one angstrom, symbolized å, is 10-10 m. 1 cm3 = ________ å3.

So the equation x² + 2y² + 3z² + 2xy + 2yz - 2zx can be put into canonical form, (x + y + z)²/2.

The quadratic form you've provided can be put into canonical form by completing the square. The process involves a few steps:

Rearrange the terms so that all of the x, y, and z terms are on one side of the equation, with a constant term on the other side. In this case, the equation is already in this form.

Divide every term by 2, to make the next step more manageable. This gives us x²/2+ y²/2 + z²/2 + xy + yz - zx

For each variable, add and subtract the square of half of the coefficient of that variable's corresponding x,y,z coefficient. In this case, x²/2, y²/2, z²/2 are all squares so no action need to be done

Group like terms: (x²/2 + xy/2 + xz/2) + (y²/2 + yz/2 + yx/2) + (z²/2 + zx/2 + zy/2)

Each of the group in step 4 is a perfect square, and can be rewritten as (x/√2 + y/√2 + z/√2)² so that the equation becomes (x + y + z)²/2

So the equation x² + 2y² + 3z² + 2xy + 2yz - 2zx can be put into canonical form, (x + y + z)²/2. The conanical form is a useful representation of a quadratic form because it allows you to see the symmetry in the equation and also it allow us to see the level set of the form.

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For the given quadratic form equation x² + 2y² + 3z² + 2xy + 2yz - 2zx has the canonical form as [tex]\frac{ (x + y + z)^2}{2}[/tex]

Here we have to find the quadratic form you've provided can be put into canonical form by completing the square.

And the process involves a few steps,

First, we have to rearrange the terms so that all of the x, y, and z terms are on one side of the equation, with a constant term on the other side.

Now we have to divide every term by 2, to make the next step more manageable,

[tex]= > \frac{x^2}{2} + \frac{y^2}{2} + \frac{z^2}{2} + xy + yz - zx[/tex]

Now, we have to add and subtract the square of half of the coefficient of that variable's corresponding x,y,z coefficient, then we get the following,

[tex]= > \frac{x^2}{2} + \frac{y^2}{2} + \frac{z^2}{2} + xy + yz - zx[/tex]

And then we have to group like terms, then we get the equation like the following,

[tex]= > (\frac{x^2}{2} + \frac{xy}{2} + \frac{xz}{2} ) + (\frac{y^2}{2} + \frac{yz}{2} + \frac{yx}{2} ) + (\frac{z^2}{2} + \frac{zx}{2} + \frac{zy}{2} )[/tex]

In order to convert each of the group in step 4 is a perfect square, and then we have to rewritten as [tex](\frac{x}{\sqrt{2} } + \frac{y}{\sqrt{2} }+ \frac{z}{\sqrt{2} } )^2[/tex]

Then we get the canonical equation as

[tex]= > \frac{ (x + y + z)^2}{2}[/tex]

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The term "sine" is derived from the Latin word sīnus, which means "bay". Sine is a mathematical function used to define a ratio between the length of a side of a right triangle and its opposite side.

It is also used to describe waveforms in trigonometry, electricity, and other sciences. The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle. The sine of a given angle in a right triangle is equal to the ratio of the length of the opposite side to the length of the hypotenuse.

This ratio can be expressed as a number between -1 and 1, with 0 representing a right angle. Sine is also used to describe waveforms in trigonometry, electricity, and other sciences. In addition, sine is used to solve problems involving triangles, circles, and various quadratic equations.

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The expression that represents the total number of pages is as follows:

number of printed pages = 10p + 12r

A teacher prints off review packets for her classes. Each 6th-grade packet is 10 pages long and each 7th-grade packet is 12 pages long.

Therefore, the expression that represents the total number of pages printed if there are p 6th-grade packets printed and r 7th-grade packets printed is as follows:

Hence,

number of printed pages = 10p + 12r

where

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The corresponding angles are equal angles. Then the correct option is D.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Let's check all the options:

The sum of corresponding angles is 180°. The statement is false.

