operation used to find the difference among two numbers.

When subtracting a smaller number from a larger number the end result is constantly a non-negative number or 0.

This is because the subtraction operation measures the distance between the two numbers, and distance is usually a positive value.

For instance, the difference among 7 and 3 is 4, that's a positive value. consequently, the difference of positive integers is always a non-negative number.

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The division expressions to the quotients and remainders are

Expression (a)

The expression is given as

(x² - x - 30) ÷ (x - 6)

The synthetic set up is

6 |   1  -1  30

   |__________

Bring down the first coefficient, which is 1 and repeat the process

6 |   1  -1  30

   |___6_-30_____

      1   -5   0

This means that

Quotient = x - 5 with no remainder

Expression (b)

The expression is given as

(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1)

Using a graphing tool, we have

(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1) = x - 4 with no remainder

This means that

(x³ + 2x² - 1) ÷ (x² - x + 1) = x + 3 R 2x - 4

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Answer:

[tex] \frac{41}{3} \times 3 \times \frac{62}{3} = \frac{806}{3} = 268 [/tex]

The boy will take approximately 64.5 minutes to walk to school if he was previously taking 43 minutes.

Using the concept of proportionality to determine the new time it will take for him to walk to school.

Let's denote:

d1 = Distance he was walking previously

t1 = Time he took previously

d2 = New distance he has to walk

t2 = New time it will take

From the given information, we know that:

d2 = 1.5 * d1

t1 = 43 minutes

Since distance and time are directly proportional, we can set up a proportion:

d1 / t1 = d2 / t2

Substituting the given values:

d1 / 43 = (1.5 * d1) / t2

To solve for t2, we can cross-multiply and solve for it:

d1 * t2 = (1.5 * d1) * 43

t2 = (1.5 * d1 * 43) / d1

Simplifying the expression:

t2 = 1.5 * 43

t2 = 64.5

Therefore, the boy will take approximately 64.5 minutes to walk to school if he was previously taking 43 minutes.

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The correct statement regarding the transformations to [tex]f(x) = 10^x[/tex] to create [tex]g(x) = 3(10)^x - 2[/tex] is given as follows:

A vertical dilation by a factor of 3 and a vertical shift down 2 units

The parent function for this problem is given as follows:

[tex]f(x) = 10^x[/tex]

The transformed function for this problem is given as follows:

[tex]g(x) = 3(10)^x - 2[/tex]

Hence the transformations are given as follows:

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Answer:

x < 6

Step-by-step explanation:

3x < 18 ( divide both sides by 3 )

x < 6

The solution to the equation when solved for m is  (v - e)/Z.

To solve for m in the equation Z = (v - e)/m, we can manipulate the equation algebraically as follows:

Z = (v - e)/m

Multiply both sides by m:

Zm = v - e

Add e to both sides:

Zm + e = v

Subtract e from both sides:

Zm = v - e

Divide both sides by Z:

m = (v - e)/Z

Therefore, the solution for m is:

m = (v - e)/Z.

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The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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The relative frequency of 140-149 pound weight class is [tex]5.6[/tex]%.

The relative frequency refers to number of times an event occurs divided by total number of events occurring, so, its means ratio of frequency of an event to the total frequency.

The relative frequency of a class:

= (Frequency of class) / (Total frequency)

The frequency of 140-149 is 2.

The total frequency = sum of all frequencies which is:

= 2+3+4+7+5+6+5+4

= 36

The relative frequency of 140 - 149 pound weight class is:

= 2 / 36

= 1/18

= 0.056.

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The probabilities are given as follows:

a) x is less than 60: 0.9495 = 94.95%.

b) x is greater than 16: 0.9909 = 99.09%.

c) x is between 16 and 60: 0.9404 = 94.04%.

d) x is greater than 60: 0.0505 = 5.05%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 42, \sigma = 11[/tex]

The probability of a value less than 60 is the p-value of Z when X = 60, hence:

Z = (60 - 42)/11

Z = 1.64

Z = 1.64 has a p-value of 0.9495.

Hence the probability of a value greater than 60 is of:

1 - 0.9495 = 0.0505 = 5.05%.

The probability of a value greater than 16 is one subtracted by the p-value of Z when X = 16, hence:

Z = (16 - 42)/11

Z = -2.36

Z = -2.36 has a p-value of 0.0091.

1 - 0.0091 = 0.9909 = 99.09%.

The probability of a value between 16 and 60 is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 16, hence:

0.9495 - 0.0091 = 0.9404 = 94.04%.

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The missing sides are;

1) √296 (2) √68 (3)  2√10  (4) 21  (5) 15√3  (6) 14√2

A right triangle is a triangle that has one angle equal to 90 degrees, which is also known as a right angle.

1) Using the Pythagoras theorem;

[tex]x^2 = 14^2 + 10^2[/tex]

x = √296

2) [tex]x^2 = 18^2 - 16^2[/tex]

x = √68

3) Tan 45 = x/2√10

x = 1 * 2√10

x = 2√10

4) Cos 30 = x/14√3

x = 14√3 * √3/2

x = 21

5) Sin 60 = x/30

x = 30 * √3/2

x = 15√3

6) Cos 45 = x/28

x = 28 * √2/2

x = 14√2

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