Pleaseeeeeee helps meeeeeeee I'd really appreciate it

The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.

A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.

We can express the total cost of an order as a function of the number of books sold, x, using the formula:

f(x) = 1.99x + 3

This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.

For example, if we sold 3 books, we can use the function to find the total cost:

f(3) = 1.99(3) + 3 = 9.97

This means that selling 3 books would cost $9.97 in total.

The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.

The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.

In contrast, a discrete function can only take on specific values, usually whole numbers or integers.

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The Converse of the Pythagorean Theorem is proved below.

What is Pythagoras Theorem ?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.

To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.

Proof:

Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.

We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:

c² = a² + b² - 2ab cos(C)

Substituting a² + b² = c² into this equation, we get:

c² = c² - 2ab cos(C)

2ab cos(C) = 0

cos(C) = 0

Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.

Thus, this completes the proof of the converse of the Pythagorean theorem.

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The order of the matrix is 2 x 2.

What is a matrix and what is meant by its order?

In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.

The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.

Determine the order of the given matrix:

In the given problem, we are asked to find the order of the matrix:

[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]

we count the number of rows and columns.

This matrix has 2 rows and 2 columns, so its order is 2 x 2.

Therefore, the order of the matrix is 2 x 2.

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Answer:

A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us

Step-by-step explanation:

i may be wrong but I tried

To find the range of a data set from a box and whisker plot, you can use the whiskers of the plot. The whiskers represent the minimum and maximum values of the data set, so the range can be calculated by subtracting the minimum value from the maximum value.

A whisker plot, also known as a box and whisker plot, is a graphical representation of the distribution of a set of data. It displays a summary of the minimum, maximum, median, and quartiles of the data set.

A typical whisker plot consists of a rectangular box with a vertical line inside, which represents the median of the data set. The lower and upper edges of the box represent the first and third quartiles, respectively. The length of the box thus represents the interquartile range (IQR), which is a measure of the spread of the middle 50% of the data.

In statistics, the range of a data set can be found from a box and whisker plot by looking at the endpoints of the whiskers.

The whiskers in a box and whisker plot extend from the box to the smallest and largest data points within a certain range of the median. The range of the data set is simply the difference between the smallest and largest data points.

To find the range of the data set from a box and whisker plot, simply identify the endpoints of the whiskers and find the difference between them. Note that the whiskers may be labeled with the actual values of the data points or labeled with a multiple of the interquartile range (IQR), which is the distance between the first and third quartiles of the data set.

It's worth noting that the range is a very basic measure of the spread or dispersion of a data set and is sensitive to outliers. Other measures of spread, such as the interquartile range, variance, or standard deviation, may provide more robust and informative summaries of the data.

Hence, the method to plot whiskers in a data range is provided.

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The point on the graph that tells you the amount of sugar you'll use if you don't make any pies is (0, 0).

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship, the variables representing the amount of sugar and time must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/3

Constant of proportionality, k = 12.

Therefore, the required equation is given by:

y = kx

y = 4x/3

When x = 0, the value of y is given by:

y = 4(0)/3

y = 0 pies.

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Answer:

volume = 290m

Step-by-step explanation:

box 1

[tex]vol= lwh\\=3*5*6\\=90m[/tex]

box 2

[tex]vol=lwh\\=8*5*5\\=200m[/tex]

total volume = 90+200 =290m

Given:-

To find:-

Answer:-

Here since the given triangle is a right angled triangle, we may use the trigonometric ratios . We can see that perpendicular and base are involved in this question whose measures are "x" and "√10" respectively with respect to 60° angle. So here we may use the ratio of tangent as , in any right angled triangle,

[tex]\implies\tan\theta =\dfrac{p}{b} \\[/tex]

and here p = x , and b = √10 . So on substituting the respective values, we have;

[tex]\implies \tan\theta = \dfrac{x}{\sqrt{10}} \\[/tex]

Also the angle here is 60° , so that;

[tex]\implies\tan60^o =\dfrac{x}{\sqrt10} \\[/tex]

The value tan60° is √3 , so we have;

[tex]\implies \sqrt3 =\dfrac{x}{\sqrt10}\\[/tex]

[tex]\implies x =\sqrt{10}\cdot \sqrt{3}\\[/tex]

[tex]\implies x =\sqrt{10\cdot 3} \\[/tex]

[tex]\implies x =\sqrt{30} \\[/tex]

The value of √30 is approximately 5.48 , so that;

[tex]\implies \underline{\underline{\red{\quad x = 5.48\quad }}} \\[/tex]

Therefore the value of x is approximately 5.48 .

