Step-by-step explanation:
9 miles per day
8 days hiking
9m x 8d = 72 miles long
Determine the greatest common divisor of the elements of the set \[ s = \{ n^{13} - n \mid n \in \mathbb{z} \}. \]
Answer:
2730
Step-by-step explanation:
We want to determine the greatest common divisor of the elements of the set [tex]S = \{ n^{13} - n \mid n \in \mathbb{Z} \}.[/tex]
We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.
Now, [tex]n^{13} \equiv n \mod p [/tex] if p-1 divides 12.
Since the of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.
Therefore, the gcd of the elements in [tex]2^{13}-2[/tex] and [tex]3^{13}-3$ is 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13.[/tex]
2*3*5*7*13=2730
Therefore, the gcd of the elements in set S is 2730.
Add: x5 - 4x + + 7x3 + 8, 9x 3 + 7x2 - 10, and -2x 5 + 7x4 - 3x + 8.
ED
Step-by-step explanation:
x5 - 4x + 7x3 + 8 + 9x3 + 7x2 - 10 - 2x5 + 7x4 - 3x + 8
Arranging
x5 - 2x5 + 7x4 + 7x3 + 9x3 + 7x2 - 4x - 3x + 8 - 10 +8
-1 + 7x4 + 16x3 + 7x2 - 7x + 6
7x4 + 16x3 + 7x2 - 7x + 5
Find the sum of 0.312, 0.14 and
0.7 (a) 0.152 (b) 0.158 (C)
Answer:
i'm sorry but the answer is 1.152
Answer:
[tex]1.152[/tex]
Step-by-step explanation:
[tex] \: \: \: \: \: 0.312 \\ + 0.14 \\ + 0.7 \\ =1.1 52[/tex]
hope this helps you.
Please answer this equation ❤️
Just take the function, and wherever it says 'x', substitute '-3' .
Then it'll say f(-3) = -2(-3)² - 7(-3) + 6 . Surely you can solve that.
As my old Electronic Circuits professor used to tell us, back around 1962:
"If
f(x) = -2x² - 7x + 6
then
f(cow) = -2cow² - 7cow + 6 ."
Of all the things I learned from him, this is the thing I remember most.
Answer:
f(-3)=9Solution,
[tex]f(x) = - 2 {x}^{2} - 7x + 6 \\ f( - 3) = - 2 \times {( - 3)}^{2} - 7 \times ( - 3) + 6 \\ \: \: \: \: \: = - 2 \times 9 - ( - 21) + 6 \\ \: \: \: = - 18 + 21 + 6 \\ \: \: \: = 3 + 6 \\ \: \: \: \: \: = 9[/tex]
hope this helps...
Good luck on your assignment..
In how many ways can the letters
in the word glacier be arranged?
Answer:
5,040 times
Step-by-step explanation:
Since there are 7 letters in the word glacier, and there is no set limit, the formula would look like this;
7x6x5x4x3x2x1
(and techinacally 0 counts as 1, but since any number x 1 is itself, it's unnecessary to put it in there)
All of this adds up to 5,040
(I also have acellus and I've already checked it and it's correct )
Answer:
5,040
Step-by-step explanation:
the subject of the formula below is y. y = 2x - pq rearrang the formula to make x the subject PLS HELP I NEED IT NOW FOR MINECRAFTS SAKE ME WANNA PLAY BUT ME NEED THE QUESTION PLS
Answer:
I am grade a man who is not in my life and I am 97 and the other is that 93inches is the urge for the pain of his life and I think that he is not a good person to be a
Answer:
2x=y
Step-by-step explanation:
Done
f(x) = x^2. What is g(x)?
Answer:
Third option.
Step-by-step explanation:
The coordinates are (1, 3)
x = 1
y = 3
Put x as 1, the output should be 3.
g(1) = 3(1)²
g(1) = 3(1)
g(1) = 3
The transformation of a function may involve any change. The function of the g(x) can be written as 3x². The correct option is C.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f(\dfrac{x}{k})Given that f(x)=x², since the function g(x) is also similar to f(x), therefore, both the function are quadratic functions.
Since f(x) is streched vertically to form g(x), therefore, the function g(x) in terms of f(x) can be written as,
g(x) = k × f(x)
y = k × x²
Also, it is passing through the point (1,3), therefore, we can write,
3 = k × (1)²
3 = k
Thus, the function of the g(x) can be written as 3x².
Hence, the correct option is C.