The angles in a vertical pair are acute. The statement is false.

Corresponding angles are supplementary. The statement is false.

Corresponding angles are congruent. The statement is True.

The corresponding angles are equal angles. Then the correct option is D.

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Each exponential expression is matched with its expanded form as;

-2⁴. Option E

2³. Option C

(-2)⁴. Option A

2². 2³. Option B

A index form can be described as a mathematical method or way of writing numbers or values that re too small or too large in simpler  and comprehensible forms.

Other forms for index forms are standard forms or scientific forms.

From the information given, we have that;

-2⁴

This is represented as;

-2 × 2 × 2 × 2

2³

The index form is written as;

2 × 2 × 2

(-2)⁴, written as

-2 ×-2 × -2 ×-2

Also, 2². 2³ is written in the form;

(2 × 2)× ( 2× 2 × 2)

Hence, index forms simplifies expressions

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The equation that gives d as a function of h is d = 7200/h

The apparent height of the tower would be 3.6 inches

From the question, we have the following parameters that can be used in our computation:

Apparent height (h) = 800 feet

Distance (d) = 9 inches

Variation = inverse variation

The inverse variation implies that

k = dh

Where k is the constant of variation

Substitute the known values in the above equation, so, we have the following representation

k = 800 * 9

k = 7200

So, we have

7200 = dh

Make d the subject

d = 7200/h

Here, we have

She was standing 2000 feet away from the tower

This means that

d = 2000

So, we have

2000 = 7200/h

Make h the subject

h = 7200/2000

Evaluate

h = 3.6

This means that the height is 3.6 inches

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Answer:

  See attached

Step-by-step explanation:

You want to know which of the graphed relations shows a function.

The graph of a function will not intersect any vertical line in more than one place. A graph that has multiple values for any given x-value is not a graph of a function.

The attachment shows the one graph here that represents a function.

<95141404393>

The Area of equilateral triangle that have the side length as 6cm is  [tex]9\sqrt{3} \; cm^{2}[/tex] .

An Equilateral Triangle is defined as a type of triangle in which all the side lengths are equal and measure of all the angles is also equal .

The Ares of Equilateral is calculated by formula  : [tex]\frac{\sqrt{3} }{4} \times a^{2}[/tex] ;

where "a" = side length ;

the side length of triangle is given as : 6 cm .

substituting the value of "a" as 6  in the formula ,

we get ;

Area = [tex]\frac{\sqrt{3} }{4} \times 6^{2}[/tex]

= [tex]\frac{\sqrt{3} }{4} \times 36[/tex]      ....because [tex]6^{2} =36[/tex] ;

Simplifying further ,

we get ;

= [tex]9\times \sqrt{3}[/tex] .

Therefore , the area of given equilateral triangle is [tex]9\sqrt{3} \; cm^{2}[/tex] .

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Answer:

Step-by-step explanation:

104 x 4 = 416

The solutions of the given trigonometric equation are 60°, 180°, and 300°.

What is a trigonometric equation?

A trigonometric equation is an equation that contains one or multiple trigonometric ratios of unknown angles.

The given trigonometric equation is:

cos ([tex]\frac{x}{2}[/tex]) - sin (x) = 0

⇒ cos ([tex]\frac{x}{2}[/tex]) - 2sin ([tex]\frac{x}{2}[/tex]) cos ([tex]\frac{x}{2}[/tex]) = 0

⇒ cos ([tex]\frac{x}{2}[/tex]) [1 - 2sin ([tex]\frac{x}{2}[/tex])] = 0

Therefore,  cos ([tex]\frac{x}{2}[/tex]) = 0 = cos (90°)  ([tex]\frac{x}{2}[/tex] can't be 270°)

