The diagram shows the curve y = -x²-x+ 20.
(i) The curve cuts the x-axis at two points A and B, and the y-axis at the point C. Find the coordinates of A, B and C.
(ii) The point D(3, h) lies on the curve. Find the value of h.
​

Thus, the derivative of the given function is found as: [tex]f'(x) = (2x) /\sqrt{(9 + x^{2} )}[/tex].

The derivative of a function f(x), also known as f'(x) or df/dx, is a measure of how quickly a function changes.  A shift in the value of x is depicted in the image by the symbol x.

Hence, df/dx is a single phrase and should not be mistaken for a fraction. It is also a clue that x is the independent variable because it can be interpreted as the derivative of a function having respect to x.

Given function:

[tex]f(x ) = \sqrt{9 + x^{2} } .dx[/tex]

Differentiating the function with respect to x, using the chain rule.

[tex]f'(x) = (9 + x^{2} )^{1/2 - 1} .(0 + 2x)[/tex]

[tex]f'(x) = (9 + x^{2} )^{-1/2} .(2x)[/tex]

[tex]f'(x) = (2x) /(9 + x^{2} )^{1/2}[/tex]

[tex]f'(x) = (2x) /\sqrt{(9 + x^{2} )}[/tex]

Thus, the derivative of the given function is found as: [tex]f'(x) = (2x) /\sqrt{(9 + x^{2} )}[/tex].

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Answer:

Step-by-step explanation:

11P3=11×10×9=990

[tex]11C_{3}=\frac{11 \times 10 \times 9}{3 \times 2 \times 1} =165[/tex]

Step-by-step explanation:

The answer is 262.5%

5/8=5÷8=0.625

2 5/8=2.625

2.625=262.5%

262.5%  and   2.625

5/8=5÷8=0.625 then 2 5/8=2.625 then we get 2.625=262.5%

All we do here Is divide then round It to the nearest 1, 10, or 100.

Division Is separate or be separated into parts, and noun of division Is a wide divergence between two groups, typically producing tension or hostility.

Adjusting the digits (up or down) to make rough calculations easier.

Answer:

what is it

Step-by-step explanation:

The prοperties that bοth rectangles and parallelοgrams share are 2 pairs οf parallel sides & 2 pairs οf sides with equal length.

Thus, οptiοn C & D is cοrrect.

Prοperties οf bοth rectangles and parallelοgrams:  

Rectangles and parallelοgrams are bοth types οf quadrilaterals, which are pοlygοns with fοur sides.

Certain prοperties are unique tο each type οf quadrilateral, as well as sοme that they share in cοmmοn. Here are the prοperties that rectangles and parallelοgrams share:

1. Bοth rectangles and parallelοgrams have parallel οppοsite sides.

2. Bοth rectangles and parallelοgrams have cοngruent οppοsite sides  

3. Bοth rectangles and parallelοgrams have cοngruent, οppοsite angles  

4. Bοth rectangles and parallelοgrams have cοnsecutive angles that are supplementary  

Therefοre,

The prοperties that bοth rectangles and parallelοgrams share are

C. 2 pairs οf parallel sides

D. 2 pairs οf sides with equal length

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A rotation can be  transformation which turns a figure. It changes its position

what is rotation ?

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, and is used to describe the movement of objects in space.

In the given question,

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, A rotation can be  transformation which  turns a figure. It changes its position

when their is rotations it turns around its axis and their will be change in its position

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The answer to the given question about inscribed angles intercepting an arc is option A. 100

As we know that the measure of an inscribed angle is half the measure of the intercepted arc, we can use the formula:

Measure of inscribed angle = 1/2 × Measure of intercepted arc

So, if the intercepted arc has a measure of 200 degrees, then the measure of the inscribed angle is:

Measure of inscribed angle = 1/2 × 200 degrees

= 100 degrees

Therefore, the answer is A. 100 degrees. In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, if an arc has a measure of 200, then an inscribed angle that intercepts that arc will have a measure of half of 200, which is 100 degrees.

