What equation can be used to find the circumference of the circle below

If matric learners do not obtain the marks they need to enter their chosen study programmes, there are several strategies they can implement to still achieve their academic and career goals:

1. Consider alternative study programmes: Matric learners who did not obtain the marks they need for their first choice of study programme should consider other programmes that may be similar or related to their original choice. They can also look at bridging courses, diploma programmes or short courses that will enable them to develop the skills and knowledge they need for their chosen career.

2. Upgrade matric results: Some learners may choose to re-write some of their matric subjects to improve their results. This can be done through night school, part-time courses or through online platforms. This will require dedication, hard work and perseverance, but it can be an effective way to meet the entry requirements for their desired study programmes.

3. Attend a tertiary institution with lower entry requirements: Matric learners who do not meet the requirements for their desired study programme at their first choice institution can consider attending another institution with lower entry requirements. This will enable them to obtain a qualification in their chosen field, which they can use to pursue further studies or career advancement.

4. Take a gap year: Taking a gap year to gain work experience or travel can provide learners with valuable skills and experiences that can enhance their application for their chosen study programme in the future. This time can also be used to upgrade their matric results or to explore other interests and career options.

In conclusion, while not obtaining the marks required to enter a chosen study programme can be disappointing, it is important for matric learners to remain positive and proactive. By considering alternative study programmes, upgrading matric results, attending institutions with lower entry requirements, or taking a gap year, learners can still achieve their academic and career goals.

The rectangle has a surface area of 6 1/4 squares.

The territory a rectangle occupies inside its 4 corners or limits is referred to as its area. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

The amount of space within a form is measured by its area. In daily life, figuring out a shape's or surface's area can be helpful. For instance, you may require know how so much paints to buy to paint a board or the amount of grass to plant on a lawn.

To find the area,

[tex]Area=lenght*width[/tex]

[tex]Area=\frac{5}{2} *\frac{5}{2}[/tex]

[tex]Area=\frac{25}{4}[/tex]

[tex]Area=6\frac{1}{4} square unit[/tex]

Therefore, the area of the rectangle is [tex]Area=6\frac{1}{4} square unit[/tex]

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Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let x be the number of points that Noah missed on the test.

Then, the number of points that Gabe missed is 2x - 3, according to the problem.

The total number of points missed by both of them is given as 18.

So, we can write an equation based on the problem statement:

x + (2x - 3) = 18

Simplifying the equation, we get:

3x - 3 = 18

Adding 3 to both sides of the equation, we get:

3x = 21

Dividing both sides of the equation by 3, we get:

x = 7

Therefore, Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.

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According to the Cartesian plane graph, it can be inferred that the circle was rotated and translated (option B).

To identify the movements that were made to circle 1 to become 2 we must carefully observe the graph. Once we have analyzed this graph we can infer the movements that were made to the circle. In this case, the rotation was performed because it can be seen that it was rotated having the coordinate (-1.5, 0.5) as a reference or point of rotation.

However, it was also translated because it was shifted a bit down and to the left. So the correct answer would be option B.

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Answer: rotation and translation

Step-by-step explanation: I took the quiz

The expοnential decay with a cοnstant percentage rate cοuld be mοdeled by this functiοn.

Expοnential decay is a mathematical prοcess that describes the decrease οf a quantity οver time, where the rate οf decrease is prοpοrtiοnal tο the current value οf the quantity. Expοnential decay οccurs when a quantity decreases by a cοnstant percentage rate οver time.

The fοrmula fοr expοnential decay is given by:

[tex]y = a(1 - r)^t[/tex]

where:

y is the final amοunt οr value

a is the initial amοunt οr value

r is the decay rate, which is the fractiοn by which the quantity decreases per unit time

t is the time in sοme unit οf measurement

The functiοn [tex]y = a(1 - r)^t[/tex] represents an expοnential decay curve, which is a curve that starts high and apprοaches zerο but never reaches it. The rate οf decay is highest at the beginning and decreases as the quantity gets smaller.

Expοnential decay is cοmmοnly seen in many natural and scientific phenοmena, including radiοactive decay, the decay οf a pοpulatiοn οf bacteria, and the depreciatiοn οf the value οf an asset οver time. Expοnential decay is alsο used in finance, engineering, and οther fields tο mοdel variοus prοcesses that invοlve the lοss οf value οr the dissipatiοn οf energy οver time.

