Let p be an odd prime number. If 5 is a square modulo p, then there exists an integer k such that 5 ≡ k² (mod p).In other words, k² - 5 is divisible by p.
We consider two cases:Case 1: p divides [tex](k - √5)Let a = k - √5 and b = k + √5[/tex]. Then a and b are conjugate complex numbers. We have [tex]ab = (k - √5)(k + √5) = k² - 5 ≡ 0 (mod p)[/tex].Since p divides a, we have a ≡ 0 (mod p). Therefore, k ≡ √5 (mod p). Since p is an odd prime, k is either equal to [tex]√5 or -√5[/tex] modulo p. In particular, k is nonzero modulo p.Case 2: p divides (k + √5)
Let [tex]a = k - √5 and b = k + √5.[/tex]
Then a and b are conjugate complex numbers. We have [tex]ab = (k - √5)(k + √5) = k² - 5 ≡ 0 (mod p)[/tex].
Since p divides b, we have b ≡ 0 (mod p). Therefore, k ≡ -√5 (mod p). Since p is an odd prime, k is either equal to √5 or -√5 modulo p. In particular, k is nonzero modulo p.In conclusion, if 5 is a square modulo an odd prime p, then k is nonzero modulo p and either k ≡ √5 (mod p) or k ≡ -√5 (mod .
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(X+7) (x-4) = 0 plz solve
Answer:
Xsquared +3x -28
Step-by-step explanation:
Use foil so first to the 3rs then first to the 4th then 2nd to the 3rd then 2nd to the 4th.
x squared minus 4x plus 7x minus 28
how many times does the number $41$ appear in pascal's triangle?
The number of rows in Pascal's triangle is equal to the number of terms in the polynomial expansion of the binomial (x + y)n, where n is a non-negative integer. Pascal's triangle is an infinite triangular matrix of integers that has many fascinating properties.
Then the number of times a number n appears in the kth position of Pascal's Triangle is given by the formula:⌊(n-k+1)/(k-1)⌋The symbol ⌊⌋ represents the greatest integer function, which returns the largest integer that is less than or equal to a given value.
Using this formula, we may calculate the number of times 41 appears in Pascal's Triangle. Since 41 is not a number that appears in the first few rows of Pascal's Triangle, we'll start with row 10, which is big enough to include 41 in a few places:
For row 10 of Pascal's Triangle, the formula becomes: ⌊(10-k+1)/(k-1)
⌋= ⌊(11-k)/ (k-1)⌋
If k = 1 or k = 10, the formula yields zero, as these positions correspond to the beginning and end of the row, where the numbers are always 1.
If k = 2, the formula yields:⌊(11-2)/1⌋
= 9
Thus, 41 appears 9 times in the second position of row 10 of Pascal's Triangle.
Similarly, if k = 3,
the formula becomes:⌊(11-3)/2⌋
= 4
Thus, 41 appears 4 times in the third position of row 10 of Pascal's Triangle.
If k = 4, the formula becomes:⌊(11-4)/3⌋
= 2
Thus, 41 appears twice in the fourth position of row 10 of Pascal's Triangle.
If k = 5, the formula becomes: ⌊(11-5)/4⌋
= 1
Thus, 41 appears once in the fifth position of row 10 of Pascal's Triangle.
Finally, if k > 5, the formula yields zero, since the number 41 does not appear in the remaining positions of row 10.
Therefore, the number 41 appears 9 + 4 + 2 + 1 = 16 times in row 10 of Pascal's Triangle.
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Four times a number increased by 3 is -89
Answer:
-21.5
Step-by-step explanation:
Answer:
-21.5
Step-by-step explanation:
so we will go backwards -89 + 3 = -86
-86/4 = -21.5
Hope this helps!
The length r of a rope should be at least 28
inches.
Answer:
can you tell me what the question is
The inequality of the problem is [tex]r[/tex] ≥ [tex]28[/tex]
If the length of the rope is at least 28 in that means that the length of the rope can be 28 or higher, so the inequality sign is ≥
There is a total of 80 firefighters in a town. There are 4 fire departments in the town: North, South, East, and West. The North Department has 23 firefighters. The East Department has 13 firefighters. Let W represent the number of firefighters in the West Department and S represent the number of firefighters in the South Department. Which of the following could represent the number of firefighters at the West and South Department? Choose ALL that apply.
are the 2 triangles below similar
Matthew's brother gave him 10 video games. Each month, Matthew purchases 5 new video games to add to his collection
Which inequality can be used to find m, the number of months after starting his collection, when Matthew will have more than
100 games in his collection?