⇒ x = 180°

Again,  [1 - 2sin ([tex]\frac{x}{2}[/tex])] = 0

⇒ 2sin ([tex]\frac{x}{2}[/tex]) = 1

⇒ sin ([tex]\frac{x}{2}[/tex]) = 1/2

⇒ ([tex]\frac{x}{2}[/tex]) = 30°, 150°

⇒ x = 60°, 300°

So, The solutions of the given trigonometric equation are 60°, 180°, and 300°.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3860\\ r=rate\to 3.08\%\to \frac{3.08}{100}\dotfill &0.0308\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-monthly, thus 24} \end{array}\dotfill &24\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3860\left(1+\frac{0.0308}{24}\right)^{24\cdot 2} \implies A = 4105.09[/tex]

The 9th term of the geometric sequence is equal to 8.0090 rounded up to the nearest thousandth.

A geometric sequence or progression is a sequence where every term bears a constant ratio to its preceding term. The nth term of a geometric sequence is calculated as ar^(n - 1) where a is the first term and r is the common ratio.

the first term a = 80

we get the common ratio by dividing the preceding term by the previous term;

r = 60/80 = 3/4

the 9th term is evaluated as follows:

80 × (3/4)^(9-1)

80 × (3/4)^8

80 × 6561/65536

524880/65536

8.0090

Therefore, the 9th term of the geometric sequence is 8.0090 approximately to the nearest thousandth.

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A dot plot is a graph of each data value plotted as a point.

A dot plot, which also known as a strip plot or dot chart, is a simple form of data visualization which consists of data points plotted as dots on a graph with an x- and y-axis. A dot plot is used to encode data in a small circle or a dot. The dot plot is presented on a number line which displays the distribution of numerical variables where a value is described by each dot.

Dot plots are used for continuous, quantitative, univariate data. Data points may be marked if there are few of them. Dot plots are one of the simplest statistical plots, and are fit for small to moderate sized data sets. Dot plots are useful for highlighting the clusters and gaps, as well as the outliers.

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According to the Inequalities  the prices for a single chair and a single table:

B. Chair: $22, Table: $60

The correct option is B.

Inequalities specify the relationship between two different values. Not equal is the definition of inequality. In most cases, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are employed to compare the values, whether is less than or more than.

8c + 3t> $350

2c + 5t < $350

Putting the value in the equation:

8c + 3t> $350

8×22 + 3×60> $350

176 + 180 > 350

356 > 350

2c + 5t < $350 equation 2

2 × 22 + 5 × 60 < $350

44 + 300 < 350

344 < 350

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Answer:

Step-by-step explanation:

a =  number of apples

"four times as many apples" written as an algebraic expression:

4a

The required value of a function of function (g°f)(-6) is given as 52.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
f(x) = -x - 2

g(x) = x²

g(f(x)) = [-x - 2]²
g(f(x)) = [x + 2]²   [since [-a]² = a²]
g(f(x)) = x² + 2x + 4

Now, put x = 6,
g(f(6)) = 6² + 2[6] + 4

g(f(6)) = 36 + 12 + 4
g(f(6)) = 52

Thus, the required value of a function of function (g°f)(-6) is given as 52.

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Answer:

Step-by-step explanation:

The values rewritten into an equivalent form as fractions include the following:

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

For instance, 5 by 8 should be read as "five eighths" and it simply means that five (5) parts out of eight (8) equal parts in which the whole part is divided.

Similarly, -3 by 2 should be read as "negative three halves" and it simply means that two (2) parts out of negative three (3) equal parts in which the whole part is divided. Additionally, the number 3 represents the numerator while the number 2 represents the denominator.

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Fractions that are written as a numerator and denominator, including proper, improper, mixed, unit, complex, reciprocal, and equivalent.