The given functiοn y = 400(1 – 0.17)x represents expοnential decay where y is the final amοunt, x is the time in sοme unit, and 0.17 is the decay rate per unit time.

In particular, this functiοn mοdels a situatiοn where a quantity is decreasing οver time at a cοnstant percentage rate οf 17% per unit time. The initial quantity, οr y-intercept, is 400.

Sοme examples οf situatiοns that cοuld be mοdeled by this functiοn are:

The value οf a car that is depreciating at a cοnstant rate οf 17% per year.

The amοunt οf a radiοactive substance that is decaying at a cοnstant rate οf 17% per hοur.

The number οf bacteria in a pοpulatiοn that is dying οff at a cοnstant rate οf 17% per day due tο a lack οf resοurces.

In general, any situatiοn that invοlves expοnential decay with a cοnstant percentage rate cοuld be mοdeled by this functiοn.

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Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

Data are pieces of information that have undergone modifications to make them transferable or computer-processable. For usage with modern computers and communication networks, data is information that has been converted into binary digital form. The topic of the data is admissible in both its singular and plural variants.

To find the z-score of a data value x, we use the formula:

z = (x - μ) / σ

where:

x is the data value

μ is the mean

σ is the standard deviation

In this case, we are given the mean μ = 21 and the standard deviation σ = 1.2. The data value x is also equal to 21.

Substituting the values into the formula, we get:

z = (21 - 21) / 1.2 = 0 / 1.2 = 0

Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

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By answering the above question, we may infer that Hence, x = -1 and x = equation  5 are the zeros of the function f(x).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

To apply this technique, the quadratic function must be rewritten in vertex form as follows: f(x) = a(x-h)2 + k, where (h,k) is the vertex of the parabola.

The coefficient -3 from the first two terms is first removed by factoring: [tex]f(x) = -3(x^2 - 4x) + 15.[/tex]

After that, we finish the square enclosed in parenthesis by calculating (4/2)2 = 4:

[tex]F(x) = -3[(x-2)2 - 4] + 15 F(x) = -3(x-2)2 + 27 F(x) = -3[(x-2)2 - 4] + 15[/tex]

The parabola is at (2, 27), and because the squared term's coefficient is negative, the parabola widens downward. Set f(x) = 0 and solve for x to discover the zeros: [tex]0 = -3(x-2)2 + 27 3(x-2)2 = 27 (x-2)2 = 9 x-2 = 9 x = 2 3[/tex]

Hence, x = -1 and x = 5 are the zeros of the function f(x).

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Dilations produce images that have a center that is the same as the pre-image.

Dilations are a type of transformation that change the size, shape, and orientation of an object. Dilation is a math operation that enlarges or reduces the size of an object or figure. It is a linear transformation that stretches or contracts shapes, which preserve the shape's angles and proportions. Dilation can be used to increase or decrease the area of a shape, or to change the distance between two points.

True statements about dilations are:
• Dilations produce images that are similar to the pre-image.
• Dilations produce images that have angles that are congruent to the pre-image.
• Dilations produce images that have sides that are proportional to the pre-image.
• Dilations produce images that have a center that is the same as the pre-image.

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Complete questions as follows-
Which statements are true about dilations? Select all that apply.
Dilations produce images that are similar to the pre-image.
Dilations produce images that are always congruent to the pre-image.
Dilations produce images that have angles that are congruent to the pre-image.
Dilations produce images that have sides that are congruent to the pre-image.
Dilations produce images that have sides that are proportional to the pre-image.

Answer:

= 0.375

Step-by-step explanation:

then 3/8 to it decimal fraction

[tex] \frac{3}{8} \\ = 0.375[/tex]

Answer:

The answer is C.)

Step-by-step explanation:

a) The altitude of the plane is approximately 8.4 kilometers.

b) The pilot has approximately 11.2 minutes before he has to land.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the lengths of the other two sides (the legs).

