Determine the range of the following graph:

If one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each, then the equation to be solved to obtain the value of "x" is [(115 + 2x) = 180] and the value of "x" will be 32.5°.

As per the question statement, one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each.

We are required to determine a Linear equation of singular value that can describe our concerned situation, and solving which, we will be able to obtain our desired value of "x".

To solve this question, we need to know about one basic yet very important property of a triangle, that is, the sum of all the three interior angles of a triangle is equal to 180 degrees.

Here, the three angles measure 115°, x° and x°.

Therefore, our required equation will [(115 + x + x)° = 180°]

                                                         or, [(115 + 2x)° = 180°]

Now solving the above mentioned equation to obtain the value of "x", we get, [(115 + 2x)° = 180°]

Or, [2x = (180 - 115)°]

Or, (2x = 65°)

Or, x = (65/2)°

or, x = 32.5°

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The value of x are 4 and 2.4 after simplifying and applying the quadratic formula.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The equation is:

4/(x - 2) + 3/(x - 3) = 5

4(x - 3) + 3(x - 2) = 5(x -2)(x - 3)

4x - 12 + 3x - 6 = 5x² - 25x + 30

5x² - 32x + 48 = 0

After solving the above quadratic equation by the formula:

[tex]\rm x = \dfrac{-(-32) \pm\sqrt{(-32)^2-4(5)(48)}}{2(5)}[/tex]

x = 4

x = 2.4

Thus, the value of x are 4 and 2.4 after simplifying and applying the quadratic formula.

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The total number of nuts is 15210 and the missing number is 5

Number of cans of mixed nuts = 45 cans

Number of nuts in each can = 338 nuts

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.

Finding the total number of nuts we get:

Total number of nuts = Number of cans*Number of nuts in each can

[tex]338\\*45\\= 1690\\+ 13520\\= 15210[/tex]

So, the missing number is 5

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Answer: -19/8

What is an improper fraction?

  An improper fraction is where the numerator is greater than the denominator. To turn -2 3/8 into an improper fraction, we will "combine" -2 and 3/8.

First, we will find what -2 becomes. -2 is the same as two wholes:

     -2 * 8 = -16

Next, we will subtract this into the numerator of the fraction:

     -16 - 3 = -19

Lastly, we will put this new numerator over the denominator:

     -2 3/8 = -19/8

Reason:

GCF = greatest common factor

LCM = lowest common multiple

GCF of 6 and 8 = 2

LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24

We can list out the multiples of each to confirm this

If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.

The smallest height that their towers could be 24 cm.

The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). The least Common Multiple and Least Common Divisor are other names for it (LCD). For instance, 12 is the least frequent multiple of 4 and 6.

GCF = greatest common factor

LCM = lowest common multiple

GCF of 6 and 8 = 2

LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24

We can list out the multiples of each to confirm this

multiples of 6 are 6, 12, 18, 24, 30, ...

multiples of 8 are: 8, 16, 24, 32, ...

If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.

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Answer:

2x=108

Step-by-step explanation: This is the equation because when it says twice a number, you are multiplying a number two times. In this case, the number is not given, so x is the variable being multiplied two times. If the number was 8, it would look like this: 2(8)=108. Of course this isn't true, but to find the actual answer you would divide two on both sides of the equation. This is so that both of the two's cancel out on the left side of the equation. and the variable is left on that side. Our goal is to isolate the variable. In these types of equations, our goal is to isolate the variable and find what the variable is worth. If we do 108 divided by 2 that gives us 54. Since there was x left on the left side of the equation and there is 108 left on the right side we have our equation. x=54

Number explanation below

2x=108

2x/2=108/2

x=54

Answer: 0.01 (One cent per year)

Step-by-step explanation:

We need to find the price the stamp increased per year.

The difference in years is 12.

2004 - 1992 = 12

The difference in price is 0.12.

0.37 - 0.25 = 0.12

So to find price increase per year we do the following:

$0.12/12 = 0.01

$0.01 is one cent per year.

Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.

We need to define the angle.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

Parts of an Angle

There are two main parts related to an angle - the arms and the vertex.

Arms of the Angle

The two rays which join at a common point to form the angle are called the arms of the angle.

Vertex of the angle

Vertex is a common endpoint that is shared by the two rays.

Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.

