Is ½ a whole number?

On solving the provided question, we can say that we have the equation

(-2, -2); y= -1/5x+9 => y = 91/10

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Here,

we have the equation

(-2, -2); y= -1/5x+9

y = -1/-10 +9

y = 91/10

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Answer:  100000

Step-by-step explanation: If you take 80 percent of a number and get 80000, then what is that number? In other words, you know that 80 percent of a number is 80000 and you want to know what that initial number is.

To solve this problem, you multiply 80000 by 100 and then divide the total by 80 as follows: (80000 x 100) / 80.

AND I LOOKED IT UP ON GOGLE

Answer:

Step-by-step explanation:

The Answer is 29 degrees

The measure of the reference angle is: [tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]

The reference angle of an angle is the smallest acute angle between the terminal arm of a quadrant and the x-axis.

Given that:

[tex]$$\theta=\frac{11 \pi}{6}$$[/tex]

First, we convert to degrees

[tex]& \theta=\frac{11 \pi}{6} * 180 \pi \\[/tex]

[tex]& \theta=\frac{11}{6} * 180 \\[/tex]

[tex]& \theta=11 * 30 \\[/tex]

[tex]& \theta=330^{\circ}[/tex]

[tex]$$\alpha=30$$[/tex]

Hence, the measure of the reference angle Is: [tex]$30^{\circ}\alpha=30[/tex]$ means that the reference angle is in the first quadrant [tex]$\theta=330^{\circ}$[/tex] means that this angle is in the fourth quadrant

In the first and the fourth quadrants,

[tex]$$\cos (\theta)=\cos (\alpha)$$[/tex]

Substitute [tex]$\alpha=30$[/tex]

[tex]$$\cos (\theta)=\cos (30)$$[/tex]

In trigonometry:

[tex]$$\cos (30)=\frac{\sqrt{3}}{2}$$[/tex]

So:

[tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]

[tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]

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In a stem-and-leaf display a single digit is used to define each stem, and a single digit is used to define each leaf.

In order to help visualize the shape of a distribution, a stem-and-leaf display or stem-and-leaf plot is a tool for presenting quantitative data in a graphical manner, comparable to a histogram.

While a stem plot is another name for a stem-and-leaf plot, it frequently refers to a different kind of chart. The term "simple stem plot" may refer to the mapping of a matrix of y values to a common x axis, along with the identification of the common x value by a vertical line and the individual y values by symbols on the line.

In order to give the reader a fast summary of the distribution, stem-and-leaf displays are helpful for illustrating the relative density and form of the data. The majority of the original numerical data is retained, frequently in complete fidelity. They are helpful for detecting the mode and emphasizing outliers as well. However, stem-and-leaf displays are only effective for data sets that are of a reasonable size (around 15–150 data points).

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definition of a kite is option c

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The solutions of the quadratic equation x^2 + 3x - 10 = 0 are x = 4 and x = -1.

The solution of the quadratic equation x^2 + 3x - 10 = 0 can be found by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where (a, b, and c) are 1, 3, and -10

So, the solutions of the equation x^2 + 3x - 10 = 0 are:

x = (-3 ± √(3^2 - 4(1)(-10)) ) / 2(1)

x = (-3 ± √(9 + 40)) / 2

x = (-3 ± √49) / 2

x = (-3 ± 7) / 2

x = (4, -1)

Complete question:

Which of the following is the solution of the quadratic equation x^2 - 3x − 10 = 0?

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Apples and pears were purchased by Catherine for the school picnic. The right formula will be y = 100-x and y < x if the total number of fruits is less than 100.

Equations are mathematical expressions with two algebraic operators on either side of the equal (=) symbol. To illustrate this relationship, the phrases on the left and right are shown to be equal to one another. A basic, straightforward equation is L.H.S. = R.H.S. (left-hand side = right side).

As per the given data in the equation,

Catherine bought apple and pears.

The overall quantity is less than 100

Let the number of apples is x and,

The number of pears is y.

She bought more apples than pears,

y < x.