In mathematical terms, if we have a right triangle with legs a and b and hypotenuse c, the Pythagorean theorem can be written as:

[tex]a^2 + b^2 = c^2[/tex]

This theorem is named after the ancient Greek mathematician Pythagoras, who was the first to prove it. The Pythagorean theorem has numerous applications in geometry, trigonometry, physics, and engineering, among other fields.

The Pythagorean theorem can also be used to determine whether a triangle is a right triangle or not. If the lengths of the three sides of a triangle satisfy the equation [tex]a^2 + b^2 = c^2,[/tex] then the triangle is a right triangle with sides a and b and hypotenuse c.

a) In the given image, we can see that the slant range, ground range, and altitude form a right triangle. We can use the Pythagorean theorem to find the altitude of the plane.

Pythagorean theorem: In a right triangle, the square of the hypotenuse (slant range in this case) is equal to the sum of the squares of the other two sides (ground range and altitude in this case).

Therefore, we can write:

[tex]Slant range^2 = Ground range^2 + Altitude^2[/tex]

Substituting the given values, we get:

[tex]14.5^2 = 10.15^2 + Altitude^2[/tex]

Simplifying and solving for altitude, we get:

Altitude ≈ 8.4 km (rounded to the nearest meter)

Therefore, the altitude of the plane is approximately 8.4 kilometers.

b) If the plane descends suddenly at a rate of 750 meters per minute, we can use the altitude of the plane (calculated in part a)) to find the time the pilot has before landing.

Time = Altitude/Descent rate

Substituting the values, we get:

Time = [tex]\frac{8.4 }{0.75}[/tex] ≈ 11.2 minutes

Therefore, the pilot has approximately 11.2 minutes before he has to land.

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The length of the measurements are;

EF = 7. 1 units

DE = 7. 0 units

Using the sine trigonometric identity, we have that;

sin θ = opposite/hypotenuse

Given that;

Opposite side = DE

Hypotenuse = DF

Substitute the values

sin 45 = DE/10

Find the value and substitute

DE = 0. 7071(10)

DE = 7. 0

Using the Pythagorean theorem;

EF² = 10² - 7²

find the square value

EF = √ 51

EF = 7.1

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ST is having a length of 3 units.

A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway.

As per the given data:

R is the midpoint of QS:
QR = RS

RS = 6

QT = 15

S is between Q and T

QT = 15

QS + ST = 15

QR + RS + ST = 15

6 + 6 + ST = 15

ST = 3

The length of ST = 3.

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The graph below shows a parabola, indicating that the possible function for f is a quadratic equation.

Graph is a data structure consisting of nodes (vertices) and edges that connect them. Graphs are used to represent networks of data, such as social or computer networks. Graphs are also used to represent mathematical and logical equations, as well as to store and display data. Graphs are composed of two basic components: nodes (vertices) and edges (arcs). Nodes represent the objects in the network, while edges represent the connections between them. Graphs can be used to model many different types of relationships and can be used to solve a variety of problems in different areas, such as computer science, mathematics, engineering, and social sciences.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 0. This type of equation is important in mathematics, as it can represent many physical situations, such as a ball thrown into the air, or a spring that is stretched or compressed. Quadratic equations can be solved using the quadratic formula, which uses the coefficients a, b and c to calculate the two solutions for x. In the graph, the parabola has an equation of the form y = ax2 + bx + c, and so the possible function for f is a quadratic equation.

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Using the Pythagorean theorem we can see that x = 9.3

Think of a right triangle with a hypotenuse of 16, a cathetus of 18 - 5 =13, and the other cathetus is x (we are ignoring the right part of the figure, only look at the triangle in the left)

Then we can use the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse) to find the value of x.

x = √(16² - 13²) = 9.3

That is the value of x.

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According to the question the height of Ruben’s school is 360 inches.

School is a place where students can learn and grow in their knowledge. It is a place where students can gain an education and become well-rounded individuals. School is a place where people can make friends, learn from each other, and explore new ideas and topics. School is a place where teachers and staff provide guidance to help students succeed in their academics and extracurricular activities.

To find the height of Ruben’s school using similar triangles and a mirror, we can use the following formula:
height of school / height of Ruben = distance from mirror to school / distance from mirror to Ruben
Plugging in the given values, we get:
height of school / 72 = 425 / 85
Cross-multiplying and solving for height of school, we get:
height of school = 72 x 425 / 85
height of school = 360 inches
Therefore, the height of Ruben’s school is 360 inches.