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Find the number of ways of arranging the numbers 1, 2, 3, . . . , 9 in a 3 × 3 grid, so that the sum of the numbers in each row is odd.
Answer: 151,200 combinations
Step-by-step explanation:
So we want to order the numbers 1, 2, .... , 9 in a:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
such that the sum in each row is an odd number.
if we add 3 odd numbers we have an odd number.
if we add 2 even numbers, and an od number, we have an odd number.
where the rows are in this case (1, 2, 3), (4,5,6) and (7, 8, 9)
We have 4 even numbers and 5 odd numbers, so one combination can be:
[tex]\left[\begin{array}{ccc}1&5&3\\4&7&6\\2&8&9\end{array}\right][/tex]
Now, we for this option we can:
permute the numbers in each row: c =3*2*1 options per row and permute the rows, also c = 3*2*1
So only for this combination we have: P = (3*2)^4 possible ways of writing it.
Now, let's find the different combinations of numbers, so you can expect that we will find a lot of combinations, now let's construct them:
Suppose that in the first row we have two even numbers and 1 odd, then for the first even number we have 4 options, for the second 3 options, and for the odd number 5 options, so we have 4*3*5 combinations.
For the second row we also want two even numbers and one odd.
For the first even number we have 2 options, for the second one, and for the odd number we have 4 options, so we have 4*2*1 combinations.
In the last row we want the other 3 odd numbers, so we have 3*2*1 combinations, this adds to:
C = (4*3*5)*(3*2*1)*(4*2*1) = 2880 combinations.
If we add the fact that the rows can interchange positions, we have other 3*2*1 combinations:
C = 2880*3*2 = 16,800 and if now we add the fact that the numbers in the first two rows can permute (it is not the same (2, 4, 5) than (2, 5, 4) or (4, 2, 5)) (this happens because in these two rows we have different types of numbers, while in the third one the permutations are already included)
So the thing that can change in the first two rows is the position of the odd number, can be first, second or third, so we have other 3 permutations for the two first rows:
C = 16,800*3*3 = 151,200 which is the total number of different combinations.
n x 3 = what’s the answer
Answer:
3n
Step-by-step explanation:
A tv costs £1300. Work out the price after a 4.2% price increase.
Answer:
Step-by-step explanation:
1300 x 1.042 = $1354.6
Simple question
Just don’t know how to put it in
please :))
Answer:
A. 102
B. 78
Step-by-step explanation:
mEG = 360 - 258 = 102°
m∠EFG = 1/2 ( major arc - manor arc) = 1/2 (258 - 102) = 78°
Connor is stuck in a traffic jam on a single-lane road. The traffic report tells him the
traffic jam stretches for 5.5 miles.
If Connor assumes each car is about 12.5 feet long, which calculation is most
reasonable for Connor to use to find about how many cars are stuck in the traffic jam?
Answer:
Cornor should divide the total length of the road on which there is traffic by the length of each of the cars
Step-by-step explanation:
The best calculation he can use is to divide the total length of the road on which we have the traffic by the length of each of the cars
Mathematically, the best way to go about this is to convert the miles to feet then divide by the length of each of the cars
Mathematically 1 mile = 5280 feet
so 5.5 miles will be = 5280 * 5.5 = 29,040 feet
It is this length we shall now divide by 12.5 ft
And that is 29,040/12.5 = 2,323.2
Which is approximately 2,323 cars
The value of y varies directly with x, and y = 40 when x = -5. Find y when x = 8
Answer: y=-64
Step-by-step explanation:
From the first sentence: the value of y varies directly with x:
y∝x
y=cx where c=variation constant
When y=40 x=-5
40=-5c
Therefore c=-8
To find y when x=8
y=cx where c=-8 and x=8
y=-8*8
y=-64
Please it’s urgent please❤️
Answer:
280 kg
Step-by-step explanation:
279.98... so it rounds up to 280
Answer:
58kg
Step-by-step explanation:
127 pounds to kg is 57.606 kgs
divide pounds by 2.205
which of the following best describes the slope of the line below
In ABC, if the lengths of sides a and c are 8 centimeters and 16 centimeters, respectively, and the measure of C is 35 degrees, what is the measure of A to two decimal places
Answer:
∠ A ≈ 16.67°
Step-by-step explanation:
Using the Sine rule in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values
[tex]\frac{8}{sinA}[/tex] = [tex]\frac{16}{sin35}[/tex] ( cross- multiply )
16 sinA = 8 sin35° ( divide both sides by 16 )
sin A = [tex]\frac{8sin35}{16}[/tex] , thus
∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{8sin35}{16}[/tex] ) ≈ 16.67° ( to 2 dec. places )
130 apples at the party. There were 3 times as many yellow apples as green apples, there were twice as many red apples as yellow apples. How many red apples were at the party
Answer: There were 78 red apples at the party.
