This number is 12 less than it’s square. What could be the number

For the function y=5 cos {x-(π/6)}-1

a) To find the average rate of change, evaluate the function at x = (2π)/3 and x = π/3, and then take the difference between the two values and divide by the difference between the two x-values:

Average rate of change = (y(2π/3) - y(π/3)) / ((2π/3) - (π/3))

First, find y(2π/3) and y(π/3).

y(2π/3) = 5 cos((2π/3) - (π/6)) - 1 = 5 cos(5π/6) - 1 = -5/2 - 1 = -7/2

y(π/3) = 5 cos((π/3) - (π/6)) - 1 = 5 cos(π/6) - 1 = 5/2 - 1 = 3/2

Plugging these values into the formula:

Average rate of change = ((-7/2) - (3/2)) / ((2π/3) - (π/3))

= -5 / (π/3)

= -15/π

Therefore, the average rate of change from x = π/3 to x = (2π)/3 is -15/π.

b) To find the instantaneous rate of change at x = π/2, take the derivative of the function and evaluate it at x = π/2.

y = 5 cos(x - (π/6)) - 1

y' = -5 sin(x - (π/6))

Plugging in x = π/2:

y'(π/2) = -5 sin(π/2 - (π/6)) = -5 sin(π/3) = -5 (√3)/2

Rounding this to the nearest tenth:

y'(π/2) ≈ -4.3

Therefore, the instantaneous rate of change at x = π/2 is approximately -4.3.

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Image transcribed:

4) Consider the function y=5 cos {x-(π/6)}-1

a) Find, in exact form, the average rate of change from x= π/3 to x=(2π)/3  (A-3 marks)

b) Find, to the nearest tenth, the instantaneous rate of change at x=π/2 (A-4 marks) 2

n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

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If 107 people attend a concert, 47 adults and 60 children went to concert using substitution method.

Given,

Let A be the quantity of tickets sold to adults.

Let C be the number of tickets sold to children.

Tickets for adults cost $3.25

Tickets for children cost $2.75

Equation,

3.25A + 2.75C = 317.75

And,

107 people attend a concert.

A + C = 107

Now using the substitution method,

C = 107 - A

Substituting value of C in equation 3.25A + 2.75C = 317.75,

3.25A + 2.75(107 - A) = 317.75

3.25A + 294.25 - 2.75A = 317.75

3.25A - 2.75A = 317.75 - 294.25

0.5A = 23.5

A = [tex]\frac{23.5}{0.5}[/tex]

A = 47

Substituting the value of A in equation C = 107 - A,

C = 107 - 47

C = 60

If 107 people attend a concert, 47 adults and 60 children went to concert.

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The speed of the y-coordinate at that moment is 12 units per second, and it is moving in the negative y-direction.

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).

We can start by taking the derivative of the equation xy = 3 with respect to time t:

x(dy/dt) + y(dx/dt) = 0

Now we can substitute the given information: when the point is at (1, 3), dx/dt = 4. Solving for dy/dt:

(1)(dy/dt) + (3)(4) = 0

dy/dt = -12/1 = -12 units per second

The negative sign indicates that the y-coordinate is decreasing.

So the speed of the y-coordinate at that moment is 12 units per second, and it is moving in the negative y-direction.

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Answer: 595

Step-by-step explanation:

Answer:

G(18 , -9)

Step-by-step explanation:

        [tex]\boxed{\bf Midpoint = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]

H(-2 , 9) ⇒ [tex]x_1 = -2 \ & \ y_1=9[/tex]

     [tex]\left(\dfrac{-2+y_1}{2},\dfrac{9+y_2}{2}\right)= \left(8,0 \right)[/tex]

Compare x and y co-ordiantes,

         [tex]\dfrac{-2+x_2}{2}= 8 \ ; \ \dfrac{9+y_2}{2}=0[/tex]

Cross multiply,

          -2 + x₂ = 16         ;  9 + y₂ = 0

                x₂ = 16 +2     ;         y₂ = -9

               x₂   = 18

G(18 , -9)

for example, let's find the 7.25% of "x"

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.25\% of x}}{\left( \cfrac{7.25}{100} \right)x}\implies \stackrel{ \textit{in decimal form} }{\text{\LARGE 0.0725}}\times x\implies 0.0725x[/tex]

Answer: 6

Solution:

Suppose that the bag contains 2 red tokens, 4 yellow tokens, and x blue

tokens.

