Given a prime $p$ and an integer $a$, we say that $a$ is a primitive root $\pmod p$ if the set $\{a,a^2,a^3,\ldots,a^{p-1}\}$ contains exactly one element congruent to each of $1,2,3,\ldots,p-1\pmod p$.For example, $2$ is a primitive root $\pmod 5$ because $\{2,2^2,2^3,2^4\}\equiv \{2,4,3,1\}\pmod 5$, and this list contains every residue from $1$ to $4$ exactly once.However, $4$ is not a primitive root $\pmod 5$ because $\{4,4^2,4^3,4^4\}\equiv\{4,1,4,1\}\pmod 5$, and this list does not contain every residue from $1$ to $4$ exactly once.What is the sum of all integers in the set $\{1,2,3,4,5,6\}$ that are primitive roots $\pmod 7$

Answer:

D. 25°

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

50+25=75, 180-175=105

Answer:

Step-by-step explanation:

It’s 0

Answer:

x = 68°

Step-by-step explanation:

This is an isosceles triangle, which means the two base angles will be the same. (56° and 56°)

All triangles angles must add up to 180, so if we take 180-56-56 we will find the missing angle (x).

180-56-56 = 68

x = 68°

The shaded region has a surface area of 7π.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

find the area of the circle with radius =3 cm,

then subtract the areas of the two circles with radius 1 cm

pir^2 = the area of a circle with radius = r

=pi(3)^2 -pi(1)^2 - pi(1)^2

= 9pi -pi-pi

= 9π-2π

= 7π

The area of shaded region is 7π.

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Answer:

The slope is 1/3. Goes 1 up and 3 to the right.

Answer:

It would be 49 cm

Step-by-step explanation:

Knowing the the perimeter of Tri RST is 28 cm and that it is a dilated by a 4:7 Scale Factor from Tri GHI:

(4/7)x = 28cm

(4/7)x (7/4) = 28cm (4/7)

x = 49cm

Hope that helps.

Answer: Approximately 28 km

The more accurate, yet still approximate value, is roughly 27.995735464379

Round that however you need to.

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Explanation:

As the diagram shows, the uppercase letters A,B,C represent the corner points of the triangle. They also represent the angles. The diagram says that:

The missing angle C is....

A+B+C = 180

C = 180-A-B

C = 180-59-91

C = 30

which we'll use later.

Convention usually has the side lengths be lowercase letters 'a', b, and c. Those lowercase letters are opposite their uppercase counterpart. We'll have side 'a' opposite angle A, then b is opposite B, and c is opposite C. This allows us to quickly label a triangle and find the missing sides and/or angles. The phrasing "solve the triangle" basically means "find all the missing sides and angles". For this problem, we're only concerned with one side.

The diagram says that side c = 14 due to it being opposite angle C.

The goal is to find side b, which is the shorter way of saying "find AC".

-------------------------

From here, we can use the law of sines to find side b

b/sin(B) = c/sin(C)

b/sin(91) = 14/sin(30)

b = sin(91)*14/sin(30)

b = 27.995735464379 which is approximate

b = 28

Side AC is roughly 28 km long.

I rounded to the nearest whole number since the "14 km" is also a whole number. Your teacher may want you to round differently.

Make sure your calculator is in degree mode.

The evaluation of the expression 2(b + 4) when b = 4 is 18

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

Expression: 2(b + 4)

Values: b = 5

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

2(b + 4) = 2 * (5 + 4)

Evaluate the products

This gives

2(b + 4) = 10 + 8

Evaluate the like terms in the equation

So, we have the following representation

2(b + 4) = 18

Using the above as a guide, we have the following:

The solution is 18

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Answer:

Answer is 600!

Step-by-step explanation:

Answer: $2.45

Step-by-step explanation:

An easy way to find the correct tip is to learn what 20% of 12.25 is

Let's convert the percentage to a decimal by moving the decimal point two spaces to the left. Now we have .2

.2 X 12.25 = 2.45

2.45 is 20% of 12.25

Answer:

Step-by-step explanation:

y - 5 = -1/7(x - 4)

y - 5 = -1/7x + 4/7

y - 35/7 = -1/7x + 4/7

y = -1/7x + 39/7

The closing side of the triangle serves as the best representation of the resultant vector for the resultant R=A+B, so selecting option C would be the appropriate response.