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a) The association test, in this case, is a chi-square test of independence,

b) The conditions for the chi-square inference procedure are:

Independence

Sample size

c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

What is the association test?

An association test is a statistical test used to determine whether there is a relationship or association between two or more variables. The type of association test used depends on the nature of the variables being examined.

a) The association test, in this case, is a chi-square test of independence, which is used to determine whether there is a significant association between two categorical variables.

b) The conditions for the chi-square inference procedure are:

Independence: The sample is a simple random sample, so independence is satisfied.

Sample size: The expected count for each cell should be at least 5, which is satisfied for all cells in the table.

c) The degrees of freedom for the chi-square test are (r - 1) x (c - 1), where r is the number of rows and c is the number of columns in the table.

In this case, the degrees of freedom are (3-1) x (4-1) = 6. The p-value associated with a chi-square test statistic of 18.930 and 6 degrees of freedom is less than 0.01.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

However, it may not be appropriate to generalize to other populations without further research to ensure the characteristics of the population are similar to those of the sample.

Hence,  a) The association test, in this case, is a chi-square test of independence,

b) The conditions for the chi-square inference procedure are:

Independence

Sample size

c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

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Answer: 456,976,000

Step-by-step explanation:  Assuming that repetition is allowed

Answer:

The least possible degree is 5.

The area of the given polygon ABCDE divided into three triangles ABC, ACD and AED is 79.5 sq. units.

What is a polygon?

A polygon is a closed figure or shape formed using line segments. Smallest polygon is a triangle containing three sides. On the basis of its sides polygons are classified as triangle, quadrilateral, pentagon, hexagon, heptagon, octagon etc. The sum of interior angles of a polygon is found by the formula (n-2)180 , where 'n' refers to the number of sides in a polygon. The sum of exterior angles of any polygon is always equal to 360°. The area of any irregular or regular polygon may be evaluated by dividing the given shape into standard shapes like square, rectangle, triangle etc and then adding up the areas of all shapes.

Here the given pentagon ABCDE is further divided into three triangles,

ABC, ACD and AED

Also given the areas of triangles:

area of ΔABC = 23.85 sq. units

area of ΔACD = 29.40 sq. units

area of ΔAED = 26.25 sq. units

∴The area of given figure= Sum of the areas of ΔABC, ΔACD and ΔAED

                                         =area of ΔABC+area of ΔACD+area of ΔAED

                                         =23.85+ 29.40+26.25

                                         =79.5 sq. units.

The area of the given figure is 79.5 sq. units

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Refer to the attached figure below for complete question.

Given that 60% of Olivia's fruit salad is made up of apples as opposed to Amadou's fruit salad's 52.63%, Olivia's fruit salad will have a more apple-forward flavor based on percent.

The amount of apples in each fruit salad needs to be compared in order to determine which salad will taste more apple-like.

There are 19 cups of fruit in Amadou's fruit salad, of which 10 cups are apples. By dividing the total number of cups of fruit by the number of cups of apples, and multiplying the result by 100, we can get the proportion of apples in Amadou's salad:

Apple's percent of Amadou's fruit salad is equal to (10/19) x 100, or 52.63%.

There are 5 cups of fruit in Olivia's fruit salad, of which 3 cups are apples. We can use the same formula to determine how much apple is in Olivia's salad:

Olivia's fruit salad contains 60% apples, or (3/5) x 100.

As a result, Olivia's fruit salad will taste more apple-like because apples make up 60% of it as opposed to only 52.63% of Amadou's fruit salad.

It is important to keep in mind that the maturity, sweetness, and freshness of the fruits used, as well as other elements like the dressing and presentation, may all affect how the fruit salad tastes.