And y < 100 - x.

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The domain and range is ,Range: |x+3|0y|[-2,+] Domain: xR .  

Explanation:

x=R Range: y=(0,+) Domain: y=2

y=x²-4

Range: y'=(x2-4)'=2x x=0,y(0)=02-4=-4 y(-4,+)

y=x²+4x+3

Domain: xR Range: (x2+4x+3)

'=2x+4 ⇒ x=-2,y(-2)=(-2) (-2)

²+4(-2)

+3=4-8+3=-1 \sy∈(-1,+∞)

Domain: x-20x2 x[2,+) Range: y[0,+)

Domain: 4 x 2 0 x 2 4 x 2 2 [-2, +2]

x24y[0,2] range

y=|x+3|-2

Range: |x+3|0y|[-2,+] Domain: xR        

The complete question is,

Determine the graphs' scope and range: y=2x y=x2-4

y=x^2+4x+3

y=sqrt(x-2)

y=sqrt(4-x^2)

y=|x+3|-2 ...?

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The domain and range is ,Range: |x+3|0y|[-2,+] Domain: xR .  

What are the steps to finding an equation's domain and range, We can easily identify the values of the independent variable x and the domain by solving the equation y = f(x). The range may then be found by solving for x. Expressing x as x=g(y) and then determining the domain of g allows us to determine the function's range (y).

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range.

x=R Range: y=(0,+) Domain: y=2

y=x²-4

Range: y'=(x2-4)'=2x x=0,y(0)=02-4=-4 y(-4,+)

y=x²+4x+3

Domain: xR Range: (x2+4x+3)

'=2x+4 ⇒ x=-2,y(-2)=(-2) (-2)

²+4(-2)

+3=4-8+3=-1 \sy∈(-1,+∞)

Domain: x-20x2 x[2,+) Range: y[0,+)

Domain: 4 x 2 0 x 2 4 x 2 2 [-2, +2]

x24y[0,2] range

y=|x+3|-2

Range: |x+3|0y|[-2,+] Domain: xR        

The complete question is,

Determine the graphs' scope and range: y=2x y=x2-4

y=x^2+4x+3

y=sqrt(x-2)

y=sqrt(4-x^2)

y=|x+3|-2 ...?

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The angle subtends by the endpoints of the diagonal at any point on the circle will be 90 degrees. Draw the two perpendicular diagonals. Then join the endpoints of the diagonals.

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

here, we have,

Construct a square inscribed in a circle using the construction tool. Insert a screenshot of the construction here.

We know that the angle subtends by the endpoints of the diagonal (longest chord of a circle) at any point on the circle will be 90 degrees.

Then for the construction of the square, we have

First, draw the two perpendicular diagonals.

Then join the endpoints of the diagonals.

Thus, the result is a square.

The angle formed by the diagonal's endpoints at any point on the circle will be 90 degrees. Create two parallel diagonals. Then connect the diagonal endpoints.

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Answer:

Step-by-step explanation:

If the arithmetic sequence is f(x) = 3x-7, x stands for the position of the number in the sequence. In other words, we are looking to solve for x when f(x) = 8:

8 = 3x - 7 and

15 = 3x so

x = 5. The position of the number 8 is the 5th position.

What does this problem ask for:

 --> position of '8' in the sequence

Since our general formula: f(x) = 3x - 7

 --> 'x' represents the position of the term in the sequence

    --> f(x) is the term in the sequence

 --> therefore, if we plug '8' into f(x)

    --> we can find 'x' which is the position of 8 in the sequence

Thus:

 [tex]8=3x-7\\3x=8+7\\3x=15\\x=5[/tex]