O 5m +10 > 100
O 5m + 10 < 100
O 10m +5 < 100
O 10m +5 > 100
Answer:
A:5m +10 > 100
Step-by-step explanation:
It said grater so > has to be pointing away from the 100.Also he gets 5 video games every month not ten video games, so it's A.
Also I did that question on the test.
Could I please have BRAINLIEST?The inequality function that should be used to find m is 5m +10 > 100.
Given that,
Matthew's brother gave him 10 video games. Each month, Matthew purchases 5 new video games to add to his collection There is more than 100 games in his collection. Here m be the no of months.Based on the above information, the inequality function is as follows:
5m +10 > 100
Therefore we can conclude that the inequality function that should be used to find m is 5m +10 > 100.
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-3w² + x2 – 5W + 4x²
Answer:
-3w^2+5x^2-5w
Step-by-step explanation:
a college bookstore makes an order to replenish its stock of three different types of paper: college rule line paper, legal rule line paper, and graph paper. in addition, the paper is purchased bound as either spiral notebooks or paper pads. the table below shows the store's order. bookstore order of different types of paper college rule legal rule graph spiral notebooks 175 175175 60 6060 75 7575 paper pads 90 9090 110 110110 125 125125 if a graph paper item from the order is selected at random, what is the percent probability that the item is bound as a paper pad? (ignore the % %percent symbol when entering your answer. for example, if the answer is 12.4 % 12.4, point, 4, percent, enter 12.4 12.412, point, 4.)
The percent probability that the item is bound as a paper pad is 68%.
The probability that a graph paper item selected at random is bound as a paper pad can be found as follows:First, the total number of graph paper items should be determined.
There are 60 graph spiral notebooks and 125 graph paper pads, for a total of 60 + 125 = 185 graph paper items.
Next, the number of graph paper items that are bound as paper pads should be determined.
There are 125 graph paper pads, so the probability of selecting a graph paper item that is bound as a paper pad is:125 / 185 = 0.68 (rounded to two decimal places)
Therefore, the percent probability that the item is bound as a paper pad is 68%.
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PLEASE HELPPPPPP
What is 1.0x 10^5 written in standard notation???????
Answer: 100000
Step-by-step explanation:
= 1.0 × 105
(scientific notation)
= 1.0e5
(scientific e notation)
= 100 × 103
(engineering notation)
(thousand; prefix kilo- (k))
= 100000
(real number)
Answer:
100000.0
Step-by-step explanation:
you would move the decimal over 5 spaces
Mrs. Chatman buys popcorn for $4.97 and a coke priced at $3.43. She gives the cashier a $20 bill. How much change should she receive? right answer please ill give brainliest
Answer:
$11.60 (see below)
Step-by-step explanation:
First, you need to find the total cost of the two items bought:
Add the two decimals together:
1 1
$ 4 . 9 7
+ $ 3 . 4 3
$ 8 . 4 0
So the total cost was $8.40.
If this was paid by $20, then you will have to subtract the cost:
1 9 10
$ 2 0 . 0 0
– $ 8 . 4 0
$ 1 1 . 6 0
So the change was $11.60.
i rlly need this asap i will award the bravest award to who ever gets it right
Answers in bold
b) 6xyc) 6xyIt's not a typo that the answers are the same for each.
Explanation:
There's not much to do for part b. The notation 6 * x can be shortened to 6x. The same can be said when going from 6*x*y to 6xy
For part c, the 2 and 3 multiply to 6. We end up with the same exact identical thing as part b. We leave the x and y as they are.
What is the solution to 9x-20-4x=40?
Answer:
5x-20=40
5x=40+20
5x=60
x=60/5
x=12
9x-20-4x=40
5x-20=40
5x=40+20
5x=60
answer: x=12
The following scores represent students' test grades in Mr. Preisser's fashion class.
Test Scores
79 83 79
88 93 88
83 79 83 79 83 79
93 88 93 88 93 88
What is the median score for Mr. Preisser's fashion class?
A
93
B
83
88
D
85.5
E
I don't know yet
Answer:
Definitely 85.5
Just worked it out
Answer:
85.5
Median: The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers). When there is an even number of terms, add the two middle terms and divide by 2.