Step-by-step explanation:
This situation can be represented by the equation
x + 3x + 2(3x) = 130 where x is the number of green apples, 3x is the number of yellow apples and 2(3x) is the number of red apples.
Now solve for x
x +3x +2(3x) =130
4x + 6x = 130
10x = 130
x = 13
Now we know that x is 13 so put it into the expression for red apples and solve for the actual number of red apples.
2 * (3*13) = ?
2 * 39 = 78
The / that is measured at 220° is a reflex angle. The opposite angle is obtuse. Find the measure of obtuse /.
Answer:
140
Step-by-step explanation:
Sum of angles around a point = 360
So, if one angle 8 reflex and measures 220, it’s adjacent side measures.
360-220 = 140.
Hope this helps.
Good Luck
If an image of a triangle is congruent to the pre-image, what is the scale factor
0 0.1
1/2
2
1
10
Answer:
The answer is C: 1
Step-by-step explanation:
For each sequence, find the first 4 terms and the 10th term.
a) 12-n
b) 5 - 2n
c) n^2+3
d) 2n^2
(Photos are Attached!)
Answer:
Step-by-step explanation:
Sequence (a),
Recursive formula of given sequence has been given as,
T(n) = 12 - n
First 4 terms of the sequence will be,
T(1) = 12 - 1 = 11
T(2) = 12 - 2 = 10
T(3) = 12 - 3 = 9
T(4) = 12 - 4 = 8
And 10th term of the sequence will be,
T(10) = 12 - 10 = 2
Sequence (b),
Recursive formula is,
T(n) = 5 - 2n
T(1) = 5 - 2 = 3
T(2) = 5 - 4 = 1
T(3) = 5 - 6 = -1
T(4) = 5 - 8 = -3
T(10) = 5 - 20 = -15
Sequence (c),
Recursive formula is,
T(n) = n² + 3
T(1) = 4
T(2) = 7
T(3) = 12
T(4) = 19
T(10) = 103
Sequence (d),
Recursive formula,
T(n) = 2n²
T(1) = 2
T(2) = 8
T(3) = 18
T(4) = 32
T(10) = 200
4. Television sets used to come with an aspect ratio of 4:3 (width is 4 units and height is 3 units). Since broadcast channels in the United States are now broadcasting in 16:9, most newer sets come with a 16:9 aspect ratio. Your brother believes that since you can rewrite the ratio 16:9 as 4^2:3^2, that means a 4:3 television set is similar to a 4^2:3^2 television set. Is this true? What argument would you use to clarify your or your brother’s thinking? What are the dimensions of a television set that would be similar to the 4:3 set?
Answer:
8
Step-by-step explanation:
Can I get help with this problem
Answer:
AC = 90, AB = 90, CAB = 180
If Shadrik can read 29 pages of a book in one hour, how many pages could he read in 15 hours if he continued to read at this rate?
Answer:
435 pgs
Step-by-step explanation:
29 pgs per hr
29(15) pgs per 15 hr
435
Answer:
435 pgs
Step-by-step explanation:
29 x 15 = 435
If ZBAC is a right angle and
m_BAD = 30°, then m DAC = [?]°.
Answer:60 degrees
Step-by-step explanation:BAC =90 Degrees
BAD= 30 degrees
Since BAD and DAC are complementary angles, they add up to 90 degrees
So, 90 degrees-30 degrees= DAC which is =60 degrees
HOPE IT WAS CLEAR
Angle DAC is determined to be 60 degrees as it is complementary to angle BAD, which measures 30 degrees.
According to the given information, angle BAD measures 30 degrees. It is stated that angle BAD and angle DAC are complementary angles, meaning they add up to 90 degrees.
To find the measure of angle DAC, we subtract 30 degrees from 90 degrees:
90 degrees - 30 degrees = 60 degrees.
Therefore, the angle DAC measures 60 degrees.