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A_n = A_n-1 + 2 represents the recursive formula.

A recursive formula is a formula or equation that describes a sequence or function in terms of itself. In other words, the formula for a given term or value depends on the formula for one or more previous terms or values.

For example, the Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

This sequence can be described recursively using the following formula:

F(n) = F(n-1) + F(n-2)

where F(n) is the nth term of the sequence, F(n-1) is the (n-1)th term, and F(n-2) is the (n-2)th term.

Another example of a recursive formula is the factorial function, which is defined for non-negative integers n as:

n! = n * (n-1)!

This formula states that the factorial of n is equal to n multiplied by the factorial of (n-1). This recursive definition can be used to compute the factorial of any non-negative integer.

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According to the information, it can be inferred that the region and grade that the sales director should target to offer a new reading product based on low reading scores is West region, 4th grade.

To select the correct conclusion we must carefully look at the graphs and identify in which regions and grades the reading score rates are low. Based on this information, we can infer that the region and grade with the lowest rates in this area is West region, 4th grade.

Due to the above, the sales manager should focus his sales strategy on new products in this population because there is a high probability that they will buy the products to improve the rates they have.

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Answer:

2289.12

Step-by-step explanation:

Answer:

2289.12

Step-by-step explanation:

the sum of 897.23 and 39.89 is 937.12

937.12+1352=2289.12

Answer:

x=9

Step-by-step explanation:

Using the method of undetermined coefficients, the particular solution is:

[tex]\mathrm{y_p(t) = 6e^{2t} \times cos(9t) + 3^{2t} \times sin(9t)}[/tex]

To use the method of undetermined coefficients, we assume that the particular solution has the same form as the forcing term, but with undetermined coefficients.

Let's start by finding a particular solution for the equation:

y′′ − 4y′ + 81y = 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Since the forcing term contains both exponential and trigonometric functions, we'll assume that the particular solution is of the form:

[tex]y_p[/tex](t) = A*[tex]e^{2t}[/tex]cos(9t) + B[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]

where A, B, and C are undetermined coefficients that we need to determine.

Let's find the first and second derivatives of [tex]y_p[/tex](t):

[tex]y'_p[/tex](t) = (2A + 9B)*[tex]e^{2t}[/tex]*sin(9t) + (2B - 9A)*[tex]e^{2t}[/tex]*cos(9t) - C[tex]e^{(-t)[/tex]

[tex]y''_p[/tex](t) = (4A - 81B)*[tex]e^{2t}[/tex]*cos(9t) + (4B + 81A)*[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex])

Substituting these expressions into the differential equation, we get:

(4A - 81B)*[tex]e^{2t}[/tex]*cos(9t) + (4B + 81A)*[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]

4[(2A + 9B)*[tex]e^{2t}[/tex]*sin(9t) + (2B - 9A)*[tex]e^{2t}[/tex]*cos(9t) - C[tex]e^{(-t)[/tex]

81[A*[tex]e^{2t}[/tex]cos(9t) + B[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]]

= 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Simplifying and grouping terms, we get:

[(4A + 18B)cos(9t) + (18A - 4B)sin(9t)][tex]e^{2t}[/tex]+ (81C + 3)[tex]e^{(-t)[/tex] = 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Since the two sides of the equation must be equal for all values of t, we can equate the coefficients of the exponential and trigonometric functions on both sides:

4A + 18B = 48 => A = 6

18A - 4B = 80 => B = 3

81C + 3 = 3 => C = 0

Therefore, the particular solution is:

[tex]y_p[/tex](t) = 6[tex]e^{2t}[/tex]*cos(9t) + 3[tex]e^{2t}[/tex]*sin(9t)

Thus, the general solution of the differential equation is:

[tex]\mathrm{y(t) = y_h(t) + y_p(t)}[/tex]

where [tex]y_h[/tex](t) is the complementary solution. Since the characteristic equation of the differential equation is r² - 4r + 81 = 0, it has two complex conjugate roots: r = 2 ± 9i. Therefore, the complementary solution is:

[tex]y_h[/tex](t) = [tex]c_1[/tex]*[tex]e^{2t}[/tex]cos(9t) + [tex]c_2[/tex][tex]e^{2t}[/tex]*sin(9t).

