What is the additive inverse of _3 7?.

if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

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If the interior angle of a regular polygon is 108°.The polygon has five (5) sides.

Method 1: Each exterior angle of a regular polygon is equal to 180-108°, or 72°, if each internal angle is 108°.Regardless of the number of sides, any figure's outer angles add up to 360 degrees.

The figure has 360/72 or 5 sides since each outer angle is 72 degrees. Therefore, the polygon is a standard pentagon. Answer.

Method 2: Using n isosceles triangles, a regular polygon with n sides is created. 54° is the basis angle, or 108/2. Each vertical angle is equal to 2*36°, or 72°, which is the semi-vertical angle of 90-54°. 360/72 equals 5, the number of isosceles triangles. Therefore, the polygon is a standard pentagon.

Method 3: [n-2]*180 or 108n, which is the sum of the internal angles of a regular polygon.

[n-2]*5=3n, or

5n-10 = 3n, or

5n-3n = 2n = 10, or

n = 5.

The polygon is a regular pentagon as a result.

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Using trigonometric identities to decode, the secret message is

2 20-14-25-12 4-19-17 20-14-11-14-25 23-2-21-14-5 23-26-5-7-2-21-14-5! A Nerd who never makes mistakes!

Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation.

The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities. Only for right-angle triangles do the trigonometric identities hold true.

All trigonometric identities are built upon the foundation of the six trigonometric ratios. It consists of sine, cosine, tangent, cosecant, secant, and cotangent. These right triangle sides—including the adjacent side, opposite side, and hypotenuse side—are used to define all of these trigonometric ratios. The six trigonometric ratios are the starting point from which all fundamental trigonometric identities are derived.

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An algebraic expression (or) a variable expression is a combination of terms by operations such as addition, subtraction, multiplication, and division. For example, let's look at the expression 5x + 7.

Algebraic Expression:

Algebraic expressions are mathematical expressions that result when you perform operations such as addition, subtraction, multiplication, and division on variables and constants. For example, let's say James and Natalie were playing with matches and wanted to create a pattern of numbers in matches. James played four games and formed No. 4. Natalie added three more games and two he formed a pattern of four. They realized they could add 3 matches to each round to get an extra '4'. From this, they concluded that, in general, 4 + 3 (n-1) double crochet stitches are required to create n 4 patterns. Here 4+ 3(n-1) is called an algebraic expression. To solve a linear equation with one variable, use the transpose method. Follow this procedure to perform the same operations on both sides of the equal sign. That is, perform operations to isolate variables.

Example:

5x + 7 = 32

Subtract 7 from both sides

⇒ 5x = 25

Divide both sides by 5

⇒ x = 5

⇒ 5x = 25

Divide both sides by 3

⇒ 2y – 12 = 24

Add 12 to both sides

⇒ 2y = 36

Divide both sides by 2

⇒ y = 18.

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The value of third angle is 30 and we can find using angle sum property.

The triangle's angles can be added up to equal 180 degrees, according to the angle sum property of triangles. A triangle has three sides, one at each vertex, and three angles. The total of the interior angles in any triangle, whether acute, obtuse, or right, is 180 degrees.

One of the most commonly employed properties in geometry is the angle sum property of a triangle. Calculating the unknown angles is primarily done using this characteristic. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.

Given

The two angles are given as 102 and 48

we need to find the third angle

Let the third angle be a then

using the angle sum property we get

102 + 48 + a = 180

a = 30

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Substitute y = 0 and solve for x to find the x-intercept, and do the same for the y-intercept.

Examples on the Y Intercept Using the y-intercept formula, we can find the y-intercept of a function by substituting x = 0 and solving for y; consequently, the given function lacks a y-intercept. 2nd Example: Find the value of "a" if the y-intercept of a function y = a (x - 1) (x - 2) (x - 3) is (0, 12).

We can solve for the y-intercept in the slope-intercept equation y=mx+b by first determining the slope between two points on a line and then writing an equation for that line.

The slope-intercept form is used to write the line's equation, which looks like this: y is equal to mx + b, where m is the slope and b is the y-intercept. We can see that the line has a slope of 6 in our equation, which is y = 6x + 2.

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Como la cuerda está formando un ángulo de 30 grados con la horizontal, la componente de la fuerza en la dirección de la cuerda se calcula utilizando el coseno del ángulo: 86.6 N.

