how many distinguishable ways are there to write $9$ as the sum of $1\text{'s},$ $2\text{'s},$ and $4\text{'s},$ where the order of the addends matters? for example, $4 4 1$ and $1 4 4$ are two different ways.

1. To get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Equation A is equivalent to Equation B

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Here, we have

1.  We are given the equation :

2x - 1 = 5x .............(A)

To get Equation B from A, we would subtract 2x from both sides of the equation.

2x - 2x - 1 = 5x - 2x

- 1 = 3x...... (B)

Hence, to get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Based on the previous answer,

2x - 1 = 5x  is equal to  -1 = 3x.

Hence, both Equation A and Equation B are equivalent expressions.

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By square root, power and sign properties, the expression - 16 · y is the square root of 16 · y² for y < 0.

Let be n a real number, x is the square root of n if and only if n = x², that is:

x = √n

In addition, we find by sign properties the following two cases according to sign of variable y:

Now we proceed to find the square root of 16 · y² for y < 0. First, write the square root described in statement:

√(16 · y²)

Second, use square root and power properties:

√16 · √y², where y < 0.

- 16 · y

In conformity with square root, power and sign properties, the square root 16 · y² for y < 0 is the expression - 16 · y.

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Here that everything is divided equally, we can say that the percentage of the diagram that is shaded equals the number of shaded parts divided by the total number of parts in the diagram.

How many of these portions to darken is determined by the fraction's numerator:

By being able to see how these charts interfere with one another, you may better comprehend the solar access at that location. This graph depicts the surrounding skyline as seen from a certain place and the course of the sun.

P= [tex]r^{2}[/tex]

P = 6*6 =36 cm

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Answer in standard form:  2x+y = 3

Answer in slope intercept form:   y = -2x+3

Both equations describe the same line. Select one of those formats to write to your teacher.

=======================================================

Reason:

The equation 2x+y = 9 solves to y = -2x+9; it is of the form y = mx+b

The parallel line will also have a slope of -2. Parallel lines have equal slopes, but different y intercepts.

The slope-intercept answer is of the form y = -2x+b

Plug in (x,y) = (-1,5) and solve for b.

y = -2x+b

5 = -2*(-1)+b

5 = 2+b

3 = b

b = 3

We go from y = -2x+b to y = -2x+3 which is in slope intercept form.

Adding 2x to both sides gets us 2x+y = 3 which is in standard form.

The amount that Johnny can borrow on a mortgage for a new house, given the Banker's Rule is between $225,000 to $270,000.

The Banker's Rule is a rule of thumb used to determine how much a person can afford to borrow on a mortgage. According to the Banker's Rule, a person should not borrow more than 2.5 to 3 times their annual income for a mortgage.

Using this rule, if Johnny makes $90,000 per year, he can afford to borrow between $225,000 to $270,000 on a mortgage for a new house. However, this is a rough estimate, and other factors such as credit score, debt-to-income ratio, and the lender's requirement also play a role in determining how much Johnny can borrow.

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The volume of the right circular cone hat has a height of 19 feet and base diameter of 178 is calculated as: 1,575.2 ft³.

To find the volume of a right circular cone, we can use the formula:

V = (1/3) * π * r² * h

Where V is the volume, π is approximately 3.14, r is the radius of the base, and h is the height of the cone.

Given that the diameter of the base is 17.8 feet, we can divide it by 2 to find the radius, which is 8.9 feet.

Substituting these values into the formula:

V = (1/3) * π * (8.9²) * 19

V = (1/3) * 3.14 * 78.41 * 19

V = 1,575.2 ft^3

Rounded to the nearest tenth, the volume of the cone is 1,575.2 ft³

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Answer:

x=2.5 and y=-1

Step-by-step explanation:

Firstly we have to state the formula to avoid making mistakes when calculating the points.

So we use the midpoint formula to be able to calculate; midpoint=(x1+x2 , y1+y2)

2 2

So when calculating x we are goin to take the coordinates A(-4,5) and C(9,y)

then we substitute into the formula accordingly so since x will be the midpoint calculation we will say, (-4+9) =2.5 meaning x = 2.5

2

Next, inorder to find y we will ...

5+y=2 and then we will have to get rid of the

2

denominator by multiplying the denominator to both sides of the equals sign. The 2 will cancel each other out then 2×2 =4 an equation will be formed ; 5+y=4 work it out then it will bring you to y= -1 as the answer

Answer: 2

Step-by-step explanation:

The size of the largest angle of the given triangle can be calculated using cosine rule : c² = b² + a² - 2abcosC , where 'C' represents the largest angle of the triangle.

As given in the question,

Let the given triangle be ABC,

Side opposite to ∠A, ∠B, and ∠C is BC, AC, and AB respectively.

BC = a

AC =b

AB = c

let us consider ∠C be the largest angle of the given triangle.

Value of ∠C can be calculated by substituting other values in the cosine rule given by :

cosine rule : c² = b² + a² - 2abcosC

If Pythagoras theorem satisfied then largest angle is right angle.

Therefore, the size of the largest angle of the given triangle can be calculated using cosine rule : c² = b² + a² - 2abcosC

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Rotation, dilation, reflection and translation are all a type of transformation.

The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation.

A rectangular array of numbers is called a matrix, and different operations are provided for it. The components are arranged in vertical columns and horizontal rows.

Rotation, dilation, reflection and translation are all a type of transformation.

A rectangular array of numbers or other objects arranged in a grid position system is called a matrix.

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The number of units that he walks will be 18 units.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be,

Perimeter of the rectangle = 2(L + W) units

Sway needs to get a few things done in and out of town. Take a gander at the guide underneath to compute his distance on the off chance that he begins at home, goes to the video store, or the supermarket, snatches a quick tidbit and finishes at home.

The perimeter of the rectangle is given as,

P = 2(6 + 3)

P = 2(9)

P = 18 units

The number of units that he walks will be 18 units.

The graph is given below.

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Answer: 18 units is the answer so B

Step-by-step explanation:

Answer: [tex]4y=-3x+16[/tex]

Step-by-step explanation:

For there to be infinitely many solutions, the equations must represent the same graph.

The points [tex](0,4)[/tex] and [tex](4,1)[/tex] lie on the line. So, the slope is [tex]\frac{4-1}{0-4}=-\frac{3}{4}[/tex]. As the [tex]y[/tex]-intercept is [tex](0,4)[/tex], the equation is [tex]y=-\frac{3}{4}x+4[/tex].

Multiplying both sides by [tex]4[/tex] yields [tex]4y=-3x+16[/tex].

Answer:

Irrational Numbers: Any real number that cannot be written in fraction form is an irrational number. These numbers include non-terminating, non-repeating decimals, for example , 0.45445544455544445555..., or . Any square root that is not a perfect root is an irrational number.

Answer=

square root of 1000, square root of 64, etc.

These numbers cant be written as a fraction.

Answer:

L^2 = area of square = As

As = 14 L H / 2      where L H /2 = area of triangle

L^2 = 14 L H / 2

H = L / 7    or L = 7 H

Let the length of one side of square = 7 in

As = 7^2 = 49 in^2        area of square

H = 7     height of one side of triangle (other side = 1)

Area of triangle = 7 * 1 / 2 = 7/2 in^2

14 * At = 49

Area of square 7 * 7 = 49 in^2      Seems to checkout

The coefficient of determination (R^2) tells you the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

It tells you how well the independent variable(s) are able to predict the dependent variable. An R^2 of 1 indicates a perfect fit, and an R^2 of 0 indicates that the model does not explain any of the variance in the dependent variable.

The residual plot is a graph that shows the residuals (the difference between the observed value of the dependent variable and the predicted value) on the vertical axis and the predicted value of the dependent variable on the horizontal axis.

The residual plot is used to check for patterns in the residuals, which can indicate a problem with the model. For example, if the residuals are not randomly dispersed around zero, it may indicate that the model is not a good fit for the data. The standard error of the estimate (s) is a measure of the average distance that the data points fall from the fitted line. It represents the average distance that the observed values deviate from the true values. Lower values of s indicate a better fit of the model to the data.

Overall, the R^2, residual plot and s are used to evaluate the goodness of fit of the model.

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1000 is the amount of garbage that was initially dumped in the landfill before any additional garbage was added. i.e: It is the quantity of garbage on Day 0.

The initial function given in the problem is n = 2000x + 1000.

The definition of a function's initial value is its starting value, which is unaffected by any variables used in the function.

The given function is:

n = 2000x + 1000

where the amount of trash is n, and the number of days is x. We'll set the variable (x) equal to zero to obtain the starting value.

Therefore, initially:

n = 2000(0) + 1000 = 1000

This indicates that the trash had a value of 1000 at day zero.

Therefore 1000 represents the amount of trash that was originally present in the landfill before dumping any extra trash.

