Determine the Domain and Range of each graph, then decide if the graph is exponential growth or decay.

On solving the provided question, we can say that the mean that 6 tests including the last test brian took.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.

(91n + 98) / (n + 1)  =  92

    91n + 98  =  92(n + 1)

 91n + 98  =  92n + 92

 98  =  n + 92

6  =  n

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When adding multi-digit numbers, it's a good idea to employ the commutative property. However, counting up becomes simpler if pupils are aware that they can change the order of the addends and begin adding with the larger number FIRST.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Here, a and b may be fractions, decimals, whole numbers, or even integers.

For instance, 1+2=2+1 and 2x3=3x2.

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Answer: 10.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9

An algebraic expression that shows a relationship between two variables   that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.

.

we are given, two linear equations x - a -3y = 0

and a - 2x -3y - 16 =0

from the first equation, x = a + 3y

we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0

                                                                     a - 2a - 6y - 3y -16 = 0

                                                          - a - 9y -16 =0

                                                   - (a + 16) = 9y

                                              y = - (a+16) / 9

now we put the value of y in the equation, x = a + 3y

                                    get, x = a+ 3 [ - (a+16)] / 9

                                      x = a + [ - (a+16)] / 3

                                          x = (3a - a -16) / 3

                              x = (2a - 16)/ 3

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2) y+ 3÷y is the equation that is not a polynomial. Using addition, subtraction, multiplication, and division of numbers .

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).

given

An algebraic mathematical equation known as a polynomial might have two components. coefficients and parameters

You can combine the solutions to these algebraic equations to achieve the result.

It follows the general formula as follows:

a + a1 + a+ …

2)y+ 3y is the equation that deviates from the formula above.

So, 2)y+ 3y is the equation that is not a polynomial.

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We can find the x-intercept by writing the equation in intercept form which  is also known as factored form, y= (x-p) (x-q) where p, q are the x-intercepts.

To find the vertex of the quadratic function we can write the function  in standard form , the vertex is located at the point where y=f (x).

A function which has a degree of two is known as a quadratic function.

Example, 3x² + 2 , here the maximum degree is 2 , hence the given function is quadratic. The general form of a quadratic equation is given as ,

f(x) = ax2 + bx + c .

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The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then there will be a total of 345 dragons in this year.

The percentage increase in the number of dragons in Westeros rose = 15%

The total number of dragons in Westeros rose in previous year = 300

So, for calculating the total number of dragons in Westeros rose in this year we will first find the value of 15% of 300 and then add it to 300.

So, finding the value of 15% of 300

As we know, for removing the percentage sign we will divide the given number by 100

So, the value of 15% of 100 = (15/100)*300 = 45

So, the value of the total number of dragons in Westeros rose in this year will be 300+45 = 345

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The correct question may be like:

If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then what will be a total of dragons in this year?

Taking into account the definition of a system of linear equations, the length and width of the rectangle is 22.5 cm and 19.5 cm respectively.

Systems of linear equations are groupings of first degree equations with the same unknowns, of which a common solution must be found.

In the systems of equations, the values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

2x + 2y= 84

x= y + 3

The substitution method is a way to solve systems of equations. To use the substitution method, you choose an equation and find an expression for one of the variables in terms of the other variable. Then substitute that expression for the variable in the other equation.

In this case, substituting the second equation in the first one you get:

2×(y+3) + 2y= 84

Solving:

2y+ 2×3 + 2y= 84

2y+ 6 + 2y= 84

2y + 2y= 84 - 6

4y= 78

y= 78÷4

y= 19.5

Replacing this value in the second equation, you get:

x= 19.5 + 3

x= 22.5

Finally, the length of the rectangle is 22.5 cm and the width of the rectangle is 19.5 cm.

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Answer:

the answer is A

[tex]x + 7 > 3[/tex]

O(-, -28] is the formula for resolving the inequality +4 = 0. Inequality is the state of having a connection between two expressions or values that is not equal to them.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

A disparity is presented to us.

