The largest integer that always divides (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n is 15.
What is positive integer?Positive integers are numbers such as 1, 2, 3, etc. They are also called countable or natural numbers. A positive number is any number greater than zero.
Let P(n) = (n+1)(n+3)(n+5)(n+7)(n+9) be a polynomial for all positive even integers, n . We have to calculate the largest integer that always divides the P(n) .
Let "l" be the largest integer that divides P(n) for each n∈N . Then, l must divide both P(1) and P(2)
i.e, P(1) = (1+1)(1+3)(1+5)(1+7)(1+9) = 2×4×6×8×10
= 2^8×5×3
P(2) = 3×5×7×9×11 , hence , l divides 15.
Since, n + 5 ≡ (n+2) mod(3), one (and exactly one) of the numbers n+1 , n+3 , n+5 must be multiple of 3 . Thus, 3/P(n) for each n∈N.
Since, n+7 ≡ (n+2)mod(5) and n+9 ≡ (n+4)mod(5),
one (and exactly one) of the numbers n+1 , n+3 , n+5 , n+7 and n+9 , must be multiple of 5.
Thus, 5/P(n) for each n∈N.
Therefore, 15/p(n) for each n∈N , so that l = 15 .
So, required value of n is 15.
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Brad had a small gathering at a local steakhouse. The steakhouse offers three dinner platters which vary by size and price. They ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 3 of the 11-ounce platters. Steak Platter Prices
• 6-ounce $9.95
• 8-ounce $12.95
• 11-ounce $15.95
If a gratuity of 16% was added to the bill, which of the following is closest to the total of the steak platters and gratuity, ignoring sales tax?
Answer:
Ok if you get this worng im so sorry but I got $6.21
Step-by-step explanation:
If the simple interest on a sum of money invested at 3% per annum for 242 years is N123, find the
principal
The principal is N16.94
Step-by-step explanation:
Simple Interest = (Principal × Rate × Time)/100
Principal = (Simple Interest × 100)/(Rate × Time)
Principal = (123 × 100)/(3 × 242)
Principal = 12300/726
Principal = 16.9421
I’ll give brainliest! Help please!!!!
i need help with this question plsss
Answer:
180
Step-by-step explanation:
because angles on the same line sum up to 180
8 ( x + 4) = 62. 4. x = _____
Answer: 0.05
Step-by-step explanation: Ur welcome
Step-by-step explanation:
8×x+8×4=62.4.x=_
8x+32=62.4.x=_
8x=62.4-32
8x=30.4
x=30.4:8
x=3.8
If a farmer sells 9.8 KL of apples and pears at the farmers market. 4/5 of this weight is apples,and the rest are pears. How many kl of pears did they sell the farmers market
Answer:
1.96
Step-by-step explanation:
A farmer sells 9.8 kl of apples and pears
4/5 of this weight is apples, while the rest are pears
Therefore the wight of pears can be calculated as follows
Let x represent the weight of pears
9.8= 4/5×9.8 + x
9.8= 0.8×9.8+x
9.8= 7.84+x
9.8-7.84= x
x= 1.96
solve x , y , and z. Please help
Answer:
z and x equal 143
y equals 37
Step-by-step explanation:
37-180=143
A student cuts out a rectangular strip of paper that has an area of 2/3 square meter. If the width of the paper strip is 1/5 meter, what is the length of the strip, in meters?
Answer:
3 1/3
Step-by-step explanation:
Perform the inverse operation: l = a/w
(2/3)/(1/5)
Find the common denominator.
It is 15 in this case.
(10/15)/(3/15)
150/45
3 1/3
Check your work.
a = 3 1/3 x 1/5
a = 2/3
This is true.
The answer is 3 1/3
-Xax
Which equation represents a line which is perpendicular to the line 4x + 3y = - 24 ?
Answer:
C
Step-by-step explanation:
4x+3y=-24
eq. of any line perpendicular to given line is
3x-4y=a
4y=3x-a
y=3/4x -a/4
where a is an arbitrary constant.
What are the steps you would take to find the area of the shaded region? Check all that apply.
Answer:
THE ANSWER IS INCOMPLETE SO IM GOING TO REPORT:/
Step-by-step explanation:
Find the volume of the given figure.
A rectangular prism is 12 feet long, 8 feet wide and 11 feet tall. What is the
surface area? *
192
440
632
O
1056
Answer:
632 square feet
Step-by-step explanation:
Surface area of the prism = 2(lw+wh+lh)
L is the length = 12feet
w is the width = 8feet
h is the height = 11feet
Substitute
S = 2(12*8 + 12*11 + 8*11)
S = 2(96+132+88)
S = 2(316)
S = 632 square feet
Hence the surface are of the prism is 632 square feet
Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and calculates the arc length to be inches. Whose paper is larger? Explain or show your reasoning.
A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The arc length of radius 6 inches is equal to,
Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches
The area of the circular paper = πr² = π×6×6 = 113.097²
The area of the square with a side of 6 inches = 36 in²
Therefore, the area of the circular paper is more than the area of the square.
