need help will give brainlist

As we have proved that if p ≡ 1 (mod 4), then -r is also a primitive root of p.

Since r is a primitive root of p, we know that every non-zero integer modulo p can be written as a power of r. That is, for any integer a with gcd(a, p) = 1, there exists an integer k such that a ≡ rˣ (mod p). This follows from the fact that the order of the element r modulo p is φ(p) = p-1, where φ denotes the Euler totient function.

Now, let us consider the case where p ≡ 1 (mod 4). This means that there exists an integer x such that p = 4x + 1. We want to show that -r is also a primitive root of p.

To do this, we first observe that (-1)² ≡ 1 (mod p) since p is an odd prime. Therefore, (-1)^(4x) ≡ 1 (mod p), which implies that (-1)²ˣ ≡ 1 (mod p).

Now, if we can show that (-1)ˣ = -1, then we will have (-1)²ˣ = (-1)ˣ*(-1)ˣ = (-1)*(-1) = 1 (mod p), which will allow us to prove that -r is also a primitive root of p.

To see that (-1)ˣ = -1, we use the fact that p ≡ 1 (mod 4) and the properties of quadratic residues. Specifically, we know that -1 is a quadratic non-residue modulo p, since if -1 ≡ a² (mod p) for some integer a, then we would have

=> [tex](-1)^{((p-1)/2) }[/tex] ≡ [tex]a^{(p-1) }[/tex]≡ 1 (mod p),

which contradicts the fact that

=> [tex](-1)^{((p-1)/2) }[/tex]= -1.

Therefore, there exists an integer b such that b² ≡ -1 (mod p).

Now, consider the product brˣ. We claim that brˣ is a primitive root of p. To see this, note that for any integer a with gcd(a, p) = 1, we can write a ≡ rˣ (mod p) for some integer k. Then, we have:

(a*brˣ)² = a² * b² * r²ˣ ≡ r²ˣ * (-1) ≡ -r²ˣ (mod p)

Since r is a primitive root of p, we know that rˣ and r²ˣ cover all the non-zero residue classes modulo p. Therefore, we can choose k such that r²ˣ ≡ -1 (mod p), which implies that (a*brˣ)² ≡ -1 (mod p).

Since a was arbitrary, this shows that brˣ is a quadratic non-residue modulo p, and therefore a primitive root of p.

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Answer:

Step-by-step explanation: Here if we put [tex]x=0[/tex] then we will get initial temperature. That is [tex]T_0=70+20=90[/tex].

The temperature will cools down [tex]70(0.8)^{10}+20=27.52(approx)[/tex].

So the final temperature after 10 minutes will be :[tex]90-27.52=62.48(approx)[/tex].

Final Answer: The temperature is 62.48 degree Celsius.

Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Answer:

line RQ

Step-by-step explanation:

The points on a line can be flipped when naming. For example, line AB is the same as line BA.

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Answer: elephant

Step-by-step explanation:

3/5 x 345 = 207

345 > 207

Answer:

cos(45°) = √2/2

B is correct.

Answer:

0.75

Step-by-step explanation:

P(A) = 9+9 = 18

P(B) = 9+9 = 18

P(A and B) = 9

P ( A or B) = 18+18-9 = 27

Probability = ans / total = 27/36 = 0.75

The probability that either event will occur is given as follows:

P(A or B) = 0.75.

We have,

The figure about the possible outcomes are shown in image.

Now, The formula used to calculate the probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

The total number of events from the Venn's diagram is given as follows:

4 x 9 = 36.

Hence the probability of each outcome is given as follows:

P(A) = (9 + 9)/36 = 0.5.

P(B) = (9 + 9)/36 = 0.5.

P(A and B) = 9/36 = 0.25.

Hence the or probability is given as follows:

P(A or B) = P(A) + P(B) - P(A and B).

P(A or B) = 0.5 + 0.5 - 0.25

P(A or B) = 0.75.

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The expression that is equivalent to 2.76 is two and nineteen twenty fifths

The number in the question is given as 2.76

This means that we have

Number = 2.76

We can rewrite this as a mixed number.

