Use the distributive property to write an expression that is equivalent to . 6−9x

Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities.

It has two main branches: differential calculus and integral calculus.

Differential calculus studies the rate of change of a function, also known as its derivative. It deals with concepts such as limits, derivatives and their properties and applications, such as optimization problems.

Integral calculus, on the other hand, deals with the accumulation of quantities, also known as integrals. It studies the concept of definite and indefinite integrals and their properties and applications, such as finding areas and volumes, solving differential equations and computing path length.

Calculus has a wide range of applications in various fields, such as physics, engineering, economics, and many more. It's also a fundamental tool for most mathematical modeling and scientific research.

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The mass of one molecule of methane is 2.658 × [tex] {10}^{-23} [/tex] and number of molecules of methane is 3.76.

Mass of one molecule of methane = mass of one carbon atom + 4×mass of one hydrogen atom

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 1.67 × [tex] {10}^{-24} [/tex]

Performing multiplication first

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 6 68 × [tex] {10}^{-24} [/tex]

Equating the exponents

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 0.668 × [tex] {10}^{-23} [/tex]

Performing addition

Mass of methane = 2.658 × [tex] {10}^{-23} [/tex]

Now, 2.658 × [tex] {10}^{-23} [/tex] is the weight of molecules number = 1

1 gram will have number of molecules = 1/ 2.658 × [tex] {10}^{-23} [/tex]

Number of molecules = 3.76

Thus, mass is 2.658 × [tex] {10}^{-23} [/tex] and 3.76 molecules are there.

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Answer:

80 students

Step-by-step explanation:

To predict the number of students who received a flu vaccine if a school had 65 cases of the flu, we would substitute 65 for y in the equation of the trend line: y = -0.25x + 85.

y = -0.25x + 85

65 = -0.25x + 85

then we solve for x by isolating it on one side:

x = (y - 85) / -0.25

x = (65 - 85) / -0.25

x = -20 / -0.25

x = 80

So, if a school had 65 cases of the flu, it is predicted that 80 students received the flu vaccine.

The value of 'x' = 12°

A circle is a closed polygon and a two-dimensional object where every point in the plane is equally spaced from a central point. Examples are rings, discs, wheels, bangles, coins, etc.

In a circle angle at the center will always equal 360°. There is a number of circular items that we can observe in the real world.

Here we have

(x²)°, 10x°, and (5x+36)° angles made by 3 sectors in a circle

As we know the sum of the angles at the center of a circle = 360°

=> x² + 10x + 5x+36  = 360  

=> x² + 15x  +36 = 360  

=>  x² + 15x - 324 = 0

Now factorize the above equation for the 'x' value

=> x² + 27x - 12x - 324 = 0  

=> x(x + 27) - 12(x + 27) = 0

=> (x + 27) (x - 12) = 0  

=> (x + 27) = 0     or     (x - 12) = 0             144 + 96

=> x = -27                      x = 12

Here 'x' cannot be negative  

Therefore,

The value of 'x' = 12°

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To evaluate the function p(x) = -x^5 + 11x^3 + 7 when x = 3, you need to substitute 3 for x in the function and then perform the arithmetic operations.

p(3) = -(3)^5 + 11(3)^3 + 7

p(3) = -243 + 363 + 7

p(3) = 137

So, p(3) = 137

One nitrogen atom and three hydrogen atoms combine to form the chemical compound known as ammonia, which has the formula NH3. Ammonia's molar mass is 17.031 g per mole or NH3.

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Answer:

answer is (d) (5, -2)

Step-by-step explanation:

When a triangle is translated, each point is moved the same distance in the same direction. To translate a point right, we add the amount of units to the x-coordinate, and to translate it down, we subtract the amount of units from the y-coordinate.

So for point A, the original coordinates are (1,5) and it is translated right 4 and down 7. The new coordinates of point A' will be (1+4, 5-7) = (5,-2)

The turning point of the function in this problem is given as follows:

(-5,2).

The function for this problem is defined as follows:

[tex]f(x) = 2\sqrt[3]{x + 5} + 1[/tex]

The parent function is the cube root function, which has a turning point at (0,0).

The transformations are given as follows:

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The slope of the line AB is 1/4, when the points are A(0, 1) and  B(1, 5).

The ratio of how much y grows as x grows by a certain amount is known as the slope of a line. The slope of a line indicates how steep it is or how much y rises as x rises. Everywhere along the line, the slope is constant (the same).