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plz help ASP i need hyelp
Answer:
equilateral acute
Step-by-step explanation:
Answer:
Equilateral Acute Triangle
Step-by-step explanation:
obi's age is twice oba's age 4 years ago obi was three times as old as oba. find their ages
Answer:
Obi's age is 18 and Oba's age is 9
Step-by-step explanation:
Let Obi's age be x and Oba's age be y
Condition 1:
x = 2y -----------(1)
Condition 2:
(x-4) = 3(y-4)
=> x -4 = 3y-12
=> x - 3y = -9 -----(2)
Putting eq (1) in (2)
2y - 3y = -9
=> -y = -9
=> y = 9
Now,
x = 2y
=> x = 2(9)
=> x= 18
Answer:
[tex]8\\4[/tex]
Step-by-step explanation:
Obi's age is [tex]x[/tex].
Oba's age is [tex]2x[/tex].
4 years ago, Obi's age was [tex]x-4[/tex].
4 years after, Obi's age is [tex]2x-4[/tex]
3 times more than Oba's, so [tex]3(x-4)[/tex]
[tex]2x - 4 = 3( x - 4)[/tex]
[tex]2x - 4 = 3x-12[/tex]
[tex]2x - 3x = -12+4[/tex]
[tex]-1x=-8[/tex]
[tex]x=8[/tex]
[tex]x-4\\(8)-4=4[/tex]
Ryan is making pancakes for the Drama Club's pancake breakfast. The table below shows the amounts of pancake mix and milk needed to make enough pancakes to feed different numbers of guests. If there are 63 guests at the breakfast, how much pancake mix and milk are needed? Show your work. (BRAINLIEST FOR FIRST ANSWER)
The amount of mix would be 16 and the amount of milk would be 8 work is in the picture
The equation 9+12m=6+15(m-1) models the following situation: Movie-rental company A charges a sign-up fee of $9 plus $12 per month, and company B charges $6 for the first month plus $15 per month after that. At a certain number of months, the cost of the two companies is equal. Which equation is a simplified version of the one above? 3m = 15 9 + 15m = 12m – 1 3m = 18 9 + 6 – 15 = 15m – 12m
Answer:
3m = 18
Step-by-step explanation:
9 + 12m = 6 + 15(m - 1)
9 + 12m = 6 + 15m - 15
3m = 18
Answer:
3m=18
Step-by-step explanation:
trust
a) What is a semi-regular tessellation? How many semi-regular tessellations are possible? Why aren’t there infinitely many semi-regular tessellations? (5 points)
Answer: Semi-regular tessellations are made of more than one kind of regular polygon. There are only 8 semi-regular tessellations.
A semi-regular tessellation is a tiling of the plane using regular polygons where the arrangement at each vertex is the same but the types of polygons may vary.
There are 8 known semi-regular tessellations.
There is a finite number of possibilities due to the constraints on the arrangements of polygons.
We have,
A semi-regular tessellation, also known as a uniform tessellation or Archimedean tessellation, is a type of tessellation or tiling of the plane where regular polygons are used to fill the space.
In a semi-regular tessellation, the arrangement of polygons at each vertex is the same, but the types of polygons may vary.
To create a semi-regular tessellation, two conditions must be met:
- Each vertex (or corner) of the tessellation must have the same arrangement of polygons around it.
- The sequence of polygons around each vertex must be the same, although the actual polygons may differ.
There are exactly 8 known semi-regular tessellations, which are formed using regular polygons.
These tessellations include combinations of triangles, squares, hexagons, and dodecagons (12-sided polygons). Some examples of semi-regular tessellations include the honeycomb pattern and the tiling known as "Truchet tiles."
As for the question of why there aren't infinitely many semi-regular tessellations, it is because the arrangement and combination of regular polygons at each vertex are constrained.
The conditions for a semi-regular tessellation limit the possibilities for the types and arrangements of polygons. While there are many ways to arrange polygons around a vertex, the number of distinct arrangements is finite.
Thus,
A semi-regular tessellation is a tiling of the plane using regular polygons where the arrangement at each vertex is the same but the types of polygons may vary.
There are 8 known semi-regular tessellations, and there is a finite number of possibilities due to the constraints on the arrangements of polygons.
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Type the expression that results from the following series of steps: Start with t, add 6, multiply by 2, then subtract 5.
Answer:
2(t + 6) - 5
Step-by-step explanation:
If we are strictly following the directions, we first add t and 6 together:
t + 6
Then we multiply by 2 AFTER we add the 2 together:
(t + 6)2
At last, we subtract 5 from everything after:
2(t + 6) - 5
And we have our answer!
Answer:
2(t+6)-5
Step-by-step explanation:
The unknown number is t
=> Adding 6 will make it t+6
=> Multiplying by 2 will make it 2(t+6)
=> Subtracting 5 will make it 2(t+6)-5