Then the likelihood of drawing a blue token is 2-4 ty, and the possibility of drawing a token that is not blue is 2+4+8

If the two likelihoods is equal, we can make the equation below.

X

2+4

2+4+*=2+4+*

Solve for x, = * = 6.

so, there must be 6 blue tokens in the bag.

Consequently, y = -2x + 1 is the equation of the slope-intercept form of the line passing.

A line can be represented using the slope-intercept form of a straight line. Typically, a linear equation in the form y=mx+c is used to represent it. It places emphasis on the slope and y-intercept of a particular line1.

m is the line's slope and c is the y-intercept in this equation. The slope of a line is the ratio of the change in y to the change in x between any two distinct places on the line. The y-intercept is the point at which the line intersects the y-axis.

x - 2y = 8 defines the given line. This equation can be expressed in slope-intercept form as follows:

y = (1/2)x - 4

This line has a slope of 1/2. A line that is perpendicular to this line will have a slope that is the negative reciprocal of 1/2, or -2.

We are aware that the line traverses the given point. (2,-3). The equation of the line can be written as follows using the point-slope form:

y - y₁= m(x - x₁)

where (x₁,y₁) is the line's passing point and m is the slope of the line.

replacing the specified values:

y - (-3) = -2(x - 2)

Simplifying:

y + 3 = -2x + 4

y = -2x + 1

So , y = -2x + 1 is the equation of the slope-intercept form of the line passing through the point (2,-3) and perpendicular to the line described by x - 2y = 8.

The work given below :

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a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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The Pythagorean Theorem describes the relationship among the three sides of a right triangle. In any right triangle, the sum of the areas of the squares formed on the legs of the triangle equals the area of the square formed on the hypotenuse: a2 + b2 = c2.

Answer:

The answer to your problem is, Right Triangle

Step-by-step explanation:

If you remember the Pythagorean Theorem describes the relationship among the three sides of a right triangle

If we can consider a hypotenuse then using formula:

a2 + b2 = c2.

Our sum of the areas of the squares formed on the legs of the triangle equals the area of the square formed on the hypotenuse.

Thus the answer to your problem is, Right Triangle

Answer:

The answer would be (x+10)(x-7)

Step-by-step explanation:

The way I learned it was the numbers would multiply to get 70, but add to get 3. Multiples of 70 are 1, 2, 5, 7, 10, 14, 35, 70. Out of these the only one that works is 10 and 7. Using foil, we get x^2-7x+10x-70 which becomes x^2+3x-70

Answer:

The answer to your problem is, ∞

Step-by-step explanation:

Well there can be multiple ways to make 2/3 equivalent to another here’s how.

We know that 4/6 is equivalent to 2/3 but how exactly?

Well put it into a fraction like this:

[tex]\frac{2*2}{3*2}[/tex] Note: The denominator and the numerator needs to be multiplied by the same number in order for the fraction to be equiavalent.

= 4/6

Thus the answer to your problem is, ∞

Revolutions per minute = (33π/4)/(2π) = 33/8  and this is  33/(8 x 60) = 33/480 revolutions per second

Ten revolutions will therefore take  10 / (33/480) = 4800/33 = 145.5 sec

Answer: the answer is "145.5" seconds

Step-by-step explanation: I took the test.

The coordinates point of polygon A'B'C'D' are: A' (0, 0), B' (-2, 5), C' (-5, 5), and D' (-3, 0).

A polygon is a two-dimensional geometric shape that is defined by a closed path consisting of three or more straight line segments. These line segments are called sides, and the points where they meet are called vertices. Polygons can have any number of sides, although the most common polygons are those with three (triangles), four (quadrilaterals), five (pentagons), six (hexagons), and eight (octagons) sides.

To find the coordinates of A', B', C', and D', we need to apply a 180° rotation to the coordinates of A, B, C, and D.

The general formula for a 180° rotation about the origin is:

(x', y') = (-x, -y)

Using this formula, we can find the coordinates of A', B', C', and D':

A' = (-0, -0) = (0, 0)

B' = (-2, -(-5)) = (-2, 5)

C' = (-5, -(-5)) = (-5, 5)

D' = (-3, -0) = (-3, 0)

Therefore, the coordinates of polygon A'B'C'D' are:

A' (0, 0), B' (-2, 5), C' (-5, 5), and D' (-3, 0).