Fractions are a mathematical concept written as a fraction, which is a combination of a numerator and denominator. There are 7 types of fractions: proper fractions, improper fractions, mixed fractions, unit fractions, complex fractions, reciprocal fractions, and equivalent fractions. Proper fractions have a numerator that is less than the denominator. Improper fractions have a numerator that is greater than the denominator. Mixed fractions are a combination of a whole number and a proper fraction. Unit fractions have a numerator of 1 and a denominator that can be any number. Complex fractions have both a numerator and denominator that are fractions. Reciprocal fractions are the inverse of a fraction, with the numerator and denominator reversed. Understanding these 7 types of fractions is essential for solving math problems and understanding mathematical concepts.

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Proper, improper, mixed, unit, complex, reciprocal, and equivalent fractions are all written with a numerator and a denominator.

Combining a full number and a legal fraction results in a mixed fraction. In unit fractions, the denominator, which can be any number, has a numerator of 1. Numerator and denominator of complex fractions are also fractions. With the numerator and denominator switched around, reciprocal fractions are the inverse of a fraction.

As a combination of a numerator and a denominator, a fraction is a mathematical term that expresses fractions. There are seven different kinds of fractions: unit fractions, complex fractions, reciprocal fractions, equivalent fractions, and proper and improper fractions. Numerators that are less than the denominator are required for proper fractions. Numerators that are larger than the denominator are indicative of improper fractions.

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On solving the provided question, we can say that - the slope we have from the graph is [tex]m = \frac{y2 - y1}{x2 - x1}[/tex] +. m= 2

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

By the graph;

[tex](x1,x2) = (0,0)\\(y1,y2)=(2,1)[/tex]

[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

m= 2

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The star is 20 parsecs away which is approximately equal to 63.66 light-years away.

What is parallax angle ?

The parallax angle, also known as the parallax shift or the annual parallax, is the angle between the observer's line of sight to a celestial object at two different points in the Earth's orbit. It is a method used to measure the distance to stars and other celestial objects.

The parallax angle is defined as the angle between the observer's line of sight to the star at two different points in Earth's orbit. The distance to a star can be calculated using the formula ,

Distance = 1 / parallax angle (in arcseconds)

In this case, the parallax angle is 1/20 arcseconds, so the distance to the star is,

Distance = 1 / (1/20) = 20 parsecs

Note that one parsec is equivalent to 3.26 light-years.

So the star is 20 parsecs away which is approximately equal to 63.66 light-years away.

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The team that had the best overall record for the season is C. Eagles; they have a larger mean value of about 22 points Falcons; they have a larger mean value of about 20.9 points

The best measure of center to compare the overall records of the two teams is the mean (average) value of the points earned in each game. This is because the mean is a commonly used measure of center in statistics and provides a good overall summary of the data set.

In this case, the Eagles have a larger mean value of about 22 points (calculated by summing the points and dividing by the number of games) compared to the Falcons' mean value of about 20.9 points. So, the correct answer would be Eagles; they have a larger mean value of about 22 points

It's worth noting that using the median value in this case is not the most accurate, because this will give you a more robust representation of the center of the dataset in cases where data have outliers.

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The height of the tree is 1.9 meters

From the question, we have the following parameters that can be used in our computation:

The height of the tree can then be calculated using the following ratio expression

Tree's height : Caden's height = Caden's distance from the tree : Caden's distance from Nova

Substitute the known values in the above equation, so, we have the following representation

Tree's height : 1.2 = 6.5 : 4.2

Express as fraction

Tree's height/1.2 = 6.5/4.2

So, we have

Tree's height = 1.2 * 6.5/4.2

Evaluate

Tree's height = 1.9

Hence, the tree's height is 1.9 meters

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Answer:

7. y-8 = [tex]\frac{3}{4}[/tex](x-4)

8. y+3 = 4(x-1)

9. y+5 = [tex]\frac{-1}{7}[/tex](x-7)

10. y-3 = [tex]\frac{5}{3}[/tex](x-3)

11. y+4 = -2(x+1)

The multiplied form of the expression 5abc⁵⋅3a²b³ is 15 a³b⁴c⁵.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given expression is,

5abc⁵⋅3a²b³.