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Answer: The area of the trapezoid can be found using the formula:

Area = (a + b)h/2

where a and b are the lengths of the parallel sides and h is the height (perpendicular distance between the parallel sides).

In this case, the parallel sides are 13ft and 15ft, and the height is 5ft.

Therefore, the area of the trapezoid is:

(13 + 15) * 5 / 2 = (28) * 5 / 2 = 140 / 2 = 70 ft^2

Step-by-step explanation: The area of the trapezoid is calculated by taking the sum of the parallel sides, multiplying by the height and then dividing by 2. The parallel sides are given as 13ft and 15ft, and the height is given as 5ft.

By substituting the given values in the formula we get (13+15)5/2 = 285/2 = 140/2 = 70 ft^2.

So, the area of the trapezoid is 70 ft^2.

There are 5 integer values of M that satisfy the given inequality.

An integer is a whole number, which means it is a number that can be written without a fractional or decimal component. Integers include positive numbers (e.g. 1, 2, 3), negative numbers (e.g. -1, -2, -3), and zero.

They are also often represented using the symbol "Z". Integers are a subset of the set of real numbers.

If M/20 is strictly between 1/3 and 3/5, then we have the following inequalities:

1/3 < M/20 < 3/5

To solve this, we can multiply both sides of the inequality by 20 to get rid of the denominator on the left side:

6 < M < 12

This tells us that M is an integer that lies strictly between 6 and 12 (i.e., 6 < M < 12), and the integers between 6 and 12 are 7, 8, 9, 10, and 11. Therefore there are 5 integer values of M that satisfy the inequality.

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Therefore ,a result, the answer to the variable problem (B) is incorrect because, even though the adjusted R-square has a lower value .

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Given : The adjusted r-squared number is always lower than the s n value The added variable always causes the modified r-squared value to fall.

If a new variable is included to the regression, the r-squared result cannot drop.

. When comparing several regression models, the adjusted r-squared is more helpful than the r-squared.

Therefore ,a result, the answer to the variable problem (B) is incorrect because, even though the adjusted R-square has a lower value than the R-square, it might not drop as you add more variables.

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Explanation:

The two interior angles 55 and 6x+8 add to the exterior angle 14x-1; this exterior angle is not adjacent to the interior angles mentioned.

Refer to the Remote Interior Angle Theorem for more information.

So,

55+(6x+8) = 14x-1

6x+63 = 14x-1

6x-14x = -1-63

-8x = -64

x = -64/(-8)

x = 8

Then we can determine angle T

angle T = 6x+8 = 6*8+8 = 56 degrees

The total number of boys is 8 and that of girls is 22.

Let x be the number of boy members in the math club. According to the problem, the number of girl members is 2 less than 3 times the number of boy members, so we can write the equation:

G = 3*B - 2

We also know that the total number of club members is 30, so we can write the equation:

B + G = 30

We can substitute the first equation into the second equation to eliminate "G":

B + (3*B - 2) = 30

Combining like terms:

4*B - 2 = 30

⇒ 4*B = 30 + 2

⇒ 4B = 32

Dividing by 4:

∴ B = 34/4

⇒ B = 8

So there are 8 boy members in the math club. To find the number of girl members, we can substitute this value back into the first equation:

G = 3*8 - 2 = 22

So there are 22 girl members in the math club.

Therefore,

The number of boys = B = 8

The number of girls = G = 22

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A one-to-one function is a function that assigns a unique output for each input in its domain, and the graph of a one-to-one function will have no vertical asymptotes, cusps, or self-intersections, and will pass the horizontal line test.

A function is said to be one-to-one (or injective) if no two distinct inputs in the domain of the function produce the same output. In other words, a function is one-to-one if it assigns a unique output to each input in its domain.

A graph of a one-to-one function will have the following properties:

The graph will pass the horizontal line test; no horizontal line will intersect the graph more than once.

The graph will have no vertical asymptotes, which would indicate that the function is not defined for certain inputs.

The graph will have no cusps or self-intersections, which would indicate that the function assigns multiple outputs to the same input.

A one-to-one function has a inverse function, which is also a function and satisfies the same properties as the original function.

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Answer:

Step-by-step explanation:

2 7/9 divided by 2

First, convert the mixed number into a improper fraction:

25/9

Then multiply by the reciprocal of 2, by multiplying it by 1/2,

which turns into 25/8

Turn it into a mixed number: 1 7/18 OR 25/8

Answer:

Gordon

Step-by-step explanation:

The domain is the x values and the range is the y values.  The y values are the not the same.  The y values for function A are all positive and the y values for function B are all negative.