8 is the 5th term

Answer: 5th term

Table of Values:
Number of Pylons: 0 | Height: 27 cm
Number of Pylons: 1 | Height: 32 cm
Number of Pylons: 2 | Height: 37 cm
Number of Pylons: 3 | Height: 42 cm
Number of Pylons: 4 | Height: 47 cm
Number of Pylons: 5 | Height: 52 cm
Number of Pylons: 6 | Height: 57 cm
Number of Pylons: 7 | Height: 62 cm
Number of Pylons: 8 | Height: 67 cm
Number of Pylons: 9 | Height: 72 cm
Number of Pylons: 10 | Height: 77 cm
Number of Pylons: 11 | Height: 82 cm
Number of Pylons: 12 | Height: 87 cm
Number of Pylons: 13 | Height: 92 cm
Number of Pylons: 14 | Height: 97 cm
Number of Pylons: 15 | Height: 102 cm
Number of Pylons: 16 | Height: 107 cm
Number of Pylons: 17 | Height: 112 cm
Number of Pylons: 18 | Height: 117 cm
Number

A recipe for a rice dish calls for 6 oz of pure wild rice and 14 oz of a rice mixture that is 10% wild rice , the mixture is 37% wild rice.

we need to find how much wild rice is in the 14 oz of the rice mixture. We can do this by multiplying the weight of the rice mixture (14 oz) by the percentage of wild rice in the mixture (10%).

14 oz * 10% = 1.4 oz

Now we add the amount of wild rice in the rice mixture (1.4 oz) to the amount of pure wild rice (6 oz) to find the total amount of wild rice in the mixture:

1.4 oz + 6 oz = 7.4 oz

Now we divide the total amount of wild rice (7.4 oz) by the total weight of the mixture (20 oz) and multiply by 100% to find the percentage of wild rice in the mixture:

(7.4 oz / 20 oz) * 100% = 37%

So, the mixture is 37% wild rice.

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A percent is a unit of measurement used to express a ratio as part of 100. It is often used to express a proportion of a whole quantity.

The percentage is defined as a ratio expressed as a fraction of 100.

When a part of a whole is represented as a percent, it means that it is expressed as a fraction of 100.

For example, if a quantity is represented as 50%, it means that it is equal to 50/100 or 1/2 of the whole.

Therefore, part of a whole is represented by a percent that is a fraction of 100, with the numerator representing the part and the denominator representing the whole. The value of the fraction is then multiplied by 100 to express the ratio as a percentage.

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Solving equations using elimination, we get the cost of pencil = 0.3, cost of rubber = 0.6

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given,

Teshome bought 6 pencils and 2 rubber erasers from a shop and paid a total of Birr 3.

Meskerem also paid a total of Birr 3 for 4 pencils and 3 rubber erasers.​

Let cost of pencil = x

cost of rubber = y

As per the question,

6x + 2y = 3

4x + 3y = 3

Upon solving the above equations using elimination,

6x + 2y = 3 × 3

4x + 3y = 3 × 2

18x + 6y = 9

8x + 6y = 6

On subtracting the above equations,

⇒ 10x = 3

⇒ x = 3/10 = 0.3, on substituting the value of x, we get,

y = 6/10 = 0.6

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Complete Question -

Teshome bought 6 pencils and 2 rubber erasers from a shop and paid a total of Birr 3. Meskerem also paid a total of Birr 3 for 4 pencils and 3 rubber erasers. Represent variables for the cost of:

a Each pencil and each rubber eraser in Question 1.

ii Formulate the mathematical equations representing each of the situations in Questions 1.

iii Solve each system and determine the cost of,

a Each pencil and each rubber eraser in Question 1.

k = 4/3 is the value of k if one of the zeros of the quadratic polynomial (k-1)x² + kx + 1.

The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here. For an equation to have equal roots the value of the discriminant is 0. The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula.

one of the zeroes of the quadratic polynomial (k - 1)x² + kx + 1 is -3.​

Let say P(x) = (k-1)x² + kx + 1; -3 is one of the zero

=> P(-3) = 0

=> (k - 1)(-3)² + k(-3) + 1  = 0

=> 9k - 9 - 3k + 1 = 0

=> 6k = 8

=> k = 8/6

=> k = 4/3

Value of k is 4/3

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The complete question is as follows:

Find the value of k if one of the zeroes of the quadratic polynomial

(k-1)x² + kx + 1 is -3

Therefore , the solution of the given problem of function comes out to be  f(x) = 3 at x =- 2 and f(x) = -5 at x = 12

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single variable, recognized output for each input.

Here,

Given :  

f(x) = 8 at x = -6

To find the f(x) = -5 at what value of x

and f(x) = 3 at what value of x

So,

From the given y table of f(x)  we can observe that

=> f(x) = -5 at x = 12

and

=> f(x) = 3 at x =- 2.

Therefore , the solution of the given problem of function comes out to be  f(x) = 3 at x =- 2 and f(x) = -5 at x = 12.

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The premium of the policy will be $4,536.30. The goal of insurance is to spread the risk of potential losses among a large group of people, so that any individual loss is not too devastating for one person to bear.

Insurance is a contract between an individual or organization and an insurance company, where the individual or organization pays a premium to the insurance company in exchange for financial protection or reimbursement in the event of an unforeseen loss or event. The insurance company agrees to pay for any covered losses or damages, up to the limits specified in the insurance policy. Insurance can be used to protect against a variety of risks, including death, injury, property damage, and liability.

The premium of the policy can be calculated using the formula:

Premium = (Probability of death * Benefit amount) + Administrative costs

In this case, the probability of death is 18.1452%, the benefit amount is $25,000, and the administrative costs are $45.

Then, the premium of the policy would be:

(0.181452 * 25,000) + 45 = $4,536.30

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Answer:  $4581.30

Step-by-step explanation:

The scatter plot will start looking like an upward line if the owner starts increasing the price by $25 every month.

A scatter plot is a graphical representation of a set of data points, where the position of each point on the x and y-axis represents the values of two variables.

If we use a scatter plot to represent the relationship between the number of months (x-axis) and the profits (y-axis) of a theater as the price of a ticket increases by $25 every month, we might expect to see the following:

A positive correlation between the number of months (x-axis) and the profits (y-axis). This means that as the number of months increases, the profits will also increase.

A linear pattern of data points, with the data points lying on or close to a straight line. This is because the price of a ticket is increasing by a fixed amount ($25) every month, so the profits will also increase by a fixed amount every month.

The slope of the line will be positive, representing the increase in profits each month.

It might look like a line that starts at low profits and as the months progress the line moves upward to the right, representing the increase in profits.

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Answer:

2

Step-by-step explanation:

3(7x+14)=84

21x+42=84

21x=84-42

21x=42

x=42/21

x=2

The number of full hours that the school will be charged would be = 6 full hours.

The amount of money charged for 2 hour = $49

The amount of money charged for 5 hours = 122.50

Therefore the amount of money charged for an hour= 49/2 = $24.5

The amount of money charged for reservation fees = $25

The amount of money the school has to spend on artist fee alone = $175 - 25 = $150

The amount of hours they can hire the artist should be the cost that is within $150 = cost for an hour + cost for 5 hours = 122.50 + $24.5 = $147.

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Drawing a 2 x graph is a simple process that requires only a few basic steps.

To start, you'll need a ruler, a pencil, and a piece of paper. Begin by using the ruler to draw two parallel lines that cross your paper.

These two lines will form the axis of your graph.

Next, use your ruler to evenly space out small tick marks along each line. These tick marks will help you create the “x” and “y” values that will form the data points on your graph.

Finally, connect the data points with lines or dots to create your 2 x graph. You can now use your graph to display the data in an easy-to-understand format.

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Answer:-3+(n-1)*7

Step-by-step explanation:

Nth term = -3+(n-1)*7

Factored form of the equation of the parabola from the given graph can be represented by : f (x) = A ( x - t ) ( x - q ).

As given in the question,

Standard equation of the parabola is given by :

f (x ) = ax² + bx + c

Let us consider the x - intercept of the given graph of parabola where graph of the parabola cuts x -axis at ( t , 0) and ( 0 ,q )

Then factored form for the given roots of the equation can be represented as:

f (x) = A ( x - t ) ( x - q )

t, q are the x-intercepts and A is called the leading coefficient.