Consider a roof or a ski slope when trying to visualise the slope of a line. Ski slopes and roofs can both have extreme gradients or be relatively flat. In reality, roofs and ski slopes can both be perfectly flat (horizontal). A line might be perfectly vertical, but a ski slope or a roof are never going to be.

The slope formula is

y₂ - y₁ = m(x₂ - x₁)

Putting the values

5 - 1 = m(1 - 0)

4 = m(1)

m = 1/4

Thus, the slope of the line AB is 1/4, when the points are A(0, 1) and  B(1, 5).

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The 2x²- 4, expression is equivalent to 2(x²-2) with the same variable and exponent we multiply with their constant value.

Distribution property: Multiplying numbers by the sum or difference is the same as multiplying each number in the sum or difference and then adding or subtracting. Example: 6(2+4)= 6(2) + 6(4)

Equivalent Expressions: Expressions are equivalent if they are equal to each other when contracted or expanded. Steps to write equivalent expression using distributive Property,

Step 1 : A list of all the elements with coefficient a

Step 2: List all the factors of constant b.

Step 3: Compare the factors identified in a and b and identify the factors they have in common.

Step 4: Choose one of the factors f such that f(ax/f + b/f). We have, f(x) = 2x² - 4 . Using the above steps,

=> 2x² - 4 = 2 × x × x - 2× 2

As we see, 2 is common factor in both

=> 2( x² - 2)

So, required expression is 2( x² - 2) .

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Complete question:

What is the equivalent of 2x² - 4?.

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

Answer:

2/9

Step-by-step explanation:

First step is to understand the question. Brian can choose 3 different color shirts and 3 different color pants.

First part asks you to choose which list has all the different outcomes.

Second part asks you what the probability of choosing a white/gray shirt with black pants.

Third part asks you to plot the probability on the number line.

Brian 3 different shirt each can be matched with 1 of the three color pants.

Ex:

Now, repeat this with the gray and blue shirt and choose the list that has all this shirt and pant combo. (notice List2 is missing white shirt and navy pants combo)

After choosing List1, find and count the desired outcome asked in part2: choose a gray or white shirt and black pants.

There are 2 outcomes out of the total 9 outcomes or 2/9.

For part3, plot 2/9 on the number line.

Look at my attachment for more detail.

Hope this helped :)

Answer:

second quartile Q₂ = 60

Step-by-step explanation:

the second quartile Q₂ is positioned at the right side of the box, that is

Q₂ = 60

The angle ∠LON is congruent to the angle ∠LMN. Then the measure of the angle ∠LON will be 162.66°.

It is a polygon with four sides. The total interior angle is 360 degrees. A Rhombus's opposite sides and angles are parallel, and each side is congruent to the other sides. Its diagonals intersect at the right angle at the center.

In Rhombus LMNO angle LMN measures 162.66 degrees.

We know that the angle ∠LON is the opposite angle ∠LMN. Then ∠LON is congruent to the angle ∠LMN. Then we have

∠LON = ∠LMN

∠LON = 162.66°

The measure of the angle ∠LON will be 162.66°.

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The system of linear equations 2x - y = 7, and y = 2x + 3, has no solution

In this case, Option C is correct

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What is the solution to a system of linear equations 2x y 7 y 2x 3?.

A) (2, 3)

B) (2, 7)

C) no solution

D) infinite number of solutions

0.06 apples does she have if,She has 3 papayas.

Calculate the item's quantity. P:Q = p/Q should be used as the format.

The total quantities for the two objects would be equal to the sum of "p" and "q."

If you can, reduce the complexity of the object ratios.

Final outcome is the ratio in its simplest form.

Much like fractions, ratios can be entirely simplified. Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Explanation:

6/100 = 0.06.

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0.06 apples does she have if,She has 3 papayas.

Calculate the item's quantity. P:Q = p/Q should be used as the format.

The total quantities for the two objects would be equal to the sum of "p" and "q."

If you can, reduce the complexity of the object ratios.

Final outcome is the ratio in its simplest form.

Much like fractions, ratios can be entirely simplified. Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

6/100 = 0.06.

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When drawing horizontal or vertical lines with a triangle, you need to use two triangles at the same time. You can draw lines at angles of 30, 45, 60, and 90 degrees by combining the two.