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The geometric solid associated with each situation are

a. a stack of 100 copies of the same book

A stack of 100 copies of the same book can be visualized as a rectangular prism because each book has the same dimensions.

b. a stack of 100 tires, all with the 19 same radius no

A stack of 100 tires, all with the same radius, can be visualized as a cylinder because each tire has a circular shape with the same radius, and when they are stacked on top of each other, they form a cylinder.

c. a stack of 100 stop signs

A stack of 100 stop signs can be visualized as a regular polygonal prism because each stop sign has the shape of a regular octagon, and when they are stacked on top of each other, they form a regular polygonal prism with a base of an octagon.

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Surface area and of rectangular prism are  502ft² and 390ft³ respectively.

A rectangular prism is a three-dimensional solid shape that has six rectangular faces, where each face is perpendicular to the adjacent faces. It is also known as a rectangular cuboid.

The rectangular prism has three pairs of congruent faces, which are opposite to each other, and each pair of faces has the same dimensions. The dimensions of a rectangular prism are typically measured by its length, width, and height, and these dimensions can be different from each other.

The formula for the volume of a rectangular prism is:

Volume = length x width x height

The formula for the surface area of a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

Sides of rectangular prism are 2ft,15ft and 13ft.

Surface area of rectangular prism=2(lb+bh+lh)

=2(2×15+15×13+13× 2)

=502ft²

Volume of rectangular prism

=lbh

=2×15×13

390ft³

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The complete question is;

Image is attached below.

la cantidad buscada es 1440.

Para encontrar la cantidad dada el 15% de la misma, podemos usar una ecuación:

15% de x = 216

Podemos convertir el porcentaje a decimal dividiendo por 100:

0.15x = 216

Luego, para despejar x, podemos dividir ambos lados de la ecuación por 0.15:

x = 216 / 0.15

x = 1440

Por lo tanto, la cantidad buscada es 1440.

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Another mathematical representation of how a rider on this Ferris wheel might move is :y =  cos(0.25x) + 40

Trigonometry is widely used in many fields, including physics, engineering, architecture, surveying, oceanography, and more. Here are several examples:

In astronomy and physics, trigonometry is used to compute the motions of moving objects, gauge the separations between planets and stars, and examine waves. Trigonometry is used in architecture and engineering to determine angles and distances for building structures like bridges and buildings.

In surveying, trigonometry is a tool used to determine angles and separations between points on the surface of the ground.

.

The function y = a cos(bx) + c, where an is the function's amplitude, b is its frequency, and c is its vertical shift, can be used to mimic the height of a rider on a Ferris wheel.

Given that the Ferris wheel's diameter in this instance is 60 meters, its radius is 30 metres. The Ferris wheel's center axle is 40 metres off the ground. This indicates that a rider is 70 metres above the earth when they are at the top of the Ferris wheel (30 + 40). A rider is 10 metres above the ground when they reach the bottom of the Ferris wheel. (40 - 30).

We can determine that the Ferris wheel's period is four minutes because it rotates once every four minutes. The following formula can be used to get our function's frequency:

f = 1/T, 1/4, and 0.25 Hz

Therefore, our function has a frequency of 0.25 Hz.

The vertical shift of our function is equivalent to 50% of the difference between a Ferris wheel passenger's maximum and minimum heights:

, c = (a_max + a_min) /2

c = (70 + 10) /2

c = 40

Therefore, 40 is the vertical shift of our function.

Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:

For example, c = (a_max + a_min) / 2 c = (70 + 10) / 2 c = 40

Therefore, 40 is the vertical shift of our function.

Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:

A=(a_max - a_min) / 2 A=(70 - 10) / 2 A=30

Therefore, our function has an amplitude of 30.

When you combine everything, you get:

Y equals a cos(0.25x) + 40

y = -25 cos(C), where C is the time in minutes since the motion started at position, is another potential mathematical model that could describe this motion. (0,-25).

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Answer:

There were 60 audience members at the seminar.

Step-by-step explanation:

Let's assume that the total number of audience members at the seminar is "x".