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Answer:

Step-by-step explanation:

Let's begin by assigning variables to represent the three mixed numbers. Let a be the greatest mixed number, b be the middle mixed number, and c be the least mixed number. Then we can write:

a + b + c = 18 (the sum of the three mixed numbers is 18)

a - c = 5 1/5 (the difference between the greatest and least mixed numbers is 5 1/5)

To solve for a, b, and c, we can use substitution. From the second equation, we can solve for a in terms of c:

a = c + 5 1/5

Substituting this expression for a into the first equation, we get:

(c + 5 1/5) + b + c = 18

Simplifying, we get:

2c + b = 12 4/5

Now we need to find three mixed numbers that satisfy this equation. We can start by choosing a value for c. Let's choose c = 2 1/2, which is the smallest possible value for c that will allow the mixed numbers to be non-negative. Then we can solve for b:

2c + b = 12 4/5

2(2 1/2) + b = 12 4/5

5 + b = 12 4/5

b = 7 4/5

Finally, we can solve for a using the equation a = c + 5 1/5:

a = c + 5 1/5

a = 2 1/2 + 5 1/5

a = 7 3/5

Therefore, three mixed numbers that satisfy the conditions of the problem are:

The greatest mixed number: 7 3/5

The middle mixed number: 7 4/5

The least mixed number: 2 1/2

And indeed, their sum is 18 and the difference between the greatest and least mixed numbers is 5 1/5.

After answering the presented question, we can conclude that baseball graphs going to a value of 27, and the fourth bar labelled basketball going to a value of 44.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle

The correct graph to display the given data is: a bar graph with the title favourite sport, an x axis labelled sport, and a y axis labelled number of students, with the first bar labelled tennis going to a value of 17, the second bar labelled soccer going to a value of 12, the third bar labelled baseball going to a value of 27, and the fourth bar labelled basketball going to a value of 44.

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Answer: A. tennis=17 , soccer= 12, baseball=27, basketball=44

BAR GRAPH make sure its not a histogram!!

Step-by-step explanation:

I took the test and got 100% on it!

The limit of f(x) as x approaches 0 is 0.

As x approaches 0, we can see that both the numerator and denominator of the expression in the given inequality approach 0. Thus, we can use L'Hopital's rule to evaluate the limit.

Taking the derivative of the numerator and denominator separately, we get:

lim x→0 [(2x - 4x^3) / 2x] = lim x→0 [1 - 2x^2] = 1

lim x→0 [x^3 / 4] = 0

Since 0 ≤ f(x) ≤ 1/4x^3, we can conclude that as x approaches 0, f(x) approaches 0 (by the squeeze theorem).

Therefore, the limit of f(x) as x approaches 0 is 0.

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The price for apples is cheaper at quick market.

From the question, we have

Quick market:

[tex]\dfrac{1.52}{6} = \text{0.25 per apple}[/tex]

Walmart:

[tex]\dfrac{1.32}{5} = \text{0.26 per apple}[/tex]

The price for apples is cheaper at quick market.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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The eccentricity (c) length is [tex]c = \sqrt{5}[/tex] and the length of the conic's straight side is 4.

[tex]\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} } = 1[/tex]

We can begin by transforming the given conic equation into the standard form:

[tex]9x^2 + 4y^2 = 36[/tex]

When we divide both sides by 36, we get:

[tex]\frac{x^2}{4} + \frac{y^{2} }{9} = 1[/tex]

When we compare this to the standard form equation for an ellipse, we can see that the major axis is 2a = 6 (since [tex]a^{2}[/tex] = 9 and a = 3) and the minor axis is [tex]b^{2}[/tex] = 4 (because [tex]b^{2}[/tex] = 4 and b = 2). Thus, the eccentricity (c) length can be computed using the formula:

[tex]c^{2} = a^{2} - b^{2}[/tex]

[tex]c^{2} = 9 - 4[/tex]

c = [tex]\sqrt{5}[/tex]

To get the length of the conic's straight side, we must first determine the distance between the two vertices on the major axis. We can deduce from the equation [tex]\frac{x^2}{4} + \frac{y^{2} }{9} = 1[/tex] that We can see that the vertices' x-coordinates are 2, hence the distance between them is 4. As a result, the length of the conic's straight side is 4.