The x values are the same for both functions, so the domain is the same for both functions.

The dimensions that will minimize the cost of 5920

Here is the process. Volume is the volume of a cylinder plus the volume of a sphere.

The surface area of a cylinder without the top and bottom plus twice the surface area of a spherical constitutes the cost of the material.

C = 2πrh + 2(4πr2)

Put what you discovered for h in this formula.

Consider Cost's derivative with regard to r. After that, zero out the derivative and find r.

Utilize the radius, r, value once you have it to solve for the height, h.

now,

V = πr2h + (4/3)πr3 = 5920

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The equations can be framed as:

For Novelists

3 x 5 = 15

and, For Artists:

3 x 3 = 9 artists

A key part to understanding ratios is that it isn't part over whole. Ratios say that there are 5 novelists Per 3 poets.

This can be rephrased to say that there are 5 novelists per 8 TOTAL people.

From here, we can use fractions:

5/8 = x/24

where x is the number of novelists

Now,

Multiplying the left side by 3/3 yields 15/24

Therefore,

there are 15 novelists at the workshop.

We can use the same method for the poets :

3/8 = y/24

= 9/24

Complete Question:

A writing workshop enrolls novelists and poets in a ratio of 5:3.  There are 24 people at the workshop.  How many novelists are there?  How many poets are there?  Write a system of equations to model each situation.  Solve by any method.

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The final value would be 1,534,947.20

Joe Schmo:

Joe Shmoe (also spelled Joe Schmoe and Joe Schmo), meaning "Joe Anybody", or no one in particular, is a commonly used fictional name in American English. Adding an "Shm" to the beginning of a word is meant to diminish, negate, or dismiss an argument (for instance, "Rain, shmain, we've got a game to play"). It can also indicate that the speaker is being ironic or sarcastic. This process was adapted in English from the use of the "schm" prefix in Yiddish to dismiss something; as in, "Fancy, schmancy" (thus denying the claim that something is fancy). While "schmo" ("schmoo", "schmoe") is thought by some linguists to be a clipping of Yiddish.

If the home appreciates 7% per year, it will be worth approximately 1,534,947 dollars in 8 years. This can be calculated by multiplying the initial value of the home (800,000) by (1 + 0.07)^8.

You can also use the following formula:

Final Value = Initial Value x (1 + rate)^Years

The final value would be 1,534,947.20

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The simplified form of the expression given is 17/11.

What is simplifying an expression?

To simplify an expression, create a similar expression devoid of any similar terms. Therefore, we will rewrite the expression using the fewest number of terms possible.

To represent a mathematical expression in the simplest form possible is to simplify it. The expression is reduced to its most basic form when any redundant or redundant parts have been eliminated using the fundamental properties of numbers, exponents, algebraic rules, etc.

Consider, the given expression.

2/2 x 85/55

⇒  170 / 110

⇒ 17 / 11

Hence, the simplified form of the expression given is 17/11.

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Answer:

108 degrees

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon is given by the formula:

(n-2) x 180 degrees

Where n is the number of sides of the polygon. In the case of a pentagon, the number of sides is 5, so we can use the formula to find the sum of the measures of the interior angles of a pentagon:

(5-2) x 180 = 3 x 180 = 540

If we know that the pentagon is regular, meaning that all its angles have the same measure, we can use this information and the formula above to find the measure of each interior angle.

If we divide the sum of the measures of the interior angles by the number of sides, we get the measure of each interior angle of the regular pentagon.

540/5 = 108 degrees

So, the measure of each interior angle of a regular pentagon is 108 degrees

A circle passes through the three vertices of an isosceles triangle that has two sides of length 3 and a base of length 2. So the area of this circle is 81π/32.

These are the specified parameters:

Sides of an isosceles triangle

a = 3

b = 3

c = 2

Find the height of an isosceles triangle

h² = a² - (c/2)²

    = 3² - 1²

    = 9 - 1

    = 8

h = √8

h = 2√2

Find the area of the triangle

A = 1/2 × c × h

  = 1/2 × 2 × 2√2

  = 2√2

Find the length of the radius of the circle

r = abc / (4 A)

 = (3 × 3 × 2) / (4 × 2√2)

 = 9/4√2

 = 9√2/8

Fnd the area of the circle

A = π × r²

  = π × (9√2/8)²

  = 81π/32

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