From the given information, we know that:

2/5 of the audience were students, so the number of students was (2/5)x

3/10 of the audience were retirees, so the number of retirees was (3/10)x

The rest were professionals, so the number of professionals was x - (2/5)x - (3/10)x = (1/10)x

We also know that there were 18 more students than professionals, so:

(2/5)x - (1/10)x = 18

Multiplying both sides by 10, we get:

4x - x = 180

Simplifying, we get:

3x = 180

x = 60

Therefore, there were 60 audience members at the seminar.

The probability of selecting at random, without replacement, two blue marbles is 5/12.

What is Probability ?

Probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty and provide a basis for making informed decisions in various fields such as science, engineering, economics, and finance.

To solve the problem, we first need to find the total number of marbles in the urn. Since there are 3 red marbles and 6 blue marbles, there are a total of 9 marbles.

The probability of selecting a blue marble on the first draw is 6/9, since there are 6 blue marbles out of 9 total marbles.

Since we are selecting without replacement, the number of marbles left in the urn changes after each draw. After the first blue marble is selected, there are only 5 blue marbles left out of a total of 8 marbles. Therefore, the probability of selecting a second blue marble is 5/8.

To find the probability of selecting two blue marbles, we multiply the probability of the first draw (6/9) by the probability of the second draw (5/8):

(6/9) x (5/8) = 30/72 = 5/12

Therefore, the probability of selecting at random, without replacement, two blue marbles is 5/12.

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Answer:

you could do 2 students in each group with one group of 3

Step-by-step explanation:

sorry if i didn't answer correctly

Answer:

sp= 8000.00.

loss percent= 20%

loss amount = 20% of sp

= 20÷100 × 8000

= 1600

now,

costprice = sp + loss amount

= 8000 + 1600

= 9600

Answer:

Step-by-step explanation:

According to the given situation,

the area of figure A= l*b

                                =4m * 5m

                                =20m²

As the measures of the figure A and B is same,

the area of figure B = the area of figure A=20m²

the length of the side C and D are = 16m-8m-4m=4m

the area of figure C = l * b

                                 =4m*5m

                                 =20m²

As the measures of the figure C and D is same,

the area of figure D = the area of figure C=20m²

Area of the figure E=l * b

                               =8m * 13m

                               =104m²

∴ the area of the shaded region is =184m²

The measures of the angles and arcs of the circle are;

The sum of the digits in the shaded = 1  + 3 + 7 + 2 + 3 + 4 + 6 = 26

26 - 14 = 12

Using the decoder wheel, we get; FVMMO

An arc is a portion or part of the circumference of the circle.

The arc angles from the diagrams indicates;

1. mPR = 90 + (90 - 67) = 113

2. mQST = mQR + mRST

mQST = 23 + 180 = 203

3. 8·x - 15 + (3·x + 8) = 180 (Linear pair angles)

11·x - 7 = 180

11·x = 187

x = 187/11 = 17

x = 17

4. LM = 3·x + 8

Therefore; LM = 3 × 17 + 8 = 59

LM = 59

5. m∠DAC = 156/2 = 78

6. mBC = 180 - 156 = 24

7. m∠ADB = 43

mAB = 43 × 2 = 86

mABD = 180 + 86 = 266

8. 2 × (7·x -3) = 17·x - 30

14·x - 6 = 17·x - 30

17·x - 14·x = 3·x = 30 - 6 = 24

x = 24/3 = 8

x = 8

9. m∠YZX = 7·x -3

m∠YZX = 7 × 8 - 3 = 53

m∠YZX = 53

10. m∠WXZ = 62/2 = 31

The angle formed by the intersection of WY and XZ is therefore;

mWZY = 180 - (2 × 53) + 63 = 137

mWXY = 180 - (2 × 31) + (17 × 8 - 30) = 224

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They are different because they are inverse expressions.

what is prime factor ?