Para calcular el valor de la normal y la fuerza de rozamiento, primero debemos calcular la componente de la fuerza de gravedad que actúa en dirección perpendicular a la superficie de apoyo. La componente de la gravedad en dirección perpendicular se calcula utilizando el seno del ángulo formado por la cuerda con la horizontal (30º):

F_normal = F_grav * sen(30º)

Donde F_grav es la fuerza de gravedad del cuerpo, que se calcula como:

F_grav = m * g

Donde m es la masa del cuerpo (40 kg) y g es la aceleración debida a la gravedad (9.8 m/s²)

Por lo tanto,

F_normal = (40 kg) * (9.8 m/s²) * sen(30º) = 392 N

La fuerza de rozamiento se calcula utilizando la fórmula:

F_fric = μ * F_normal

Donde μ es la coeficiente de rozamiento estático entre el cuerpo y la superficie de apoyo. Como no se especifica el valor del coeficiente de rozamiento, no se puede calcular la fuerza de rozamiento.

La tensión en la cuerda es igual a la fuerza neta en la dirección de la cuerda. Como la cuerda está formando un ángulo de 30 grados con la horizontal, la componente de la fuerza en la dirección de la cuerda se calcula utilizando el coseno del ángulo:

T = F * cos(30º) = 100 N * cos(30º) = 86.6 N

(Los valores de las respuestas están en notación científica)

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For the number 10, the prefix used is 10. The correct option is A.

Prefixes derived from numerals or other numbers are known as numeral or number prefixes. They are used to coin numerous series of words in English and many other languages.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given number is 10. The prefix used for the number 10 is deci.

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The percent of decrease from 95 to 19 is 80%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.

Given that, what is the percent of decrease from 95 to 19,

Percent of decrease = final value - initial value / initial value x 100

Here, final value = 95

initial value = 19

Therefore,

Percent of decrease = 19-95 / 95 x 100

= -76 / 95 x 100

= -0.8 x 100

= -80%

Here, - sign is representing the decrease,

Hence, the percent of decrease from 95 to 19 is 80%

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Answer: A. The y-intercept of a graph is the point at which the graph crosses the y-axis. In the graph provided, the y-intercept appears to be at (0, -500). This means that Tasha's account balance starts at -500 dollars.

B. The y-intercept does not make sense in this situation, as a savings account balance cannot be negative. It is not possible to have negative dollars in a savings account.

C. Tasha's possible error is that she may have misinterpreted the y-axis to represent a negative balance, when in reality it represents zero balance. The y-intercept represents the initial balance of the account, which should be zero or a positive number. This error can be corrected by starting the y-axis from zero and making sure the y-intercept is positioned at a positive value.

Step-by-step explanation:

Answer:

8/10 = 4/5

6/12 = 1/2

10/20 = 1/2

4/5= 4/5

3/12= 1/4

13/21= 2/3

9/24 = 3/8

7/14 = 1/2

15/30 = 1/2

12/16 = 3/4

Step-by-step explanation

Hope this helps

First, find out how much each text will cost, which is always $ 0.25. When there are no text messagers, collukate the fee to $2 per hour .

When 50 texts are added, the price goes up for each text when there are two of them (57,5-50=7.5).  [tex](7.5 \div 30=0.25)[/tex] Zach would incur costs if there were no texts. [tex](50-20 \times 0.25=45)$[/tex] , And Laura's price without a text is $65 Thus, (65-45=20) would apply. [First, find out how much each text will cost, which is always $ 0.25. When there are no text messagers, collukate the fee to $2 per hour.]

Laura's monthly cell phone service fee is $65 plus $0.10 for each text message sent. Based on how many texts Zach sends, the following table displays the cost of his cell phone service. When no text messages are sent, Zach's cell phone service is $2 per hour less expensive than Laura's.

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Answer:sqrt 38

Step-by-step explanation:32+8-2 is 38

The equation-CuSO4.5H2O(s)→CuSO4.3H2O(s)+2H2O(g) for blue copper sulfate crytal I two-thirds the ma of the red fluorite crytal.

The following steps are used to make copper sulfate crystals:

Add a few drops of diluted sulfuric acid to a beaker of water.

Water heating. Add the powdered copper sulfate gradually as it begins to boil.

The ma of the blue copper sulfate crystal I two-thirds the ma of the red fluorite crystal

The equation-

CuSO4.5H2O(s)→CuSO4.3H2O(s)+2H2O(g)

the ma (in grams) of the blue copper sulfate crytal

It is 30 divided by 1/3 or 3.