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The total cost of 3 computers, 6 printers, and 30 CD’s will depend on the specific combinations of each type of product. However, as an estimate, you can expect to pay anywhere from $1,000 to $4,000 depending on the quality of the products you purchase.

Cost is the amount of money that must be paid for goods or services. It can refer to the price of a single item, the total expense of a purchase, or the amount of money paid for a particular service. Cost is an important factor in calculations such as profit, budgeting, and pricing. It is also a factor in determining the value of goods and services when comparing different providers.

The total cost of 3 computers, 6 printers, and 30 CD's would depend on the type of products you are looking to purchase. Computers will vary in price depending on the make and model, as well as the features included. For example, a basic laptop might cost anywhere from $200 to $400, while a high-end gaming laptop could cost upwards of $2,000. Similarly, printers also vary in price depending on the features and type, ranging from $50 to $500. CDs can cost anywhere from $0.50 to $7.00 each, depending on the type and quality.

Therefore, the total cost of 3 computers, 6 printers, and 30 CD’s will depend on the specific combinations of each type of product. However, as an estimate, you can expect to pay anywhere from $1,000 to $4,000 depending on the quality of the products you purchase.

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The equations that represent the plants' height after any given number of days are as follows;

y = 2x + 5

y = 3x + 3

The height of the first plant is 33 cm.

The height of the second plant is 48 cm.

Based on the information provided above, the first plant is 5 cm high and the plant grows 2 cm per day. Therefore, the total height, y, can be represented by this equation:

y = 2x + 5

where:

x represents the number of days.

For the second plant, we have:

y = 3x + 3

After 15 days, the total height of each plant is given by;

First plant, y = 2x + 5 = 2(15) + 3 = 33 cm.

Second plant, y = 3x + 3 = 3(15) + 3 = 48 cm.

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Answer: To compare −7/8 and −5/6, we can convert them to a common denominator.

Multiplying the denominator and numerator of −7/8 by 6, we get:

−7/8 = −(7/8) × (6/6) = −42/48

Multiplying the denominator and numerator of −5/6 by 8, we get:

−5/6 = −(5/6) × (8/8) = −40/48

Now we can compare the two rational numbers:

−42/48 is less than −40/48, since negative numbers get larger as their value gets closer to zero.

Therefore, we have:

−7/8 < −5/6.

The correct sign to compare the two rational numbers is "<".

Step-by-step explanation:

Answer:

C.  [tex]\frac{n+4}{2}[/tex]

Step-by-step explanation:

"the sum of a number (n) and 4" --> n + 4

"divided by 2" --> this means the whole expression will be divided by 2

Therefore, the final answer is the third option!

Hope this helps!! :)

The answer is m = 0.

One identity that we can write here is:

cos²(θ/2) = - sin²(θ/2) + 1

Here we want to find something that is equal to cos²(θ/2) for every value of theta, that will be an identity.

The general identity for trigonometric functions is:

cos²(θ) + sin²(θ) = 1

So we can rewrite this as:

cos²(θ) = - sin²(θ) + 1

If instead of theta, the argument is theta over two, we could rewrite this as:

cos²(θ/2) = - sin²(θ/2) + 1

That is the identity.

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The percent decrease in the amount of land that Patty owns now is approximately 15.00%. Destiny's time at yesterday's race was 187 minutes.

To find Destiny's time at yesterday's race, we can first calculate the time reduction as a percentage of her previous time, and then subtract that reduction from her previous time.

The time reduction is 15% of 220 minutes -

0.15 x 220 = 33

So, she took 33 minutes less at yesterday's race.

Her time at yesterday's race is -

220 - 33 = 187 minutes

Therefore, time value is obtained as 187 minutes.

The percent decrease in the amount of land that Patty owns can be calculated by finding the difference between her old and new land sizes, dividing that by her old land size, and then multiplying by 100 to convert to a percentage.

The difference between her old and new land sizes is -

2,220 - 1,887 = 333

Dividing that by her old land size and multiplying by 100, we get -

(333/2220) x 100 ≈ 15.00

Therefore, the percent decrease is obtained as 15.00%.

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