A vector in mathematics is a quantity that has both magnitude and direction but no specific location. Illustrations of such numbers include velocity and acceleration. The term "vector" refers to something that has both magnitude and direction. When viewed geometrically, a vector can be thought of as a directed reference line, the direction of which is indicated by an arrow and whose length corresponds to the vector's magnitude. A quantity or phenomenon known as a vector has two distinct qualities that are its size and direction. Also included in the term is a description of how these values are represented geometrically or mathematically. Vectors are present in electromagnetic fields, as well as in weight, velocity, force, and velocity.

given

As stated in the issue, we must determine the resultant vector by adding vectors A and B.

The triangle law of vector addition, which states that the total is supplied by the triangle's closing side, can be used to calculate the vector's outcome.

Option C is the proper response, thus.

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Answer:

x^2(x^2 - 15) + 9(x-6)(x+1)

Step-by-step explanation:

To factor the expression x^4 - 15x^2 + 54 completely, we need to find the common factors in each term. In this case, we can see that the terms x^4 and -15x^2 share a common factor of x^2. To factor this out, we can use the difference of squares factorization:

x^4 - 15x^2 + 54 = x^4 - 15x^2 + (9x^2 - 9x^2) + 54

= x^2(x^2 - 15) + 9(x^2 - 6)

= x^2(x^2 - 15) + 9(x-6)(x+1)

Since x^2-15 can't be factored further. The expression is fully factored.

We can check this by multiplying it back and it should be the same as original expression.

this question is related to numbers and the solution is as follows,

Rover eats 3/4 can of cat food in a day.

given

in 60 days it will consume 60 x 3/4 cans = 45 cans of cat food

3 cans cost = $5 and a pack contains 3 cans

45 cans is equivalent to= 45/3

= 15 packs

15 packs cost = 15 x $5 = $75

So it will cost $ 75 to feed Rover for 60 days

Bobo eats 1/2 of a can of cat food per day

in 60 days it will consume 60 x 1/2 cans = 30 cans of cat food

3 cans cost $5 and a pack contains 3 cans

30 cans are equivalent to 30/3 = 10 packs

10 packs will cost = 10 x $5 = $50

So it will cost $50 to feed Bobo for 60 days

In total, in 60 days it will cost $75 +$ 50 = $125 to feed both cats in 60 days.

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As calculated from the data we get the result as that $ 125 is required for the cat food of both the cats in a month.

We are given that in 60 days he will consume  ,

60 x 3/4 cans

= 45 cans of cat food

The cost of 3 cans cost = $5

and one pack has 3 cans in it.

Therefore, 45 cans is equivalent to

= 45/3

= 15 packs

So , the cost of 15 cans will be ,

15 packs cost = 15 x $5 = $75

Therefore ,$75 is used for 60 days of cat food for Rover.

Now , we know that Bobo eats 1/2 of a can food in a day.

Therefore, in 60 days he will  eat,

60 x 1/2 cans

= 30 cans of food

As we know, 3 cans cost $5 and a pack contains 3 cans

Therefore, 30 cans = 30/3 = 10 packs

10 packs will cost = 10 x $5 = $50

So , $50 is spend to feed Bobo , in a month.

Therefore , if will combine their cost we will get that ,

$75 +$ 50 = $125 is required to feed both the cats in one month.

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Answer:

b

Step-by-step explanation:

Answer:

B. Students of the high school

Step-by-step explanation:

It is high school because you just want to ask that area.

Answer:

5.5 + 4 +3

Step-by-step explanation:

The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The triangle ABC and PDF are concurrent by AAS,

The AAS concurrency required two angles and one side to be equal,

Here,

AB = PD,

∠ ABC = ∠ PDF

Now one more angle is required to be equal,

∠ ACB = ∠ PFD  

Thus, the missing angle is ∠ ACB and ∠ PFD.

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Amount of pineapple juice is more in Jo's drink and amount of Orange juice is less in Jo's drink as compare than the tropical punch recipe because these are not in that ratio as in the tropical punch recipe.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.