The answer is 10

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Answer:

Length of Carla's living room is 20 feet

Step-by-step explanation:

The perimeter of a rectangle is 2(L + W)
In the case of both dining and living rooms, we are given the widths as dining room width = 18, living room width = 12 and asked to calculate living room length from the information given

Let x be the length of the dining room and y the length of the living room

Perimeter of dining room = 2(18 + x)

Perimeter of living room = 2(12 + y)

Since these are equal
2(18 + x) = 2(12 + y)

=> 18 + x = 12 + y

Subtract x from both sides:
18 = 12 + y - x

Subtract 12 from both sides:
18 - 12 = y - x

Simplifying and rearranging terms we get

- x + y = 6  [1]

We are also given that:
The length of her dining room is 1 foot less than 3/4 the length of her living room.

This mathematically translates to:
[tex]x = \dfrac{3}{4}y - 1[/tex]

which can be re-written as

[tex]x - \dfrac{3}{4} = -1 \; \cdots[2][/tex]

So the two equations are

[tex]- x + y = 6 \;\cdots [1][/tex]

[tex]x - \dfrac{3}{4}y = - 1 \; \cdots [2][/tex]

Notice that the coefficients of x are the same(1) but with opposite signs

Add [1] and [2]

[tex](-x + y) +(x - \dfrac{3}{4}y) = 6 - 1\\\\-x + x + y - \dfrac{3}{4}y = 5\\\\\dfrac{1}{4}y = 5\\\\y = 20\\\\[/tex]

So the length of the living room is 20 feet

(If you wanted to find the length of the dining room, substitute 20 into equation 1 to get -x + 20 = 6 which will give x = 14 and is the length of the dining room)

A circle has a total degree of 360 so 1/6 is a circle is a 60 degree angle turn.

An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle.

A total angle of circle is 360 degrees so if a turn is of a 60 degree so then 6 turns are possible to make a whole circle giving us 1/6 part as the total of which the only 60 degree turn is taken.

Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees.

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The notation "FG)(x" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F". The notation for this is usually represented as "F(G(x))", where "x" is the input for both functions.

The rule for this notation is that the innermost function is applied first. In this case, the function "G" is applied to the input "x" first, and then the output of that function is used as the input for the function "F". The composition of the functions F and G is denoted by the notation F(G(x)) and the result of this notation is a new function obtained by applying F to the result of G on x.

The function "F" is applied to the output of the function "G", meaning that the output of the function "G" is used as the input for the function "F".. For example, if the function "F" is applied to the input "x" first, followed by the function "G", the notation would be represented as "G(F(x))", and the resulting function would be different.

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The correct answer is B. The set of output values (y-values) of a function.

The range of a function is the set of all possible output values (y-values) of the function. It is the set of values that the dependent variable (y) can take on, given the domain (set of input values or x-values) of the function.

It can also be represented graphically by plotting the function on a coordinate plane and observing the set of y-values that the function takes on.

We have the following options:

A. The set of input values (x-values) of a function

B. The set of output values (y-values) of a function

C. The set of all possible x-y pairs of a function

D. The set of all possible x-values of a function

Therefore, The correct answer is B. The set of output values (y-values) of a function.

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The factors of the polynomial x^3-9x^2+27x-27 are (x -3), (x - 3) and (x - 3)

The polynomial you provided is x^3-9x^2+27x-27. If you know one of the factors of this polynomial, we can use that to find the remaining factors.

One factor of this polynomial is (x-3) as it gives remainder zero when divided by (x-3)

quotient is  x² - 6x + 9

remainder is zero

So the remaining factors are (x-3) and x² - 6x + 9

Alternatively, we can factor the remaining quadratic polynomial  x² - 6x + 9

by using Factor theorem or by using difference of squares

x² - 6x + 9 = (x - 3)²

So the remaining factors are (x-3) and (x - 3)

So the original polynomial can be factored as (x-3)(x-3)(x-3) = (x-3)³

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Answer:

14

Step-by-step explanation:

If d is 5

2(5) + 4(5) - 9 - 7

10 + 20 - 9 - 7

30 - 16

= 14

They combine their money to buy as much ice cream as they can afford. If . each pair of socks costs $4.50, what is the maximum number of pairs of socks .

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Three-fifths is equivalent to 6/10.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let the number of fifth be = x

So,

(1/5)x = 6/10

Now,

Solve for x.

(1/5)x = 6/10

x = (6 x 5) / 10

x = 30/10

x = 3

Thus,

There are three-fifths to make 6/10.

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Answer:

Step-by-step explanation:

14+(-8)14+(-8)

-122+14=-108+-8=116

The graph of an absolute value is always equal to or greater than zero and can never be negative.

We define the absolute value function f: R→R as:

f(x) = |x|

The absolute value function is also named the modulus function.

An alternative form to express the function is

|x| = -x if x ≤ 0 and x if x ≥ 0

The absolute value function is defined for all real numbers.