Therefore, the factored form the parabola from the given graph is equal to f (x) = A ( x - t ) ( x - q ).

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The value of k must be 4 to make the given quadratic equation a perfect square.

The result of multiplying a polynomial by itself is a perfect square. A perfect square is a number that can be written as the product of an integer multiplied by itself or as the integer's second exponent.

When a number's square root, which is the product of an integer and itself, is an integer, it is said to be a perfect square or a square number.

The quadratic equation is : [tex]$k \cdot y^2-4 \cdot y+1=0$[/tex]

First to make it a complete square : Divide each term by k to make the leading coefficient of [tex]$\mathrm{x}^2=1$[/tex]

Now the equation becomes : [tex]$y^2-4 \cdot \frac{y}{k}+\frac{1}{k}=0 \ldots \ldots \ldots(1)$[/tex]

Divide the coefficient of y by [tex]$2-4 \cdot \frac{y}{2 \times k}=-2 \cdot \frac{y}{k}$[/tex] in order to make it a complete square.

The complete square of the above equation is : [tex]$\left(y-\frac{2}{k}\right)^2=0$[/tex]

Now, expanding this. We get

[tex]$y^2+\frac{4}{k^2}-\frac{4}{k} \cdot k=0$$[/tex]

Now, comparing the constant terms of the above equation with equation 1

[tex]$$\begin{aligned}& \Longrightarrow \frac{4}{k^2}=\frac{1}{k} \\& \Longrightarrow k=4\end{aligned}$$[/tex]

Therefore, the value of k must be 4 to make the given quadratic equation a perfect square.

The complete question is:

For what value of k, the quadratic equation ky²-4y +1 0, is a perfect square?

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The rate is the height of the pile changing when it is 8 feet is:

dh/dt=60/256π

The volume of a cone is defined as the amount of space or capacity a cone occupies, and it is measured in cubic units like cm³, m³, and in³.

The volume of a cone is given as V = (1/3)πr²h.

If the radius of the base of the cone is "r"

height of the cone is "h",

Let r = radius of the base at time t

    h = height at time t

    V = volume of cone at time t

Given:  dV/dt = 20

Find dh/dt when h = 8

V = (1/3)πr²h   Since 2r = 4h, r = 2h

V = (1/3)π[2h]²h

  = (2/3)πh³

dV/dt = (4/3)πh²(dh/dt)

Now, substitute the values we get

20 = (4/3)π(8)²(dh/dt)

20=4/3π×64(dh/dt)

20=256π/3(dh/dt)

60/256π=dh/dt

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Joanne doesn't have enough money to buy all the paint she needs?

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

The area based on the information will be:

= (12 + 10( × 9 / 2

= 144m²

The number of times required will be

= 144 / 3.

= 48

The cost of tin will be:

= 48 / 8 × 25

= 150

Since Joanne has £145 to spend on paint and the cost needed is £150, she doesn't have enough money.

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The range of given parabolic function [tex]x^2+3[/tex] is [3,∞).

Domain: the domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The fact that the fraction's denominator is not equal to zero and that the digit inside the square root bracket is positive both point to the domain.

Range: the range of a function is the set of all possible values for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.

[tex]f(x)=x^2+3\\[/tex]

here domain of the given function is R.

and for x=0, f(x)=3 which is the lower range of given function and for higher range is infinity.

so range of given function is [3,∞).

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The difference in the measures of the two angles is 90 - 84 = 6 °

Theorem of Complementary Angles states that two angles are complementary if the sum of their measures is equal to 90°.

This question can be solved using the theorem of complementary angles, which states that if two angles add up to 90°, then they are complementary angles.

1. Since <A is a right angle, m<A = 90°

2. To find the measure of angle B, solve the equation 9x - 24 = 90.

3. 9x = 114, so x = 12.5.

4. Therefore, m<B = 9x - 24 = 108 - 24 = 84.

5. The difference in the measures of the two angles is 90 - 84 = 6°

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