[tex]y+4\leq 0[/tex]

The answer to the inequality must be discovered.

For each side of the inequality, deduct 4

y +4 - 4 ≤ 0 - 4

y ≤ -4

y ∈ ( - ∞ , - 4 ]

As a result, the solution set for the given inequality is provided by y (- , - 4].

O(-, -28] is the formula for resolving the inequality +4 = 0. Inequality is the state of having a connection between two expressions or values that is not equal to them.

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The unit price of one gallon of paint is going to be $35.96.

We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.

In this question, it is given that 1/4 gallon of paint costs $8.99 so for 1 gallon we will have to multiply both the paint amount and the money which buys it to 4 which will conclude that 1 gallon costs $8.99 × 4 is equal to $35.96. So, 1 gallon of paint will cost $35.96.

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The Slope of log - log graph  represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .

What is Logarithm ?

The Logarithm is defined as  power to which a number must be raised to get some other number .

A log-log plot is the plot in which  both the x-axis  and y-axis use a log scale.

The plot of  logarithms of variables helps in extracting  the information about the power relationship. The case of  freely falling object is  used to illustrate a log - log plot.

A plot of the logarithm of freefall distance as a function of logarithm of time gives  a straight line of slope 2.

Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.

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The manager should expect the defective nails of 350-pound delivery to contain 23.3 pounds .

The defect rate is a measurement of the proportion of production units that are flawed or useless relative to a certain number of units. Businesses use this assessment to assess the quality of their products and how they affect their bottom line. Although lower rates are desired, no industry has a set acceptable fault rate. Therefore, businesses must choose their goal defect rate.

Defect rate is crucial because it enables firms to calculate the proportion of output units that fail quality checks. This assists the firms in identifying any issues with quality control or manufacturing and estimating the cost of each fault. To estimate the profitability of a product, businesses can also compare failure rates among comparable or dissimilar products.

In ever 4.5 pounds of nail defective nails are = 0.3 pounds

In ever 1 pounds of nail defective nails are = 0.3/4.5 pounds

In ever 350 pounds of nail defective nails are = (0.3/4.5)*350 pounds

⇒ the defective nails in 350 pounds of nails= 105/4.5

⇒ the defective nails in 350 pounds of nails= 23.3 pounds

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Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.

A relationship between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. Different inequalities are employed to contrast values of all sizes. By changing the two sides until only the variables are left, one can solve many straightforward inequalities. But a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.

given

the inequality for x 1/3 x - 3 -1 5/6 must first be resolved.

2 plus 3 on both sides

Simply multiply both sides of 1/3x by 3x31/2,

and then graph x31/2 on a number line.

Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.

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Answer:

50x - 200y = 75

3x + y = -5

Step-by-step explanation:

Standard form of a line

Ax + By = C

0.5x +-2y -0.75  Multiply through by 100

50x - 200 - 75 = 0  Add 75 to both sides

50x - 200y = 75

y = -3x - 5  Add 3x to both sides

3x + y = -5

Answer:

B

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 2 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes

then slope of parallel line is 3

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (3, 5 ) , then

y - 5 = 3(x - 3) ← equation of parallel line in point- slope form

Answer:

no sign (not positive or negative)

Step-by-step explanation:

The value of the expression

4.3 ⋅ (-3.2) ⋅ 0

is 0, as the value of any number multiplied by zero is 0.

The number zero is neither positive or negative; hence there is no sign.

The function which can which can define the number of flowers in the arrangement is f(x) = 64 + 18x. The domain is found to be [ 0 , 5 ] and the range is [ 64 , 154 ].

Let the number of flowers which is to be calculated be x,

now we know that she already have 64 flowers and that each arrangement will have 18 flowers.

Therefore, the number of flowers can be given by the function , f(x) = 64 + 18x.

Now , we know that the maximum number of flowers which she can buy externally is 5 , which means the domain becomes  [0,5] .