Answer:

The length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:

We have been given the side opposite the 30° angle, so:

[tex]\implies b=\sqrt{10}[/tex]

The side labelled "x" is the side opposite the 60° angle, so:

[tex]\implies x=b\sqrt{3}[/tex]

Substitute the found value of b into the equation for x:

[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]

[tex]\implies x=\sqrt{10 \cdot3}[/tex]

[tex]\implies x=\sqrt{30}[/tex]

Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

[tex]\hrulefill[/tex]

We can also calculate the length of side x using the tangent trigonometric ratio:

[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]

where:

From inspection of the given right triangle:

Substitute these values into the formula:

[tex]\implies \tan 30^{\circ}=\dfrac{\sqrt{10}}{x}[/tex]

[tex]\implies \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{10}}{x}[/tex]

[tex]\implies x\sqrt{3}=3\sqrt{10}[/tex]

[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}[/tex]

Rationalise the denominator by multiplying the numerator and denominator by √3:

[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac{3\sqrt{10}\sqrt{3}}{3}[/tex]

[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]

[tex]\implies x=\sqrt{10\cdot3}[/tex]

[tex]\implies x=\sqrt{30}[/tex]

Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

Answer:

a-no for the first triangle, because the total of the inner angles must be 180, the last angle must be 90.

b-yes- a triangle with angles 90, 50, and 40 is possible

c-yes. 65+45+70=180.

Step-by-step explanation:

Around [tex]312.57[/tex] yards are required to complete a full lap of the circuit.

The entire movement of an item, independent of direction, is called distance. Regardless of an object's beginning or finishing position, distance may be defined as the amount of ground it has travelled.

As a result, distance is indeed a scalar quantity. The whole path an item has taken can be used to define the distance from it. Think about it this way. If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the automobile must be 13 km.

The circumference of a semicircle with diameter d is [tex](pi/2)d[/tex]. Therefore, the length of each semicircular section is [tex](pi/2) * 36 = 18pi[/tex].

The total distance around the track is the sum of the lengths of the two straight sections and the two semicircular sections.

Distance around track [tex]= 2(100 yards) + 2(18pi yards)[/tex]

[tex]= 200 yards + 36pi yards[/tex]

[tex]= 312.57 yards[/tex] (rounded to two decimal places)

Therefore, the distance around the entire track is approximately [tex]312.57[/tex]yards.

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The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -

experimental probability = number of on-time trains / total number of trains

From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -

number of on-time trains = 15

total number of trains = 20

Substituting these values into the equation, we get -

experimental probability = 15 / 20

Simplifying the fraction, we get -

experimental probability = 3/4

Therefore, the experimental probability value is obtained to be 3/4 or 0.75.

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The quadratic equation on the graph can be written as:

y = x² + 6x + 8

Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:

y = a*(x - h)² + k

Here we can see that the vertex is at (-3, -1), replacing that we will get:

y = a*(x + 3)² - 1

Now we can also see that it passes through the point (-2, 0), replacing these values we will get:

0 = a*(-2 + 3)² - 1

0 = a - 1

1 = a

Then the quadratic is:

y  = (x + 3)² - 1

Expanding that we get:

y = x² + 6x + 9 - 1

y = x² + 6x + 8

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1 + 2i in polar form is 5√2∠63.4°.

What is a polar form ?

In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).

D. 5√2∠63.4°

To convert a complex number from rectangular form to polar form, we use the following formulas:

r = √(a^2 + b^2)

θ = tan^-1 (b/a)

Where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = 1 and b = 2, so:

r = √(1^2 + 2^2) = √5

θ = tan^-1 (2/1) = 63.4°

Therefore, 1 + 2i in polar form is 5√2∠63.4°.

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Answer: If Jamie is selling bags of carrots for $5 each and already has $30 what would he use to calculate how much money he made.

True. The length of AB can be gotten by 3^2 + b^2 = 4^2.

True.  The perimeter of the trapezoid shown is not 22 units.

The length of AB can be gotten by 3^2 + b^2 = 4^2.

9 + b^2 = 16

b^2 = 16 + 9

b = 5

Then we have to count the boxes to get the length of the other sides

CD = 4

AD = 8

BC = 5

AB = 5

Then the perimeter would be be 5 + 5 + 8 + 4

= 22

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The volume of the cone in cubic centimeters in terms of π = 120π cm³. That is option B.

To calculate the volume of a cone, the formula that is to be used;

Volume = 1/3 πr²h

Where;

Height = 10 centimetres

Radius = 6 centimetres

Volume = 1/3 × π × 6²× 10

= 360π/3

= 120π cm³

Therefore the volume of the cone whose dimensions are given = 120π cm³.