A positive integer factor that is also a prime number is known as a prime factor in mathematics. Otherwise put, a prime factor is a prime number that may be multiplied by additional prime factors to produce the original integer. For instance, since 24 can be written as the product of the numbers 2, 2, 2, and 3, the prime factors of 24 are 2, 2, 2, and 3. There is only one set of prime factors for every positive integer since a number's prime factors are always unique. Finding a number's prime factors is a technique called prime factorization. It is a fundamental idea in number theory and has lots of real-world uses, including in computer science and cryptography.

given

Due to the way division operates, the quotient of three by one-fifth differs from the quotient of one-fifth by three. You get a greater quotient when you divide a larger number by a smaller number, and a smaller quotient when you divide a smaller number by a larger number.

To demonstrate these two scenarios, consider the following two tales:

The Quotient of Three Divided by One-Fifth is the first story.

There once were three pals named Chris, Ben, and Alex. They made the decision to split the five equally sized slices of pizza. Due to his extreme hunger, Alex chose to grab three of the slices for himself, leaving Ben and Chris with just two pieces each.

We write the expressions first mathematically:

three divided by one-fifth:

(3) / (1/5)

one-fifth divided by three:

(1/5) / (3)

We now use the double c method to find the results:

(3) / (1/5) = (3 * 5) / (1 * 1) = 15/1 = 15

(1/5) / (3) = (1 * 1) / (5 * 3) = 1/15 = 0.066666667

The difference between the two is:

15-0.066666667 = 14.93333333

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Answer: Number 4 is the answer.

Hope this helps!

Answer:

Let's start by using the formula for finding the percentage: percentage = (part/whole) x 100 In this case, we know the percentage (2%) and the part (88 problems), but we don't know the whole (total number of problems on the test). So we can write: 2% = (88/whole) x 100 Simplifying, we get: 0.02 = 88/whole Multiplying both sides by the whole, we get: whole x 0.02 = 88 Dividing both sides by 0.02, we get: whole = 4400 Therefore, there were 4400 problems on the English test.

Answer:90 problems

Step-by-step explanation:

To solve the problem, we can use the formula:% correct = (number of correct answers / total number of questions) * 100%Since the student received a grade of 2%, we can write:2% = (number of correct answers / total number of questions) * 100%Simplifying this equation, we get:total number of questions = number of correct answers / 0.02We know that the student missed 88 problems, so the number of correct answers is:number of correct answers = total number of questions - 88Substituting this into the equation above, we get:total number of questions = (total number of questions - 88) / 0.02Simplifying this equation, we get:total number of questions = 50 * (total number of questions - 88)Solving for the total number of questions, we get:total number of questions = 90Therefore, there were 90 problems on the English test

Answer: The decay rate is 8.4%, which means that the sample will have 91.6% of its original mass after one year, 91.6% of that amount after two years, and so on.

Therefore, we can write the relationship between y and t as:

y = 600 * (0.916)^t

This is an exponential decay function, where the initial value is 600 milligrams and the decay factor is 0.916 (1 minus the decay rate of 8.4%). As time t increases, the mass of the sample y decreases exponentially.

Step-by-step explanation:

Remark

I take it the semicircles cover the full width of the paper.

So the radius is [tex]24\div2 = 12 \ \text{cm}[/tex]

Since there are two of them, the area = a full circle.

Step One

Find the area of the rectangle before the cuts were made.

[tex]\text{Area = L} \times \text{W}[/tex]

[tex]\text{L = 30}[/tex]

[tex]\text{W = 24}[/tex]

[tex]\text{Area} = 30 \times 24 = 720 \ \text{cm}^2[/tex]

Step Two

Find the area of the circle cut outs.

[tex]\text{r} = 12[/tex]

[tex]\text{Area} = \pi \times \text{r}^2[/tex]

[tex]\text{Area} = 3.14 \times 12^2[/tex]

[tex]\text{Area} = 3.14 \times 144[/tex]

[tex]\text{Area} = 452.16 \ \text{cm}^2[/tex]

Step Three

Find the total area left

[tex]\text{Total Area Left = rectangle - circle}[/tex]

[tex]\text{Total Area Left} = 720 - 452.16[/tex]

[tex]\text{Total Area left} = 267.84 \ \text{cm}^2[/tex]   Answer

Answer:

The correct answer:

D. (h, k)