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Complete question:

Calculate the length of the eccentricity and straight side of the conic [tex]9x^{2} + 4y^{2} = 36.[/tex]

Brandon invested $4700 at 3% interest and $1100 at 8% interest using a linear equation.

An algebraic equation of the form y=mx+b is a linear equation. m is the slant and b is the y-capture. A "linear equation in two variables" with y and x as variables is sometimes referred to as the one above.

A linear equation is one in which a variable is raised to its first power. One example of a one variable is ax+b = 0. x is a variable and an and b are genuine numbers.  

Let x represent the amount invested in the first account, which earns interest at a rate of 3%, and let y represent the amount invested in the second account, which earns interest at a rate of 8%. Since the aggregate sum contributed is $5800, we have:

x + y = 5800 The first account has earned 0.03x in interest, while the second account has earned 0.08y in interest. After one year, we have earned $229 in total interest, so we have:

We now have two equations with two unknowns: 0.03x + 0.08y = 229

We can solve for x and y using either the elimination or substitution method. x + y = 5800. In this instance, we will employ substitution.

Find a solution to the first x-equation:

x = 5800 - y

Substitute this expression for x:

0.03(5800 - y) + 0.08y = 229

174 - 0.03y + 0.08y = 229

0.05y = 55

y = 1100

Now substitute this value of y into either equation to solve for x

x + 1100 = 5800

x = 4700

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Volume of the water that has flowed through the pipe in 3 minutes is 36489.6

The flow of water through a pipe is determined by several factors, including the pressure difference between the two ends of the pipe, the diameter and length of the pipe, the viscosity and density of the water, and any obstructions or bends in the pipe.

The rate of flow, or the volume of water that passes through the pipe per unit of time, can be calculated using the formula:

Q = A × V

where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the water.

now area = angle / 360πr²

A= 70 / 360(3.14)(4.8)²

14.06

Now Length = Speed x time

L = 14 x 3 x 60 = 2520 cm

Now Volume = area x length

2520 x 14.06 = 36489.6

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The value of angle x as represented can be determined to 1 decimal place as required to be; 57.8°.

It follows from the task content that the given triangle can be solved for variable x using the sine rule.

Therefore;

11 / sin x = 8 / sin (38)

sin x = 11 sin (38) / 8

x = 57.8°.

Ultimately, the value of angle x as required in the task content is; 57.8°.

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Answer: g (-5)

-127

Step-by-step explanation:

Answer: 125 + 25 = 150 i think is the answer

Step-by-step explanation: To evaluate g(5), substitute x = 5 into g(x)

g

(

5

)

=

5

3

+

(

5

×

5

)

×

x

=

125

+

25

=

150

As x gets larger and larger, the value of y approaches zero.

The graph of [tex]y = (1/2)^x[/tex] does not have an x‑intercept.

The graph of [tex]y = (1/2)^x[/tex] does not have a vertical asymptote because there isn't a vertical line that the graph above approaches.

In Mathematics, an exponential function can be represented by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided about this graph, an exponential function which it models is given by;

[tex]y = (1/2)^x[/tex]

When x = 100, the value of y is given by;

[tex]y = (1/2)^{100}[/tex]

For the x-intercept when y = 0, we have:

[tex]0 = (1/2)^x[/tex]

By taking the ln of both sides, we have:

0 = 1 (false).

In conclusion, this exponential function [tex]y = (1/2)^x[/tex] does not have a vertical asymptote because its denominator can never be equal to zero.

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The option that has the same variation or mean absolute deviation would be option c

Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean of that dataset.

It is a measure of how spread out the data is around the mean, and it is calculated by finding the absolute difference between each data point and the mean, adding up all of these absolute differences, and then dividing by the total number of data points.

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A graph shows the solution to the system of linear inequalities include the following: B. graph B.

In order to graph the solution for the given system of linear inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of linear inequalities and then check the point of intersection;

x + 5y ≥ 5          .....equation 1.

y ≤ 2x + 4         .....equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of linear inequalities is the shaded region above the solid lines, and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (6, 2).

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Answer:

B

Explanation:

Answer:

The new coordinates of point C after reflection and translation are (-2, -2).

Step-by-step explanation:

I hope it helps:)