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23. Daniel bought a gallons of paint at the store for a project. At the end of his project,
Daniel had 1 gallons of paint left. How much paint did Daniel use for his project?
A. 3. gallons
B.3 gallons
c. 2. gallons
D. 6 gallons
Answer:
Based on your responses and my understanding from what you have said the answer is B.
Step-by-step explanation:
HELPPPPPPPPPP
What is the value of x in the triangle?
Answer:
x=130
Step-by-step explanation:
Hello There!
Remember the sum of the angles in a triangle is 180
So we can find the missing angle by subtracting the given angles (25 and 25 in this case) from 180
so x = 180 - 25 - 25
180 - 25 = 155
155 - 25 = 130
x = 130
Please help me please
Answer:
1) g < -6
2) x < -5
3) f < 2
4) y ≤ -2
5) p ≥ 2
in a school the number of girls exceeds the number of boys by 15% find the ratio number of boys to number of girls
Answer:
20:3
Step-by-step explanation:
no.of boys /no.of girls =20:3
Helppp I need to finish this !!!!!
Answer:
filled in dot on -2 and shade the rest to the right (see below)
Step-by-step explanation:
This can also be read as "x is equal to or greater than -2." The "alligator" mouth, aka the inequality sign, is "eating" the x, meaning it's greater than the -2.
First graph the -2. Because it's also equal to, the dot on the -2 is filled in.
The inequality also acts as an arrow. It's pointing to the right, so the rest of the number line to the right is shaded.
This arrow method works only when the variable is on the left side so that is read "x is greater/less than a number."
Given the coordinates of A(3, 6), B(5, 2), and C(9, 4), which coordinates for D make ABCD a square?
Answer:
(7,8)
Step-by-step explanation:
The point D is (7, 8) for which the given coordinates of A(3, 6), B(5, 2), and C(9, 4), make a square.
What is a square?It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.
Line AB and CD are parallel to each other.
Line AB:
(y- 6) = -2(x-3)
y - 6 = -2x+6
2x+y = 12
Line CD:
2x + y = d
Plug (9,4)
18+4 = d
d = 22
2x + y = 22 ...(1)
Line BC:
(y - 2) = 1/2(x-5)
2y -4 = x-5
-x + 2y = -1
x - 2y = 1
Line AD:
x - 2y = e
3 - 12 = e
e = -9
x-2y = -9 ...(2)
The intersection point of (1) and (2)
x = 7 and y = 8
Thus, the point D is (7, 8) for which the given coordinates of A(3, 6), B(5, 2), and C(9, 4), make a square.
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Find the slope from the table:
X | Y
0 | -1
2 | 3
5 | 9
6 | 11
Answer:
The slope is 2
Step-by-step explanation:
Pick two points.
ex: (0,-1) and (2,3)
do the equation below where 0=x1, -1=y1, 2=x2, 3=y2
y2-y1 divided by x2-x1
3-(-1) divided by 2-0
4/2
=2
sorry this was kind of hard to explain on a computer :/
7x −28 solve for inequality
Answer:
7(x-4)
Step-by-step explanation:
You can use an Algebra calculator btw.
IM RUNNING OUT OF TIME SO PLss ANYONEEE
Answer:
x= -2
Step-by-step explanation:
If the slope is zero, that means the line is horizontal.
Answer: y=7
Step-by-step explanation:
Caleb made a scale drawing of a theater. He used the scale 7 inches = 10 feet. What is the scale factor of the drawing?
Answer:
10 feet = 120 inches
120 / 7 = 17.1428571429
So, the scale is 17.1428571429 to 1.
Step-by-step explanation:
which point on the number line represents --3/4
Answer:
D
Step-by-step explanation:
Because it is 3 tics closer to 1. which would be 3/4 of 1
EAR is rotated 180° about the origin.
plsss help
Answer:
rotating ΔEAR 180° inside the right angle parallelogram circumscribed by.
original coordinates:
A (-6, 4)
R (-2, 2)
E (-5, -6)
post rotation coordinates:
A (-2, -6)R (-6, -4)E (-3, 4)That the wrong answer
Answer:
what's your question?
Step-by-step explanation:
I need help with this pls I out 30 points
Answer:
Step-by-step explanation:
Age: Frequency:
50-54 2
55-59 5
60-64 3
65-69 3
I’m about to spam questions if you can answer them please do .
Answer:
id say anything between 15 to 30 i dont have the stuff i need to answer this 100% accurately
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
90 plus 40 ,then you subtract it from 180
The area of a square is 75 inches squared. A student correctly wrote the length of each side of the square as a√3. What is the value of a?
Answer: 5 in.
Step-by-step explanation:
Given
The area of the square is [tex]75\ in.^2[/tex]
The side length of the square is [tex]a\sqrt{3}[/tex]
Area of square[tex]=(\text{length})^2[/tex]
[tex]\therefore 75=(a\sqrt{3})^2\\\Rightarrow 75=3a^2\\\Rightarrow a^2=25\\\Rightarrow a=5\ in.[/tex]
Thus, value of a is 5 inch
Anyone know how to do this?
Answer:
??
Step-by-step explanation: