A teacher claims that the relationship between
number of hours studied for a test and test score can be
described by g(x) = 45 + 9x, where x represents the
number of hours studied. Graph this function

Answer:

16. G

17. C

Step-by-step explanation:

2836 numbers books produced will the costs from the two methods be the same.

From the given data

There are two production methods could be used so we can get two equations for cost (c) from two methods

Let x be the numbers of books produced.

Now, To calculate the total production cost.

Total production cost by selling  books = Fixed one time cost + Cost for production of  books.

From method 1  the equation we get

C = 24.75x + 13238    

and from method 2 the equation we get

C = 11.75x + 50107

Method 1 cost = Method 2 cost

24.75x + 13238 = 11.75x + 50107

24.75x - 11.75x  = 50107 - 13238

13x = 36869

 x  = 36869/13

 x  = 2836

x = 2836 numbers of books will have same cost.

By using variables, you may represent the unknowable amounts. As you follow the description, perform each mathematical conversion individually. For instance, if you are asked to increase an item by 4, you can do it by adding 4 to the item. There are various ways to translate descriptions into mathematical formulas, such as multiplying something by 2 if it is, for instance, doubled.

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The distance between A(7,-7) and B(13,0) is 9.2 units

The formula for calculating the distance between two point is expressed as;

D = √(x₋₂-x₁)²+(y₂-y₁)²

Given the coordinate points A(7,-7) and B(13,0).

Substitute

AB = √(13-7)²+(0-7)²

AB = = √(6)²+(-7)²

AB = √36+ 49

AB = √85

AB = 9.2 units

Hence the distance between A(7,-7) and B(13,0) is 9.2 units

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Answer:24

Step-by-step explanation:

71 + 25=96

96 divided by 4 equals 24

you have to add her profit and her expenses to see how much she needed to sell

Answer: 14

Step-by-step explanation:

First. take the prime factorization of all three numbers:

42: 21*2 ==> 3*7*2

70: 35*2 ==> 5*7*2

84: 42*2 ==> 21*2*2 ==> 3*7*2*2

Notice any common factors? That's the GCF.

GCF: 7*2=14

GCF: 14

Answer:

14

Step-by-step explanation:

The greatest number that divides 42, 70, and 84 exactly is their greatest common factor.

Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70

Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The GCF of 42, 70, and 84 is 14.

The greatest number that divides 42, 70, and 84 is 14.

What is GCF?

The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a set of whole numbers. For instance, the GCF is equal to 6 for the set of numbers 18, 30, and 42.

How do I get the GCF of something?

The greatest common factor among numbers can be discovered in a number of ways.

Factoring:

List each number's factors in order to calculate the GCF by factoring. The factors that evenly divide into the number with no remainder are known as whole numbers. The GCF is the largest number that appears on each list of common factors for each number.

Example: Find the GCF of 18 and 27

The factors of 18 are 1, 2, 3, 6, 9, 18.

The factors of 27 are 1, 3, 9, 27.

The common factors of 18 and 27 are 1, 3 and 9.

The greatest common factor of 18 and 27 is 9.

Prime Factorization:

List all of each number's prime factors to determine the GCF by prime factorization. List the prime factors that each of the original numbers has in common. Include the most instances of each prime factor that each original number has in common. To find the GCF, multiply these by one another.

You'll observe that the prime factorization approach may be simpler than straight factoring as numbers grow larger.

Example: Find the GCF (18, 27)

The prime factorization of 18 is 2 x 3 x 3 = 18.

The prime factorization of 27 is 3 x 3 x 3 = 27.

The occurrences of common prime factors of 18 and 27 are 3 and 3.

So the greatest common factor of 18 and 27 is 3 x 3 = 9.

There is another method but it focuses on more complex numbers.

Hope this helps!

A balanced chemical equation for this reaction  is given as

NO2(g)+NO3(g)→N2O5(g)

This is further explained below.

Generally, A chemical reaction occurs that takes place when two or more molecules contact with the appropriate orientation and sufficient force to generate a new product.

This process is referred to as a chemical reaction. During this procedure, atomic bonds are both broken and formed in the course of the operation.

Synthesis, decomposition, from another, and double displacement reactions are the four primary categories of chemical reactions. Synthesis is the process of creating new molecules from existing ones.

In conclusion, A balanced chemical equation for this reaction  is given as

NO2(g)+NO3(g)→N2O5(g)

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The answer to this question is:

−|−5⋅(−7)|  = −35

The non-negative quantity of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, the number 5 has a value of 5 and an absolute value of 5.

So, here first we have to solve the expression written inside the modulus and then the remaining part.

−| −5⋅(−7) |  = −| −5*(−7) |

                   = −| 35 |

The absolute value of  | 35 | is  non-negative value of 35

                        | 35 | = 35

So, −| −5⋅(−7) | =  −| 35 | = −35

Therefore,  −|−5⋅(−7)|  = −35

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Answer:

primary school is a primary school

Answer:the meaning of primary school is elementary school basically grades Kinder-5th grade

Step-by-step explanation:

Answer:

the answer is

Step-by-step explanation:

Q/R= G/F

= QF=GR

divide both sides by Q

Q and Q are off so

therefore F= GR/Q

There are 3 computer games she can brought at $75.

