What is the remainder when f(x) = x4 + 7x3 + 17x2 + 20x is divided by x2 + 4?

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!

The total money that will be cost for Mrs. Herrera to purchase candy for her is $10.9889

Given, Number of students that 100% attendance in the class is √196 -1 that is equal to

14-1 = 13.

So, number of students is 13.

Cost of one candy = $0.79+7%(tax)

Cost of one candy = $0.79 + (7% of 0.79)

Cost of one candy = $ 0.79 + 0.0553

Cost of one candy = $0.8453

So , total cost that Mrs. Herrera to purchase candy will be

Total cost = Number of student X Cost of one candy

Total cost = 13 X $0.8453

Total cost  = $ 10.9889

Hence, The total cost for Mrs. Herrera to purchase candy for her is $10.9889

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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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The measure of angle EFH, m ∠EFH is 71°

The measure of angle EFG, m ∠EFG is 142°

From the question, we are to determine the measure of angle EFH and angle EFG

From the given information, we have that

FH bisects ∠EFG.

Thus, we can write that

m ∠EFH = m ∠GFH

From the given information,

m ∠GFH = 71°

∴ m ∠EFH = 71°

Also,

Since FH bisects ∠EFG

Then,

m ∠EFH + m ∠GFH = m ∠EFG

71° + 71° = m ∠EFG

142° = m ∠EFG

m ∠EFG = 142°

Hence, the measure of angle EFH, m ∠EFH is 71°

The measure of angle EFG, m ∠EFG is 142°

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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:

g = -4

Step-by-step explanation:

Hope this helps :)

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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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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Answer:

16. G

17. C

Step-by-step explanation:

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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1 hour & 45 minutes is the distance between his home and school.

What is distance short answer?

d=rt

distance = rate of speed times time

d= 33X = 44(7/4-X)

33X = 77- 44X

77X = 77

X = 1 hour

33X = 33 miles

44(7/4 - 4/4) = 33 miles each way

1 hour & 45 minutes = 1 3/4 hours or 7/4 hours

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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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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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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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Multiply the first equation by 7 and the second equation by 2, and then add.

2f - 5g=-9

-7f + 3g=4

To eliminate any variable , we need to make the coefficients same with different sign and add it

the coefficient of 'f' in first equation is 2

the coefficient of 'f' in second equation is -7

We already have different sign so we make the coefficients same

To make the coefficient same , we multiply the first equation by 7  and second equation by 2

So equation becomes

14f - 35g = -63

-14f + 6g = 8

Now when we add both equations, 'f' gets cancelled

-29g = -55

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Answer:

A

Step-by-step explanation:

Edge2022

Numbers without fractions are referred to as "whole numbers," and they are made up of positive integers and zero. It is denoted by the letter "W," and its corresponding set of numbers are 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12,..

A mathematical procedure called addition symbolizes adding objects t to a larger collection. The plus sign ( + ) is used to denote it.

Some examples of the addition of whole numbers is:

1 + 8 = 9

10 + 19 = 29

A mathematical operation known as subtraction symbolizes the process of determining the difference between two numbers or units. The negative sign is used to denote it ( - ).

An example of subtraction of whole numbers is:

10 - 2 = 8

40 - 25 = 15

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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:

A : Equation 4

B: Equation 1

C: Equation 3

D: Equation 2

Step-by-step explanation:

For direct proportionality, it means as one variable increases, the other increases. E.g. as X in eqn 4 increases y increases. Same thing applies to decrease. This is cause y and x are on the "same level". In eqn 2 and 3, y and x are NOT on the same level because of the division sign.

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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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Answer:

24; 0

Step-by-step explanation:

Absolute value means number of the value away from zero, either positive or negative.  So the absolute value of -24 (for example) is 24 because it is 24 integers away from zero.

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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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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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

If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the Poisson probability distribution.

How do you find the probability of success for each trial?

What is the probability formula?

Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) E is the event, P is the probability, and S is the sample area.

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Answer:

Step-by-step explanation:

8).

Given,

For no. Of shirts = 10, price per shirt = $9

For no. Of shirts = 25, price per shirt = $8.40

.

Linear equation be,

y = mx + b

x 10 25

y 9 8.4

9 = 10m + b  (i)

8.4 = 25m + b (ii)

Now,

(i) 9 = 10 m + b  b = 9 - 10m

(ii)  8.4 = 25m + b 8.4 = 25m + 9 - 10m

8.4 - 9 = 15m m = -0.6/15 = -0.04

m = - 0.04

b = 9 - 10m = 9 - 10(-0.04) = 9+0.4 = 9.4

b = 9.4

The linear equation,

y = mx + b

y = -0.04x + 9.4

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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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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