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Answer:

the answer is A

Step-by-step explanation:

To check your answer, move 4 units to the right and 3 units up

The x- and y-intercepts of the graph of x + y = 18 both have the values of 18

The x-intercept of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0

The equation of the graph is given as

x + y = 18

To calculate the x-intercept, we set the value of y to 0

This is represented as

y = 0

So, we have the following equation

x + 0 = 18

Evaluate the like terms

x = 18

To calculate the y-intercept, we set the value of x to 0

This is represented as

x = 0

So, we have the following equation

0 + y = 18

Evaluate the like terms

y = 18

This means that the x-intercept has a value of 18 and the y-intercept has a value of 18

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The option that describes the sample you would ask is A. twenty students from one elementary class in your town.

It should be noted that a simple random sampling simply means a form of sampling whereby everybody has an equal chance of being selected.

In this case, it should be noted that the person wanted to take a simple random sample for a study on screen time in elementary school students in the town. Therefore, twenty students can be chosen to illustrate this.

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The overall rating is 31 and the average rating is 3.8.

A large number of data points are reduced into a single value using averages. It is a visual depiction of all the data set's available numbers. The average is derived by adding up all the data values and dividing them by the total number of data points.

The word "average" is used in many different contexts in daily life. The average is computed and a single value is used to represent the values for quantities with fluctuating values.

Overall rating = 4+5+5+3+5+4+2+3

Overall rating = 31

Average rating = Overall rating/ Total number of ratings

= 31/8

= 3.8

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From the question, we have:

P(n) = P(n - 1) + n²

P1 = Po + 1² = 0 + 1 = 1

P2 = P1 + 2² = 1 + 4 = 5 (This is option C)

P3 = P2 + 3² = 5 + 9 = 14 (This is option B)

P4 = P3 + 4² = 14 + 16 = 30 (This is option D)

Therefore the number of snowballs cannot be 25.

So, the correct option is A, which is 25.

x° = 49°

Alternate interior angles are formed when two parallel lines are cut by a transversal and the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal. These angles are equal.

Pairs of alternate angles around the transversal are equal to each other. Angles can either be alternate interior or exterior angles. Sum of the angles formed on the same side of the transversal of the two parallel lines is equal to 180°.

Given , ∠t = 49°,

Therefore angles x° will also 49° because alternate angles are equal when two parallel lines are cut by a transversal.

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Answer:

y=3x-5

Step-by-step explanation:

parallel lines have the same slope

Total cost of phone in a day $650

What is Algebra ?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.

Total cost of rent in a day =  $500

Total cost of per phone     = $150

The equation which represents values in term of c:

             150p + 500 = C

The total cost he had in a day :

                              = 150 + 500

                              = $650

Hence, the total cost throughout  the day is $650

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By solving a quadratic equation, we will see that the necklace hits the ground 2 seconds after it is dropped.

We know that the function:

f(t) = 16*t^2

Represents the distance that an object falls down in t seconds.

If the necklace is dropped from a height of 64 feet, the necklace will hit the ground when the distance that an object falls down in t seconds is equal to 64 feet, so we just need to solve the quadratic equation:

f(t) = 64

16*t^2 = 64

t^2 = 64/16 = 4

t = √4 = 2

The necklace will hit the ground after 2 seconds.

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Answer:

Step-by-step explanation:

The image of the function f(x) = x , after the translation is g(x) = x -2 .

In the question

it is given that

the function f(x) = x ,

and f(x) has to be translated 2 units to the right means subtract 2 from the function .

which means g(x) = f(x) - 2

substituting f(x) = x , we get

g(x) = x - 2

the answer in the form of mx+b is g(x) = x - 2

(can refer to the graph given below)

Therefore , The image of the function f(x) = x , after the translation is g(x) = x - 2 .

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The equation of the line parallel to 3x-6y=3 and passes through (-2, 3) is y = 1 / 2 x + 4

The equation of the line passes through (-2, 3) and it is parallel to the equation 3x - 6y = 3.

Therefore, the equation of a line can be represented as follows:

y = mx + b

where

Parallel lines have the same slope.

Hence,

3x - 6y = 3

3x - 3 = 6y

y = 1 / 2 x - 1 / 2

Therefore, the slope of the equation is 1 / 2.

Let's find the y-intercept using (-2, 3).

3 = 1 / 2 (-2) + b

3 + 1 = b

b = 4

Therefore, the equation is y = 1 / 2 x + 4

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Answer: -11

Step-by-step explanation:

The measure of x, m∠DEG, m∠GEF  and m∠DEF will be 5,112°,68°and 180° respectively.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that,

m∠DEG = (23x-3)°

m∠GEF = (12x+8)°

As m∠DEF is a straight angle its angle measurement is 180

As a result,

m∠DEF=m∠DEG+m∠GEF

180°=m∠DEG+m∠GEF

Put the given values

180°=(23x-3)°+(12x+8)°

180=35x+5

35x=180-5

35x=175

x=5

Substitute the value of x to obtain all the angles as

m∠DEG=(23x-3)°

m∠DEG=(23(5)-3)°

m∠DEG=112°

For m∠GEF,

m∠GEF=(12x+8)°

substitute the value of x

m∠GEF=(12(5)+8)°

m∠GEF=68°

Thus, the measure of x, m∠DEG, m∠GEF  and m∠DEF will be 5,112°,68°and 180° respectively.

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From the table given:

1. The type of function that best models each situation is:

2. The functions are given as follows:

For this problem, we have that each month, the amount increases, but the increase is approximately a factor of the previous amount, meaning that an exponential equation best models the data.

The points are given as follows:

(1, 5), (2, 12), (3, 23), (4, 50), (5, 62), (6, 80).

Using an exponential regression calculator, the equation is:

[tex]D(t) = 3.738 \times (1.749)^t[/tex]

For this problem, we have that each month, the amount increases, but the increase is approximately a constant from previous amount, meaning that an linear equation best models the data.

The points are given as follows:

(1, 11), (2, 19), (3, 29), (4, 38), (5, 50), (6, 73).

Using a linear regression calculator, the equation is:

H(t) = 11.771t - 4.533.

The amount initially increases, then it decreases, meaning that a quadratic model best represents the data.

The points are given as follows:

(1, 142), (2, 150), (3, 165), (4, 141), (5, 120), (6, 91).

Using a quadratic regression calculator, the equation is:

L(t) = -5.875t² + 30.582t + 116.9.

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The equation for the given sentence is 5x = 6/x

Given,

The product of five and a number is the quotient of six and the same number.

We have to translate this sentence into an equation:

Equation:

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So here,

The product of five and a number is the quotient of six and the same number

We can take the number as x.

Then,

5 × x = 6 ÷ x

5x = 6/x

Multiply x on both sides

5x × x = 6/x × x

We get,

5x² = 6

Divide both sides with 5

5x²/5 = 6/5

We get,

x² = 6/5

x = √6/5

That is, the equation for the given sentence is 5x = 6/x

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The value of d to the power of 6 and d to the power of 0 equal together is d^6.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

The information given regarding the power is illustrated thus:

d^6 + d^0

In this case, the addition of the power will be 6 + 0 = 6. Therefore, the value is d^6.

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The domain of the relation as given in the task content; (x,y): y = x(x-3) / (x+4)(x-7) is the set of all real number values except; -4 and 7 and hence is represented as; { x : x R, x ≠ -4, x ≠ 7}.

It follows from the task content that the domain of the relation given in the task content be determined.

On this note, since the domain of a relation or function simply refers to the set of all possible input values of such function.

Since the relation in this scenario is a rational function, it follows that the domain is the set of all real number values except that which renders the relation undefined.

Therefore, since the values which render the relation undefined, render the denominator equal to 0; we have;

(x+4)(x-7) = 0.

x = -4 OR x = 7.

Ultimately, the domain of the relation is the set of all real numbers except; x = -4 and x = 7.

Therefore, when represented by set builder notation; we have; { x : x R, x ≠ -4, x ≠ 7}.

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After using substitution method - The new height of the painting will be 247cm.

What is the substitution method?

To solve many simultaneous linear equations, use the substitution method in algebra. As implied by the name, this strategy involves replacing a variable's value from one equation with another.

we are given the original width of the painting to be 6cm and the original height to be 19cm.

after enlarging the size of the painting the new and enlarged width becomes 78cm

and we assume the new and enlarged height of the painting to be xcm.

we now the ratios

original height : original width = enlarged height : enlarged width ,

will remain equal,

Hence substituting the numerical values in the ratios we get

19/6 = x/78

19 * 78 = 6x

1482/6 = x

247cm =x

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Explanation.

The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)

To do this, we can use the formula:

In our case, we have

We will simply put all the values above into the formula to get the equation of the line

Simplifying further

Cross multiplying

Therefore, the equation of the line is