Step-by-step explanation:
79, 83, 88, 93
83 + 88 = 171
171 ÷ 2 = 85.5
A Little League baseball stadium last row consists of 793 fans. The 11th row has 553 fans, the 12th row has 601 fans, the 13th row has 649 fans, and so on. How many rows are there?
Answer:
I am pretty sure it is 16 rows.
Step-by-step explanation:
I subtracted 601 by 553, and got 48. I did the same with 649 and 601 and got 48. You would then add 48 to 649 and keep going until you get to 793. Then you would count how many times you added. The times you added plus 13, should get you 16. You should have added 3 times in all
45 points in 3 games
Answer:
what do you mean? for the question
a fruit basket contains 12 red apples 6 green apples pineapple and oranges .in simplest form write the ratio of green apples to pineapples
Answer:
I think that the ratio is 1:1
Step-by-step explanation:
Because since the ratio is 6:6, you have to divide both side by 6 and get 1:1. You can't divide it no more (unless if you want it as a decimal). Hope this helped. This is an update.
Given the function
f(x) = -3x2 + 4
What is the additive inverse function of f(x)?
O g(x) = -3x2 - 4
O g(x) = -4x2 - 3
O g(x) = 3x2 - 4
O g(x) = 4x2 + 3
Answer:
C
Step-by-step explanation:
got it right on edge
Answer:
C
Step-by-step explanation:
g(x) = 3x2 – 4
Heat is transferred through a piece of metal by _____. conduction convection radiation
Answer: conduction
Step-by-step explanation:
Answer:
conduction
Step-by-step explanation:
its obvioues lol
Given: NM || PO and Angle 1 is congruent To angle 3
Prove: LM || NO
Given
Transitive property
Alternate interior angle theorem
Converse alternate interior angle theorem
Answer:
i. LM || NO (converse alternate interior angle theorem)
ii. <1 ≅ <2 (alternate interior angle theorem)
Step-by-step explanation:
Two or more lines are said to be parallel if they do not meet when extended, even till infinity.
Alternate angles are said to be equal in measure.
Given that;
<1 ≅ < 3,
Since <2 ≅ <3 (alternate interior angle theorem)
Then,
<1 ≅ <2 (transitive property)
Also,
<1 ≅ <2 (alternate interior angle theorem)
Therefore since <1 ≅ <2, thus;
LM || NO (converse alternate interior angle theorem)
∠1 and ∠2 are alternate interior angles .
Alternate interior anglesAlternate interior angles are the angles formed when a transversal intersects two coplanar lines. Alternate interior angles are congruent. Therefore,
∠2 ≅ ∠3 (alternate interior angles)
Since line LM is parallel to line NO, ∠1 and ∠2 are alternate interior angles.
Therefore,
∠1 ≅∠2 (alternate interior angles)
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Which of the following is not a way to show that triangles are similar?
a) AAA similarity
b) SAS similarity
c) SSA similarity
d) SSS similarity
Option c) SSA similarity is not a way to show that triangles are similar.What is similarity?The term "similarity" implies that two things are similar. In geometry, two figures are similar if they have the same shape but are of different sizes.
There are various methods to show that triangles are similar, such as AAA similarity, SAS similarity, SSS similarity, and so on.SSA similarity is not a way to show that triangles are similar. SSA similarity is where two triangles share a pair of angles and one side that is opposite to one of the angles, but the triangles are not necessarily congruent. If two triangles have an equal angle and their corresponding sides are in the same ratio, they are only similar, not congruent. This method is inadequate for determining whether or not triangles are similar.
In geometry, two triangles are said to be similar if they have the same shape but are not necessarily the same size. In other words, the corresponding angles are equal, and the corresponding sides are proportional. It can be shown that if any two angles of one triangle are equal to any two angles of another triangle, then the third angles must also be equal. In this case, the triangles are said to be similar.Various methods exist to demonstrate that triangles are similar, including the AAA similarity, SAS similarity, SSS similarity, and so on. These methods all have different criteria for determining similarity.AAA similarity is when two triangles have three corresponding angles that are equal. The triangles are then considered to be similar.SAS similarity is when two triangles have two corresponding sides that are in proportion, and the included angle is equal. In this case, the triangles are said to be similar.SSS similarity is when two triangles have corresponding sides that are proportional. If all three pairs of corresponding sides are proportional, the triangles are similar.SSA similarity is not a method for proving similarity since it is not unique. In other words, two triangles can have the same angle-side-angle configuration and not be similar. The reason for this is that it is possible for one triangle to have a longer side than the other. In this case, the triangles would not be similar.