2 + a/b

Such that:

a/b = 0.76

From the list of options, we have

two and nineteen twenty fifths = 2 + 19/25 = 2.76

This means that the correct expression is two and nineteen twenty fifths

Hence, the expression that is equivalent to 2.76 is two and nineteen twenty fifths

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Complete question

Which of the following is equivalent to 2.76?

2.76%

27.6%

two and nineteen twenty fifths

twenty five over nineteen

The type of graph would have the title, "Monthly Company Profit for the Year?" is line graph (option a).

Using a line graph to display monthly company profits allows for the visualization of the overall trend and any fluctuations or changes in the profits over the year. It also allows for easy comparison of the profits from one month to another, as well as identifying which months were particularly profitable or unprofitable.

In mathematical terms, a line graph can be defined as a graph in which the data points are plotted as individual points, and a line is drawn to connect the points.

The line represents a mathematical function that can be used to model the relationship between the variables being plotted. In the case of the monthly company profits, the function would model the relationship between time and profit.

Hence the correct option (a).

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Answer:

Step-by-step explanation:

Given expression is 7 1/3t-(10 2/3t-6)

Now, convert the proper fraction present in the question to improper fractions.

proper fractions are 7 1/3 and 10 2/3

so, 7 1/3 =(7*3+1)/3 = 22/3

     10 2/3 = (10*3+2)/3=32/3

= >22t/3 - (32t/3 -6)

= >22t/3 - 32t/3 +6

= >6 - 10t/3

This is the final solution.

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Based on the information, the regular polygon has 35 sides.

In order to determine the number of sides that a regular polygon has if the sum of the interior angles is given, you can use the formula:

sum of interior angles = (n - 2) x 180°

solve for n, you can rearrange the formula as:

n = (sum of interior angles ÷ 180°) + 2

Then, plug in the given sum of interior angles and solve for n.

b. Using the formula above, we can find the number of sides of the regular polygon with a sum of interior angles of 6,300°:

n = (6300° ÷ 180°) + 2

n = 35

The regular polygon has 35 sides.

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The required surface area of the given rectangular prism is 202 square yd.

Here, we have,

Given that,

the surface area of a rectangular prism with a base length of 9 yd, a base width of 5 yd, and a height of 4 yd is to be determined.

We have,

Surface area is defined as the measure of a region or surface is called as surface area.

Here,

The surface area of the rectangular prism is given as,

S = 2(lw + lh + wh)

S = 2 [9×5 + 5×4 + 4×9]

S = 202 square yd.

Thus, the required surface area of the given rectangular prism is 202 square yd.

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The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

We can derive an inequality from the problem statement which is:

8X + 12Y ≥ 1000

This inequality represents the amount of money the basketball team needs to raise by selling donuts.

X is the number of half dozen boxes sold

Y is the number of full dozen boxes sold.

To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:

If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:

8(50) + 12(50) = $400 + $600 = $1000

So this is a valid solution that meets the fundraising goal.

If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:

8(100) + 12(0) = $800

This is not enough to meet the fundraising goal, so it is not a valid solution.

If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:

8(0) + 12(100) = $1200

This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.

Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

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One possible representation of such a vector is u = (3, 2), which has a magnitude of approximately 3.605 and makes an angle of about 33.69 degrees with the positive x-axis in the standard Cartesian coordinate system.

Firstly, it is important to understand the meaning of the double vertical bars (|| ||), which denote the magnitude or length of a vector. For instance, if we have a vector

=> v = (2, 3),

then its magnitude can be computed as

=>  ||v|| = √(2² + 3²) = √13.

Similarly, if we have a vector u = (u₁, u₂), then its magnitude can be expressed as

=>  ||u|| = √(u₁² + u₂²).

The given condition

=> ||-4u|| ≈ 14.42

can be rewritten as

=>  4||u|| ≈ 14.42

=>  ||u|| ≈ 3.605.

This means that the magnitude of vector u is approximately equal to 3.605.

Therefore, to obtain a possible representation of vector u with a magnitude of approximately 3.605, we can solve the following system of equations:

||u|| = √(u₁² + u₂²) ≈ 3.605

θ = tan⁻¹(u₂/u₁)

Note that there are infinitely many solutions to this system, since the direction of u is not uniquely determined.