To find the range we will put the value of domain in the given function.

when x = 0 ,

f(0) = 64

when x = 5,

f(5) = 154

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Answer:

15

Step-by-step explanation:

To find f(-3), substitute x with (-3)

f(x) = -x² - 8x

f(-3) = - (-3)² - 8*(-3)

      = - (9) + 24

       = - 9 + 24

       = 15

Answer:

15

Step-by-step explanation:

f ( x ) = - x² - 8x

Accordingly, to find the value of f ( -3 ) you have to replace x with ( - 3 ).

f ( -3 ) = - (-3)² - 8 × -3

f ( -3 ) = - 9 + 24

f ( -3 ) = 15

Answer:

Sure! Here's a system of equations we can set up to represent this situation:

Let x be the price of a bag of popcorn and y be the price of a drink.

Then we can set up the following system of equations:

x + 3y = 16.50 (equation for Jack's purchases)

2x + 5y = 29.75 (equation for Jill's purchases)

To solve this system of equations, we can use the substitution method.

First, we can solve for x in equation 1:

x = 16.50 - 3y

Then, we can substitute this expression for x into equation 2:

2(16.50 - 3y) + 5y = 29.75

Simplifying this equation, we get:

33 - 6y + 5y = 29.75

Combining like terms, we get:

33 - y = 29.75

Subtracting 29.75 from both sides, we get:

33 - 29.75 - y = -y

Simplifying, we get:

3.25 - y = 0

Subtracting 3.25 from both sides, we get:

-y = -3.25

Dividing both sides by -1, we get:

y = 3.25

So, the price of a drink is $3.25.

Now we can substitute this value for y back into equation 1 to solve for x:

x + 3(3.25) = 16.50

Simplifying, we get:

x + 9.75 = 16.50

Subtracting 9.75 from both sides, we get:

x = 6.75

So, the price of a bag of popcorn is $6.75.

To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.

Step-by-step explanation:

Elena made 2 batches of bird food, each with 1/8 cup cracked corn, 3/4 cups sunflower seeds, and 1/4 cup dried cranberries, for a total of 1.75 cups of bird food.

Elena made two batches of bird food using a combination of cracked corn, sunflower seeds, and dried cranberries. Each batch uses 1/8 cup of cracked corn, 3/4 cup of sunflower seeds, and 1/4 cup of dried cranberries.

To find the total amount of bird food she made, we need to add the ingredients of the two batches together.

Since she made two batches and each batch contains 1/8 cup of cracked corn + 3/4 cup of sunflower seeds + 1/4 of dried cranberries, the total amount of bird food is 2 × (1/8+3/4+1/4) = 2 × (7/8) = 7/4 = 1.75 cups.

This is the best estimate of the total amount of bird food made by Elena. It's important to note that this estimate is based on the assumption that the proportion of ingredients in each batch is the same, and that the ingredients are measured accurately.

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Scale factor required to map the first line segment onto second line segment is 3/9=0.33

The scale factor is the ratio of the length of the image to the length of the pre-image.

In this case, we're looking for the  that would map the first line segment (length 9cm) onto the second line segment (length 3cm).

To find the scale factor, we can divide the length of the image by the length of the pre-image:

scale factor = length of image / length of pre-image

In this case:

[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]

[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]

So the scale factor to map the first line segment onto the second line segment is 1/3.

It means the 1st line is 3 times longer than the second one.

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Answer:

x = - √2/2

Step-by-step explanation:

We know that x = rcosθ and y = rsinθ. The unit circle always have radius of 1 unit. Therefore, r = 1 as defined. Hence:

x = cosθ, y = sinθ

x = cosθ, θ = arcsin(y)

x = cos{arcsin(-√2/2)}

Find the measurement or θ that makes sinθ = -√2/2 and that is π + π/4 = 5π/4.

x = cos(5π/4)

And cos(5π/4) = - √2/2 as well. Hence, x = - √2/2.

Answer:

related to their eyes. How would you assign random numbers to conduct a simulation based on this

Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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