Option c) SSA similarity is not a way to show that triangles are similar. Two triangles can have the same angle-side-angle configuration and not be similar if one triangle has a longer side than the other. If two triangles have an equal angle and their corresponding sides are in the same ratio, they are only similar, not congruent. Therefore, the correct option is c).
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The math department at a university is hiring a new professor. Two candidates for the job will be interviewed by the same five current department members. Each member will score candidates on a scale of 1 to 10, according to several important criteria. From the candidates' applications, the department head suspects that Candidate 1 is more qualified for the job than Candidate 2. These data are best analyzed using a. a one-sample t procedure. b. a two-sample t procedure. c. a matched pairs procedure.
The data in this scenario are best analyzed using a two-sample t procedure. The reason is that there are two distinct groups or samples being compared: the scores given by the department members to Candidate 1 and Candidate 2.
The department head suspects that Candidate 1 is more qualified, and the objective is to determine if there is a significant difference in the scores between the two candidates. A two-sample t procedure allows for the comparison of means between two independent groups. It tests the null hypothesis that there is no difference in the means of the two groups. In this case, the null hypothesis would be that there is no significant difference in the scores given by the department members to the two candidates. By conducting a two-sample t-test, the department can assess whether the evidence supports the department head's suspicion and make an informed decision regarding the hiring process.
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The ratio of the complements of two angles is 3:2
please answer my question
100+10% =
Answer:
110
Step-by-step explanation:
10% of 100 is 10
100+10=110
Solve. x/4 + ½ = 1/8
x = ____ (Simplify your answer.)
Answer:
[tex] \frac{x}{4} + \frac{1}{2} = \frac{1}{8} [/tex]
[tex] \frac{x}{4} = - \frac{3}{8} [/tex]
[tex]x = - \frac{3}{2} = - 1 \frac{1}{2} [/tex]
The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.
Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.
x/4 + 1/2 = 1/8
Take the 1/2 term on the other side,
x/4=1/8 - 1/2
Taking the LCM on the Right side,
x/4 = (1-4) / 8
x/4 = -3/8
Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,
x = ( -3/8) * 4
x = -3/2
The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.
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PLZ HELP FAST ! find the value of x
Answer:
The answer to x is 7
Step-by-step explanation:
because 4x7 is 28 and + 4 = 36
fastest to lowest
= 13.04 seconds
= 13.06 seconds
= 13.4 seconds
= 13.6 seconds
= 13.12 seconds
Malaki puts $250 in his savings account at 2.5% interest. How much will he have in his account after 7 years?
Malaki will have approximately $296.16 in his Savings account after 7 years.
To calculate the amount Malaki will have in his savings account after 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount in the account,
P is the principal amount (initial deposit),
r is the annual interest rate (expressed as a decimal),
n is the number of times interest is compounded per year, and
t is the number of years.
Given:
P = $250 (initial deposit),
r = 2.5% = 0.025 (interest rate expressed as a decimal),
n = 1 (interest compounded annually),
t = 7 (number of years).
Plugging these values into the formula, we have:
A = $250(1 + 0.025/1)^(1*7)
A = $250(1 + 0.025)^7
A = $250(1.025)^7
A = $250(1.184654712)
A ≈ $296.16
Therefore, Malaki will have approximately $296.16 in his savings account after 7 years.
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Choose the mixed number for this decimal.
2.1
A.
2
1
10
B. 2
C. 2
11
100
D.
12
100
Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
A.5√2 /2
B.5√3
C.5√2
D.5√3 /2
The value of the variable is A.5√2 /2
How to determine the valueWe are given to find the value of the variable 'x' in the figure.
We can see that the figure is a right-angled triangle with the length of the hypotenuse as follows:
h = 5 units.
Now, with respect to the angle of measure 45°, the length of the perpendicular is x units.
That is, p = x units.
From relations between trigonometric ratios, we have;
sin θ = opposite/hypotenuse
substitute the values, we get;
sin 45 = perpendicular/hypotenuse
1/√2 = p/h
1/√2 = x/5
cross multiply, we get;
x = 5/√2
x = 5√2/2
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