Unitary method

Unitary method is defined as the process of finding the value of a unit and then the value of a required number of units.

Given,

Arianna buys computer games from an online store.

Each game she orders costs $22 and shipping for her total is $9.

Arianna can spend no more than $75.

Here we need to find how many computer games did Arianna Brought.

Let x be the number of computer games she brought.

We know that,

Cost for one game = $22

Shipping cost = $9.

She spent = $75.

So, it can be written as,

=> 22x + 9 = 75

=> 22x = 75 - 9

=> 22x = 66

=> x = 66/22

=> x = 3.

So, she can brought 3 computer games at $75.

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The measure of angle c is 54 degrees

The given parameters are

a = 15x + 81

c = 10x + 24

Angles a and c are supplementary angles

So, we have

a + c = 180

This gives

15x + 81 + 10x + 24 = 180

Evaluate the like terms

25x = 75

Divide by 25

x =3

Substitute x =3 in c = 10x + 24

c = 10 * 3 + 24

Evaluate

c = 54

Hence, the measure of angle c is 54 degrees

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Answer:

see explanation

Step-by-step explanation:

the 2 expressions are difference of squares and factor in general as

a² - b² = (a + b)(a - b)

Then

4w² - 36

= (2w)² - 6²

= (2w + 6)(2w - 6)

and

25[tex]x^{4}[/tex] - 64y²

= (5x²)² - (8y)²

= (5x² + 8y)(5x² - 8y)

Answer is h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π ) - [tex]\frac{1}{2}[/tex]

∵The maximum point (- 2π. 3 )

        minimum point (- π / 2 , - 4)

and h(x) = a cos (b x + c)+ d

∴ a + d = 3                                d = - 1/ 2

                                  ⇒  

 -a + d = -4                              a = 7 / 2

{solve the equation}

and   -2πb + c = 0                      b = 2 / 3

                                       ⇒

       - ( π/ 2) b + c =  λ              c = 4 / 3 π

∴ h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π) - [tex]\frac{1}{2}[/tex]

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant

here detail explanation:

Sine Function

Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:

Sin a =Opposite/Hypotenuse = CB/CA

Cos Function

Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.

Cos a = Adjacent/Hypotenuse = AB/CA

Tan Function

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.

Tan a = Opposite/Adjacent = CB/BA

Also, in terms of sine and cos, tan can be represented as:

Tan a = sin a/cos a

Secant, Cosecant and Cotangent Functions

Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:

Sec a = 1/(cos a) =  Hypotenuse/Adjacent = CA/AB

Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB

cot a = 1/(tan a) = Adjacent/Opposite = BA/CB

Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant.

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The measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.

Angles are bisected if they are divided into two equal parts.

If the angle BC bisects <ABC, hence <ABD and <DBC are equal, hence;

2(11x + 23) = <ABC

Given the following parameters

<ABC = 25x + 34

2(11x + 23) = 25x + 34

Expand

22x +46 = 25x + 34

22x-25x = 34 - 46

-3x = -12

x = 4

Determine the measure of the angles

<ABD = 11x + 23 = <DBC
<ABD = 11(4) + 23

<ABD = 44 + 23

<ABD = 67 degrees

<ABC = 2(67)

<ABC = 134 degrees

Hence the measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.

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The property which justifies the statement, ∠LMN ≅ ∠LMN is: C. reflexive property of ≅.

In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

The reflexive property of congruence states that a line segment, an angle, or geometric shape (geometric figure) is always congruent to itself.

This ultimately implies that, for all angles M , ∠M ≅ ∠M. In this context, we can reasonably infer and logically deduce that the property which justifies the statement, ∠LMN ≅ ∠LMN is reflexive property of ≅.

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The number such that one-half of the number is three more than one-fourth of the number is 12.

It is given in the question that a number  is such that one-half of the number is three more than one-fourth of the number.

We have to find the number.

Let the number be x.

According to the question, we can write,

x/2 = x/4 + 3

Solving the linear equation, we get,

x/2 - x/4 = 3

(2x - x)/4 = 3

x/4 = 3

x = 4*3

x = 12

Hence, the number such that one-half of the number is three more than one-fourth of the number is 12.

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Answer:

-35

Step-by-step explanation:

Question =7-24÷8×4+6

=7-192÷4+6

=7-49+6

=-41+6

=-35

Therefore,right answer is (-35)

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The equation -2x=3/8 is not a literal equation.

A literal equation can be defined as an equation which primarily of letters.

It is an equation  made up of several variables or letters.

Examples of literal equations are;

We can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.

Given the equation;

-2x=3/8

We can see that there is only one variable to be worked out and hence, is not a literal equation.

Thus, the equation -2x=3/8 is not a literal equation.