To multiply the given expression,

Use multiplication mathematical operation,

15abc⁵.a²b³

15 a³b⁴c⁵

The required expression is 15 a³b⁴c⁵.

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The corresponding angles and sides of the two triangles need to be given in order to prove congruence by side-angle-side.

In order to prove congruence by side-angle-side, the corresponding angles and sides of the two triangles must be given. The sides must be proportional, which means that two sides of one triangle must be equal to two sides of the other triangle, and the angles between these two sides must also be equal. In other words, if two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal, then the two triangles are congruent. This can be expressed as “If two sides and the included angle of one triangle are equal to the corresponding sides and angle of a second triangle, then the two triangles are congruent.” In order to prove congruence by side-angle-side, all of the corresponding sides and angles must be given in order to show that they are equal.

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The additional information that is needed to prove the triangles are congruent by Side-Angle -Side us that the corresponding angles and sides of the two triangles need to be given .

What is Side-Angle-Side Congruence ?

The Two Triangles can be called as  Congruent by Side-Angle-Side rule  if any 2 sides and angle included between sides of one triangle is equivalent to corresponding 2 sides and angle between sides of second triangle .

In order to prove the Congruence by Side-Angle-Side, the corresponding angles and the sides of the 2 triangles must be given.

The sides must also be in proportional, that means that the two sides of one triangle must be equal to two sides of other triangle, and

the angles between these two sides of the triangle must  be equal.

So , In order to prove a triangle congruent by Side-Angle-Side, all of the corresponding sides and angles must be given in order to prove  that they are equal.

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Answer: C. 3,500 grams

Step-by-step explanation:

Rodney got D as the answer by because he thought there are three zeros and adding 3 and 5 to the 1,000  35,000.

Because we know the unit rate: 1(kilogram) = 1,000(grams)

Rodney chose the incorrect answer.

Therefore, 3.5 x 1000 = 3,500 is correct

Answer:

The correct answer is C. 3500g

Step-by-step explanation:

3.5kg×1000=3500g

Rodney got answe D. by moving the decimal place of 3.5kg over by 4 places instead of 3.

His equation could have been 3.5kg×10000= 35000

Rodney did NOT choose the correct answer

d. positive or negative square root of 2 comma ±

The zeros of the function f(x) = x4 − 4x2 − 5 are the values of x that make the equation equal to 0. To find these, we must solve the equation f(x) = 0. We can do this by factoring the equation to give (x2 + 5)(x2 − 2) = 0. This gives us the solutions x2 = −5 and x2 = 2. From this, we can find the zeros of the function, which are ±√2 and ±i. Therefore, the zeros of the function f(x) = x4 − 4x2 − 5 are positive or negative square root of 2 comma ±i.

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Answer:

22

From the numbers already shown it looks like each time they are adding 5 to the number before it.

The total amount of money that Johnny will have to pay is f(10) = 30.

What are expressions?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Given is that it costs Johnny $15 a month plus $1.50 per song to download music. This situation is represented by the expression →

1.5(x) + 15.

The expression is given by -

f(x) = 1.5(x) + 15

where [x] is the number of songs downloaded.

For [x] = 10 songs, the total amount of money that Johnny will have to

pay is -

f(10) = 1.5 x 10 + 15

f(10) = 15 + 15

f(10) = 30

Therefore, the total amount of money that Johnny will have to pay is f(10) = 30.

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The cost that Johnny has to pay to download 10 songs is 30$

as per given in the question,

johnny's  regular cost is 15$ a month

$1.50 is to be added for every song download

The cost to be find for 10 songs download

the equation which can be formed is

let x be the number of songs

1.5 times the number of songs + the cost of every month

therefore

1.5(x) + 15

the total number of songs to be downloaded is  10

so,

1.5(10) + 15

=> 15 +15

=> 30 $

Now the cost that has to pay by johnny after the downloading of 10 songs is 30 $

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