However, one possible solution is u = (3, 2), which has a magnitude of

=> ||u|| = √(3² + 2²) = √13 ≈ 3.605

and makes an angle of

=> θ = tan⁻¹(2/3) ≈ 33.69 degrees

with the positive x-axis.

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Answer:

22 m^2

Step-by-step explanation:

multiply the sides

Answer: 2.1468 times 10^15

Step-by-step explanation: you times them together

Answer:

Let's start by using the formula for the perimeter of a rectangle, which is:

P = 2L + 2W

where P is the perimeter, L is the length, and W is the width.

We're given that the perimeter is 78 meters, so we can write:

78 = 2L + 2W

Simplifying this equation, we get:

39 = L + W

We're also given that the length is 6 meters less than four times the width, so we can write:

L = 4W - 6

Now we can substitute this expression for L into the equation we got earlier:

39 = (4W - 6) + W

Simplifying this equation, we get:

39 = 5W - 6

Adding 6 to both sides, we get:

45 = 5W

Dividing both sides by 5, we get:

W = 9

So the width of the rectangle is 9 meters. We can use this value to find the length:

L = 4W - 6 = 4(9) - 6 = 30

So the length of the rectangle is 30 meters.

There are 6 whole weeks will it take her to save $160.

We have to given that;

Amy is going on a road trip with her friends and needs to save $160.

And, she starts saving 18% of her weekly earnings at the pool,

Now, Let number of weeks it take her to save $160 is, x

Hence, We get;

160 = 160 x 0.18 x t

t = 1/0.18

t = 5.55 weeks

Thus, There are 6 whole weeks will it take her to save $160.

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The statement that is true for the Cartesian coordinate system is A. the values below the X-axis are negative values of x.

The Cartesian coordinate system, also called rectangular coordinate system, helps plot coordinates in a two-dimensional plane. This model contains two axes -- the x-axis (horizontal) and y-axis (vertical) -- that meet at the origin. The values beneath the x-axis represent negative y-values, not x-values as some assume.

Likewise, above the x-axis represents positive y-values, not x-values. Meanwhile, points along the x-axis aren't considered either positive or negative but rather labeled based on their distance away from the origin as per this structure's guidelines.

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The lateral surface area of the pyramid is 112 sq. in.

The correct answer is an option (B)

From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.

The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.

Using the formula of the area of triangle, the lateral surface area would be,

A = 4 × (1/2 × base × height)

A = 4 × (1/2 × 8 × 7)

A = 4 × (4 × 7)

A = 4 × 28

A = 112 sq. in.

This is the required lateral surface area.

The correct answer is an option (B) 112 in²

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Find the complete question below.

The net below shows a square pyramid. What is the lateral surface area? A. 176 in^2

B. 112 in^2

C. 64 in^2

D. 210 in^2

The inequality that can be used to find the number of sales she needs to make is D. 100 + 15x ≥ 500.

In this scenario, Aaliyah wants to earn at least $500. The fixed amount she earns is $100, and she earns $15 for each sale.

Therefore, the total amount she earns can be represented as 100 + 15x, where x is the number of sales she makes. To ensure that she earns at least $500, we can set up the inequality 100 + 15 x ≥ 500.

With this inequality, we can see that the sum of the $ 100 base salary and the $ 15 per sale would add up to a sum that is either $ 500 or above.

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I think it is C.

C. 2 tons = 64, 000 ounces

The expression factoring out the greatest common factor is  (3pf - 21p²)(f + 2).

We have the expression as

3pf² - 21p²f + 6pf - 42p²

Now, factorising the expression as

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +2)

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The value of the variable x is 51.340 degrees

Note that their are six different trigonometric identities in mathematics.

These identities are;

Also, these identities have their different ratios, they are;

sin θ= opposite/hypotenuse

tan θ = opposite/adjacent

cos θ = adjacent/hypotenuse

From the information given, we have that;

Opposite = 10cm

Adjacent = 8cm

Substitute the values

tan x = 10/8

Divide the value, we have;

tan x = 1.25

Find the tangent inverse, we get;

x = 51. 340 degrees

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