For x≥0, f(x) returns the same value, that is, x.

For x<0, f(x) returns the negative of the value of x.

So, we arrive at the conclusion that the domain and range of absolute value function are R and [0, ∞).

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A rectangle is a four-sided geometric shape with opposite sides that are parallel and equal in length. The opposite sides are called the length and width of the rectangle. Area = (30m - 0.5m) x (40m - 0.5m) = 29.5m x 39.5m = [tex]1162.75 m^2[/tex]

a. The maximum area of turf that Toby needs to buy can be found by using the measurements given by James, which are the length and width of the rectangle.

The area of a rectangle is found by multiplying its length and width, so the maximum area of turf needed would be:

Area = length x width = 30m x 40m = [tex]1200 m^2[/tex]

b. The minimum area of turf that Toby needs to buy can also be found by using the measurements given by James, but this time taking into account the margin of error due to the measurements being given to the nearest metre.

If the true length and width of the rectangle are slightly less than the measurements given by James, the mini  mum area of turf needed would be:

Area = (30m - 0.5m) x (40m - 0.5m) = 29.5m x 39.5m = [tex]1162.75 m^2[/tex]

So the minimum area of turf that Toby needs to buy would be [tex]1162.75 m^2[/tex]and the maximum area of turf that Toby needs to buy would be [tex]1200 m^2.[/tex]

In general, the measurements given by James could be off by half a meter in both directions, therefore the minimum area of turf that Toby needs to buy would be the area calculated by taking into account the margin of error, in this case, it's [tex]1162.75 m^2.[/tex]

The maximum area of turf that Toby needs to buy would be the area calculated using the measurements given by James, which is [tex]1200 m^2.[/tex]

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The SSA theorem tells us that if two angles and a non-included side of one triangle are congruent to two angles and also the corresponding non-included side of another triangle, then it is claimed that the two triangles supplied are congruent to one another.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are similar objects. To put it another way, if two triangles are similar, then their respective sides are proportionately equal and their corresponding angles are congruent.

The SSA congruence rule is not a reliable standard for determining if two triangles are congruent to one another.

Hence, there is no such SSA similarity from which you can make predictions that whether the two triangles are similar or not.

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The value of k for which the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 have infinitely many solutions is 4.

To solve this question, we need to find the value of k for which the two equations are equivalent. Equivalence means that the coefficients of x and y are the same and the constant terms are the same.

From the given equations, we can see that the coefficients of x and y are the same in both equations, which is 6x. The constant terms, however, are different. The first equation has a constant term of -8, while the second equation has a constant term of -16.

To make the equations equivalent, we need to make the constant terms the same. We can do this by dividing the second equation by 2. This gives us 6 ky - 8 = 0. We can see that the constant term is now the same as the first equation. Therefore, the value of k that makes the equations equivalent is k = 4.

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The complete question is:

For what value of k do the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 has infinitely many solutions?

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Answer:

x = 2

y = 5

Step-by-step explanation:

A system of equations is a set of two or more equations that contain multiple variables. To solve a system of equations, you can use different methods such as substitution, elimination or graphing.

The given system of equations is:

y = 2x + 1

y = x + 3

We are trying to find the x and y values that make both equations true at the same time.

One way to solve this system is to use the substitution method, by replacing one of the variables in one equation with the other equation.

Let's replace y from the second equation with the first equation:

x + 3 = 2x + 1

Subtract x from both sides:

3 = x + 1

Subtract 1 from both sides:

2 = x

Now that we have the value of x, we can substitute it back into either one of the original equations to find the value of y.

Let's substitute it back into the first equation:

y = 2(2) + 1

y = 5

So the solution to this system of equations is x = 2 and y = 5. It means that both equations are true when x = 2 and y = 5

You can also check your solution by substituting x and y back into the equations and see if both of them are true.

The probability that a pupil would excel in math's or English = 0.691

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages range from 0% to 100% can be used to describe probabilities.

120 students are enrolled in total. Let A represent the scenario in which a student receives a mathematics award, and B represent the scenario in which a student receives an English award. The odds of these events are as follows:

48 won awards for mathematics

78 won awards for English.

14 students  won awards for mathematics and English.

P(A) = 48/120

P(B) = 78/120

P(A ∩ B) = 14/120

Due to the fact that 14 students shared the honors from both events, the following equation should be written for overlapping sets:

P(A or B ) =   P(A) + P(B)  -  P(A ∩ B)

                 = 48/120 + 78/120 - 14/120

                  = 56/ 81

                  = 0.691

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