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Answer:

4.

a-9=15

or. a=15+9

or. a=24

5.

n-9=13

or. n=13+9

or. n=22

6.

b-8=9

or. b=9+8

or. b=17

7

x-5=16

or. X=16+5

or X=21

8

n-6=17

or. n= 17+6

or. n=23

Step-by-step explanation:

minus sign changes into plus sign when changing sides

Answer:

p=84

Step-by-step explanation:

p=6×14

p=84

answer: p=84

The correct number line is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

The mathematical expression of a connection between two values, stating that one value is larger than, less than, or not equal to another value, is called an inequality. Common symbols for inequality include (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, the inequality 2x + 3 > 7 denotes that the value of 2x + 3 is larger than 7. Depending on the circumstance, inequalities can be resolved algebraically or visually. A collection of values that meet the connection implied by the inequality is the answer to an inequality.

Here, the inequality is y - 2 < -5, which can be rewritten as y < -3.

Hence, the correct option is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.

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Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

Answer:

C)  2, 7, 6 can form a triangle.

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.

To determine which group of given side measures will form a triangle, sum each pair of sides and compare to the third side. If all three inequalities are true, the group will form a triangle.

Given side lengths: 9, 4, 3

  ⇒ 9 + 4 > 3

  ⇒ 9 + 3 > 4

  ⇒ 4 + 3 [tex]\ngtr[/tex] 9

Therefore, this group cannot form a triangle.

Given side lengths: 8, 1, 7

  ⇒ 8 + 1 > 7

  ⇒ 8 + 7 > 1

  ⇒ 1 + 7 [tex]\ngtr[/tex] 8

Therefore, this group cannot form a triangle.

Given side lengths: 2, 7, 6

  ⇒ 2 + 7 > 6

  ⇒ 2 + 6 > 7

  ⇒ 7 + 6 > 2

Therefore, this group can form a triangle.

Given side lengths: 12, 10, 22

  ⇒ 12 + 10  [tex]\ngtr[/tex] 22

  ⇒ 12 + 22 > 10

  ⇒ 10 + 22 > 12

Therefore, this group cannot form a triangle.

Answer:

Step-by-step explanation:

Ranking:

Compound the interest every month instead of every two months.

Increase the interest rate by 1%.

Let the account increase for one more year.

Increase the starting amount by $100.

Calculations:

If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.

If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.

If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.

If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.

The Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

Accοrding tο the Pythagοrean theοrem, the square οf a right triangIe's hypοtenuse (the side οppοsite the right angIe) equaIs the sum οf its οther twο sides' squares.

Outside waII's Iength and width are equaI if it is a square. Let's caII this Iength "x"

Using the Pythagοrean theοrem, we can find the Iength οf the diagοnaI οf the square:

diagοnaI² = height² + width²

Since the height is 9 ft and οne side οf the square is 12 ft, we can write:

diagοnaI² = 9² + 12²

diagοnaI² = 81 + 144

diagοnaI² = 225

Taking the square rοοt οf bοth sides, we get:

diagοnaI = √(225)

diagοnaI = 15 ft

Therefοre, the Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

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We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.

Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.

To get mt = m, substitute u = tk into mt = mu (tk).

Rewrite m(tk) as (mt)k using the associative property of multiplication.

To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.

Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.

Since 1 Equals k, we get u = tk = t(1) = t.

We get mt = mt by substituting u = t into the original equation mt = mu.

As a result, we have demonstrated that mt = mu when t | u.

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Answer: A 48 x 24/16 = r

Step-by-step explanation:

48 x 24 = the total number of drinks

Since there are 16 drinks in each row you want divide to get the number of rows in each drink.

Ex: 48 x 24= 1,152 (total drinks)

16 drinks in a row

1,152/16 = 72

72 rows

Answer:

1. -2/7

2. 7/6

3. 53/8

4. do u mean sum? if yes then the answer is 1

5. 5/12

6. 2/5

7. -2/3

8.

9.90

10.240

11.60

12. 4/15

13.4/7

14.8/5

15.24/7

16.15/16

17.4/9

18.8/7

19.-2/5

20.-1/12

1. Calculating the output when using -6 as the input, we have:

Rule 1: subtract 7  = -13

Rule 2: square the input = 36.

Rule 3: divide by 3 = 12

Rule 4: divide the input into 3 = -2

Rule 5: write π = -2π

Rule 6: volume of a cube = -216cm³

A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.

2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.

b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.

c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.

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Answer:

Supplementary Angles: The angles 1 & 2 are supplementary angles, as, when combined together, their total angle measurement is 180°, or a straight line. Supplementary angles, by definition, is either two angles in which, when combined, the sum is equal to 180°.

Adjacent Angles: The angles 1 & 2 are adjacent angles, as they share a common side and vertex. Vertexes, by definition is the corner point.

Why it is not:

Complementary Angles: Complementary angles suggest that, when two angles are combined together, their total angle measurements is 90°, or it creates a right angle. In this case, the total measurements of the combination of ∠1 & ∠2 is a straight line, or 180°. Therefore, complementary angles is not your answer.

Vertical Angles: Vertical angles suggest that, when there are two angles, they are directly opposite of each other. Vertical angles would share the same angle measurements.

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