The Number of cups of pineapple juice = 222 liters

The Number of cups of orange juice = 333 liters

Thus ,

Total number of cub of juice = 222+333

                                               = 555 cups

In Jo's drink

The Number of cups of pineapple juice = 333 liters

The Number of cups of orange juice = 444 liters

Thus Total number of cub of juice = 333+444

                                                        = 777 cups.

The ratio of amount of pineapple juice and amount of Orange juice is 2:3 in the tropical punch recipe

Whereas the ratio of amount of pineapple juice and amount of Orange juice is 3:4 in Jo's drink

Thus we can see that Amount of pineapple juice is more in Jo's drink And Amount of Orange juice is less in Jo's drink.

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Answer:

Step-by-step explanation:

Of that list, only the square and the rectangle have the property you are asking for.

Try drawing it. The parallelogram has a shorter diagonal from the two obtuse angles than the diagonal from the two acute angles.

The rhombus has the same property as the parallelogram.

The kite has a far longer diagonal  from the angle enclosed by the two long sides going to the angle enclosed by the two shorter sides,  than a line going from the angle enclosed by one shorter and one longer side to the other angle made the same way.

Answer:

The equation you have provided is 8 + 9x = 7, where x is the unknown number.

To solve for x, you can first subtract 8 from both sides of the equation to get

9x = -1

Then divide both sides by 9

x = -1/9

So the number x is -1/9, which means that the product of x and 9 is equal to -1.

Keep in mind that this is not a natural number and it is not possible to represent the solution as a whole number.

Step-by-step explanation:

Therefore, Bob must pay $2530 in income tax for last year if Bob made 15,000 in taxable income last year.

The basis of an income tax system is referred to as taxable income. In other words, the amount of revenue that was subject to taxation.

Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core activities.

The first $8000 of Bob's taxable income is taxed at 15%:

Tax on first $8000 = $8000 * 0.15 = $1200

The remaining $7000 of Bob's taxable income is taxed at 19%:

Tax on remaining income = $7000 * 0.19 = $1330

Total tax = $1200 + $1330 = $2530

So Bob must pay $2530 in income tax for last year.

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Answer:

115 degrees

Step-by-step explanation:

The incenter is where the angle bisectors of a triangle meet.  So [tex]m\angle{PQK}=15^\circ \text{ and } m\angle{PQR}=30^\circ[/tex].

To find the measure of angle RKQ, we need to find the measure of angle PRQ.  In the big triangle, the sum of angle measures is 180 degrees, and we know two of the angles, 50 deg and 30 deg (for a total of 80 deg).  That leave 100 degrees for the measure of angle PRQ.

But RK is an angle bisector, so [tex]m\angle{KRQ}=50^\circ[/tex].

We now know two of the angles in [tex]\triangle{KRQ}[/tex], 50 deg and 15 deg.  Those total 65 degrees, so [tex]m\angle{RKQ}=180^\circ - 65^\circ=115^\circ[/tex]

Answer: No rectangle can make this shape

Step-by-step explanation:

Answer: 640

Step-by-step explanation:

1. To help identify what place value to round write out the numbers with their place

the hundreds value in this question is 600

the tens value in this question is 40

and the ones value is 8

Since the questions asks to round to the nearest 10, you would look at the number after 4 and see if it is equal or greater than 5, if so, you would round it up to the next number, which would be 5 and write it like 640.

The best explanation of Irrational Numbers is that , the numbers  that cannot be expressed as a ratio of integers are called as Irrational Numbers .

What are Irrational Numbers ?

The Irrational numbers are the real numbers that cannot be represented in the form of a ratio ([tex]\frac{p}{q}[/tex]) . In other words, the real numbers that are not rational numbers are called as irrational numbers.

For Example : [tex]\pi[/tex] is an irrational number as   [tex]\pi =3.1415925...[/tex] The decimal value in the expansion never stops at any point.

Some Property of Irrational Numbers are :

(i) The Irrational numbers consist of only non-terminating and non-recurring decimals.

(ii) The Irrational Numbers  are real numbers only.

(iii) The Addition, subtraction, multiplication, and division of any two irrational numbers may or may not be a rational number.

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Answer:

more information is needed

Step-by-step explanation:

inadequate info :(