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A relation will be only a function if and if only for every single value of x there must be only one output thus {(1,1),(1,2), (1,3), (1,4)} will not be a function, therefore, option (C) will be correct.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

Given the coordinates,

In option (B)  {(1,4),(2,4),(3,4),(4,4)} in this for y = 4  → x = 1,2,3,4 so it will be a function becuase for every single x value there is a single y value but for a single y value, there could be two x.

In option (D) {(1,1),(1,2), (1,3), (1,4)} for x = 1 → y = 1,2,3,4 so it will not a function.

Hence "{(1,1),(1,2), (1,3), (1,4)} will not be a function".

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Answer:

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these.

Step-by-step explanation:

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Answer is

VY = 17

UZ =21

WV = 14.7

TV = 29.4

TU = 38

SOLVING STEPS

WV = [tex]x^{2}[/tex]+[tex]15^{2}[/tex] =  [tex]21^{2}[/tex]

       ⇒[tex]x^{2}[/tex]  + 225 = 441

      ⇒ [tex]x^{2}[/tex] =  441-225

      ⇒ [tex]x^{2}[/tex] = 216

      ⇒ x = [tex]\sqrt{216}[/tex]

VY = 17

UZ =21

WV = 14.7

TV = 29.4

TU = 38

The circumcentre of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcentre.

Method to Calculate the Circumcentre of a Triangle

Steps to find the circumcentre of a triangle are:

Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC

how to calculate the slope of the particular line :

By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)

Find out the equation of the other line in a similar manner

Solve two bisector equations by finding out the intersection point

Calculated intersection point will be the circumcentre of the given triangle

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Answer:

g = -4

Step-by-step explanation:

Hope this helps :)

The equation of the line i slope intercept form is y = 4x - 22.

Slope is the amount a point moves in y axis upon the amount a point move in x axis.We can also say that slope is rise over run.

According to the given question we have to  an equation of line that passes through (5,-2) and (7,6) in slope intercept form.

We know equation of a line in slope intercept form is y = mx + b.

Two points are given (5,-2) = (x₁,y₁) and (7,6) = (x₂,y₂) and we know              slope (m) = (y₂ - y₁)/(x₂ - x₁).

∴ slope (m) = { 6 - (-2) }/( 7 - 5)

  slope (m) = 8/2

  slope (m) = 4.

Now the equation can be written as

y = 4x + b.

Putting any of the given pair of points for x and y in y = mx + b.

6 = 4(7) + b

6 = 28 + b

b = - 22.

∴ The required equation is y = 4x - 22.

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The total number of students which are there in the sporting events are 87.

The total number of mini foam fingers which the sporting event coordinator has is 200. Since he gives 2 foam fingers to each student present in the event therefore each student has 1 pair of mini foam fingers.

So, in total there are 200/2 = 100 pairs of mini foam fingers.

The total number of mini foam fingers left after distribution is equal to 26.

So total pairs of mini foam fingers left = 26/2 = 13

Therefore, the number of students which are present in attendance is given by:

Total pairs of foam fingers - total pairs of foam fingers left

=> 100-13 = 87

Therefore, total number of students in attendance are 87.

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The value of the exponent equation [tex]\frac{8}{125} ^{-2/3}[/tex] is 25/4 or 6.25.

According to the question the exponent equation that we have been given is :

          [tex]\frac{8}{125} ^{-2/3}[/tex]

First, we will change the negative sign of the exponent and to change the negative sign of the exponent we will reciprocal the fraction that is

        = [tex]\frac{125}{8} ^{2/3}[/tex]

Which is also equal to

  =   [tex]{125} ^{-2/3}/8^{2/3}[/tex]

Now we know that 5³ =125 and 2³ = 8. Thus replacing the numerator and denominator by it we get,

  =  [tex](5^{3}) ^{2/3}/(2^{3}) ^{2/3}[/tex]

  =  5²/2²

  = 25/4

  = 6.25

Hence the value of the exponent equation is 25/4 or 6.25

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In order for Abraham to receive an A, he will need to earn a total of 1.5 points, which is the rational number that may be used to represent that amount.

It is important to keep in mind that a number is considered rational if it can be expressed in the form of a fraction.

It is possible when decimals and numbers have worked effectively.

In light of the fact that Abraham must get a grade of A– in mathematics in order to achieve an A, the rational number that can be used to symbolize the number of points that Abraham must earn in order to get an A will be the number 1.5.

Where can I find out more about rational numbers

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The equation representing Main Street if Main Street passes through the point (5, 2) is; y = 2x - 8

We are given the linear equation that represents 5th Avenue as;

y = 2x - 3

Now, main street is parallel to 5th avenue and as such will have the same slope.

Thus, equation of the line passing through (5, 2) representing main street is;

y - 2 = 2(x - 5)

y - 2 = 2x - 10

y = 2x - 10 + 2

y = 2x - 8

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The values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3

To multiply matrix, we follow patterns depending on the type of matrix. Thus, from the given matrix, we can say that;

(1 * -1) + (0 * -1) + (1 * 3) = a

-1 + 0 + 3 = a

a = 2

Similarly;

(1 * -1) + (0 * 2) + (1 * 4) = b

-1 + 0 + 4 = b

b = 3

Thus, the values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3

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