Additionally, the values of the side lengths of this triangle are always inversely proportional to one another. and x2 is the side length that is in opposition to the 90-degree angle. likewise, the side length that is in opposition to the 90-degree angle is 72. Additionally, the side length at the opposite end of the 45-degree angle is 2.

Tips for Remembering the 30-60-90 Triangle Rule Remembering the ratio 1 is all it takes to remember the 30-60-90 triangle rules: √3 : 2, and being aware that the longest side length is always in opposition to the largest angle (90 degrees) and the shortest side length is always in opposition to the shortest angle (30 degrees).

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The formula of quadratic function at vertex form is  f(x) = a(x – h)² + k

The term vertex in math is referred as a point where two or more curved lines or edges meet.

Here as a consequence of this definition we know that the point where two lines meet to form an angle and the corners of polygons and polyhedral are vertices.

Here we need to identify the formula of quadratic function at vertex form

As we all know that If a parabola opens upward, then it has a lowest point.

Where as If a parabola opens downward, then it has a highest point.

Here this lowest or highest point is the vertex of the parabola.

Here we have take the parent function f(x) = x² has its vertex at the origin.

And now you can identify the vertex of other quadratic functions by analyzing the function in vertex form.

So, the vertex form of a quadratic function is written as

=> f(x) = a(x – h)² + k

Here a, h, and k are constants.

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The area of hexagon is 20 square units.

polygon, in geometry, any closed curve consisting of a set of line segments connected such that no two segments cross

Hexagon is a six-sided polygon or 6-gon creating the outline of a cube.

Each square in the grid below has area 1 unit.

The total number of grids are 8×8=64 grids.

1 grid of area 1 unit.

As 20 grids are used to form the hexagon.

So the area of hexagon is 20 square units.

Hence,  the area of hexagon is 20 square units.

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Answer: 20

Step-by-step explanation:

Two unique vectors, AB and AC, may be defined by three points (A, B, and C). The cross product of the two vectors may be used as the plane's normal because they both lie on it.

It makes intuitive sense that the reason for this is that since a plane has a dimension of 2, creating one requires exactly two linearly independent vectors. The two vectors' origin and tips are the three points; if the three points were collinear, you wouldn't have two linearly independent vectors.

As long as the three points that make up a plane in a three-dimensional space are not on the same line, they can be used to define it. There is only one plane that can be reached by any three non-collinear locations. There are at least three non-collinear points on a plane. A line that contains two points that are in a plane is also in that plane. When two planes collide, a line forms at the point of intersection.

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The range of a function is the set of all possible output values of the function. The range of f(x) = arcsin(x) is different than the range of g(x) = arccos(x) because the domain of each function is different.

The function f(x) = arcsin(x) is the inverse sine function, and its domain is the set of all real numbers between -1 and 1, inclusive. This is because the sine function has a range of [-1,1], and the inverse sine function takes the input value from the range of sine function and gives the corresponding angle in radians. So the range of arcsin(x) is [-π/2, π/2]

On the other hand, the function g(x) = arccos(x) is the inverse cosine function, and its domain is the set of all real numbers between -1 and 1, inclusive. This is because the cosine function also has a range of [-1,1], and the inverse cosine function takes the input value from the range of cosine function and gives the corresponding angle in radians. The range of arccos(x) is [0, π]

So, in summary, the difference in the range of f(x) = arcsin(x) and g(x) = arccos(x) is due to the difference in the domain of each function.

Answer:

Ok this is going to be a bit confusing, and I may have-actually nevermind.

Step-by-step explanation:

The range of a function is the set of all possible output values that the function can produce. The range of f(x) = arcsin(x) is different than the range of g(x) = arccos(x) because the domain of the two functions is different.

The domain of f(x) = arcsin(x) is -1 <= x <= 1. This means that x can only take on values between -1 and 1 inclusive. The range of f(x) = arcsin(x) is -(pi/2) <= f(x) <= (pi/2). This is because the arcsine function maps the interval [-1, 1] onto the interval [-(pi/2), (pi/2)].

On the other hand, the domain of g(x) = arccos(x) is also -1 <= x <= 1, but the range of g(x) = arccos(x) is 0 <= f(x) <= pi. This is because the arccosine function maps the interval [-1, 1] onto the interval [0, pi].

Both functions are defined for the same values of x, but the range of arcsin(x) is between -(pi/2) and (pi/2) while the range of arccos(x) is between 0 and pi. This means that the range of arcsin(x) is a subset of the range of arccos(x).

Another way to see this is that the arcsin(x) and arccos(x) are inverse functions, meaning that arcsin(x) = y is equivalent to arccos(sin(y)) = x and arccos(x) = y is equivalent to arcsin(cos(y)) = x.

Therefore the range of arcsin(x) will be the set of all possible y such that -1 <= sin(y) <= 1 and the range of arccos(x) will be the set of all possible y such that -1 <= cos(y) <= 1.

for  x² + 2x + 16 = 0, we have to add (2/2)²  number would have to be added to "complete the square"

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

x² + 2x + 16 = 0

Subtract 16 on both sides

x² + 2x = -16  

(Add (2/2)²  on both sides)

x²  + 2x + 1 = -16 + 1    

Factor using Perfect Square Trinomial and add -16 and 1

(x + 1)²  = -15    

Square root on both sides

x + 1 = ±√-15    

Subtract 1 on both sides and use i = √-1

x = -1 ± i√15    

Hence, for  x² + 2x + 16 = 0, we have to add (2/2)²  number would have to be added to "complete the square"

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The relationship between the x- and y-coordinates is described by a linear equation in two variables known as the equation of a line.

A line's slope and y-intercept are expressed in its slope intercept form as y = m x + c. Where the line meets the y-axis is known as the y-intercept.

y = 5 x is the equation for the given line.

Adding 0 to RHS and writing it in the slope-intercept form results in.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

A line's equation is written as ax + by + c = 0. Here, the variables x and y are the variables, while the constant term c is the coefficients. Slope-intercept form, point-slope form, two-point form, intercept form, and normal form are a few additional ways to determine and describe a line's equation.

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Full Question = What is the slope and the y-intercept of the equation y=5x?

The required inequality is 3.5x > 63 oz, where x represents windows Savannah cleans.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x be the number of windows Savannah cleans.

The amount of window cleaner Savannah uses can be represented by the equation:

3.5x = oz

To represent the inequality that Savannah uses more than 18 windows, we can write:

x > 18

This inequality states that the number of windows Savannah cleans (x) is greater than 18.

Combining both the equation and the inequality we can write

3.5x > 63 oz

It tells us that the amount of window cleaner Savannah uses (3.5x) is greater than 63 oz when she cleans more than 18 windows.

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The simplification of the given algebraic expression is; -³/₂x²

We are given the algebra expression as;

(3x³ + 15x²)/(-2x - 10)

Let us factorize the numerator to get;

(3x³ + 15x²) = 3x²(x + 5)

Similarly, let us factorize the denominator to get;

(-2x - 10) = -2(x + 5)

Thus, our original equation is now;

(3x³ + 15x²)/(-2x - 10) = [3x²(x + 5)]/-2(x + 5)

= -³/₂x²

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The maximum number of minutes that it is possible to talk without spending more than $5.00 is <= 11.30

While many calls are included in the contract's inclusive minutes and hence are free of charge, some fall outside of bundle packages and are paid "per minute" or "per call" instead. The normal minimum and maximum rates for domestic calls inside the UK are listed below.

The prices listed on this page are simply illustrative and shouldn't be taken as a complete list of call costs. Actual costs vary depending on your communication provider, as well as a variety of elements such unique calling plans, the time of day, and the precise number contacted. Before dialing, you should double-check with your provider.

An x-minute call costs $2.40 + $0.23x. An inequality that states that an x-minute call costs at most $5.00 can be written as:

$2.40 + $0.23x <= $5.00

To solve for x, we first subtract $2.40 from both sides:

$0.23x <= $2.60

Then, we divide both sides by 0.23:

x <= 11.30

The solution is x <= 11.30, which means that it is possible to talk for at most 11.30 minutes without spending more than $5.00. However, since the number of minutes must be an integer, the maximum number of minutes that it is possible to talk without spending more than $5.00 is 11 minutes.

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Answer:3x^2+2x

Step-by-step explanation

The scale factor for the triangle is 8 : 1.

The first option is the correct option.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

A triangle with a perimeter of 24 meters was created from a triangle,

with a perimeter of 3 meters using a scale factor.

Then the scale factor,

= Actual triangle / scale triangle

= 24 / 3

= 8/1

= 8: 1

Therefore, 8: 1 is the scale factor.

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Answer:

8:1

Step-by-step explanation: