Answers
Answer:
you need to show the number is prime
Step-by-step explanation:
To show 2^7 -1 is prime, you have to show it is not divisible by any prime less than its square root. That root is approximately 2^(7/2) = 2^3×√2 ≈ 11.3.
The primes of in that range are 2, 3, 5, 7, 11. The prime we're testing is ...
2^7 -1 = 128 -1 = 127
The sum of digits is 10, which is not a multiple of 3: not divisible by 3.
The units digit is 7, not 0 or 5: not divisible by 5.
The test for divisibility by 7 is to subtract twice the units digit from the rest of the number: 12 -2(7) = -2. This is not 0 or a multiple of 7, so 127 is not divisible by 7.
We know that 11² = 121, so 127 is not divisible by 11.
All of the tests for primality pass, so 2^7 -1 is a Mersenne prime.
_____
Additional comment
It is known that 2^n -1 being prime requires n to be prime. (The converse is not true: 2^11 -1 = 2047 = 23×89 is not prime.) The discovery of Mersenne primes is an ongoing process involving thousands of computers around the world. Only about 50 such primes are known.
You will notice that we have made use of some divisibility rules in order to simplify the process of dividing by small numbers. These can be helpful in many situations, so can be useful to learn.
Related Questions
An 18-foot ladder is leaning against a wall. The bottom of the ladder is 4.5 feet from the base of the wall.
How high up the wall does the ladder reach? Round your answer to the nearest tenth, if necessary.
A
13.5 feet
B
18.6 feet
o
С
22.5 feet
D
17.4 feet
Answers
Answer:
d
Step-by-step explanation:
use Pythagoras theorem
that is a²+b²=c²
so 4.5²+b²= 18²
rearrange to b²=18²-4.5²
so you get b=
[tex] \sqrt{303.75} [/tex]
that is equal to 17.42842506
i keep this all day what is 6 + 6 × 6 + 6 ÷ 6=
Answers
Answer:
43
Step-by-step explanation:
6 + 6 × 6 + 6 ÷ 6
using BIDMAS, we do the division first
6÷6=1
then multiplication
6×6=36
leaving us with:
6+36+1=43
Hopefully this helped- have a good day)
Let's do
6+6×6+6÷66+36+17+3643Done!
Make x the subject of the formula: y=x^{2} + 5
Answers
First, multiply both sides by (x - 5), so you end up with:
(x-5)y = x + 2
Which can be expanded to give you:
xy - 5y = x + 2
Now add 5y to both sides to obtain:
xy = x + 2 + 5y
Now subtract x from both sides:
xy - x = 2 + 5y
Factorise x out:
x(y - 1) = 2 + 5y
Divide both sides by (y - 1):
x = 2 + 5y/y - 1There you go, x is now the subject.
Using the GCF you found in Part b re write 35 +63 factor one factor is the GCF and the other is the sum of the two numbers that do not have a common factor show your work
Answers
Answer:
7(9 + 14)
Step-by-step explanation:
The Greatest Common Factor of 35 and 63 is 7; both 35 and 63 are evenly divided by 7. Thus, 35 + 63 can be rewritten as 7(5) + 7(9), or 7(14)
So 35 + 63 = 7(9 + 14)
Answer:
= 98
Step-by-step explanation:
solve for x: 2-3(2x-2)=17
Answers
Answer:
x = - 1.5
Step-by-step explanation:
2 - 3(2x - 2) = 17 ← distribute parenthesis
2 - 6x + 6 = 17 , simplify
8 - 6x = 17 ( subtract 8 from both sides )
- 6x = 9 ( divide both sides by - 6 )
x = [tex]\frac{9}{-6}[/tex] = - [tex]\frac{3}{2}[/tex] = - 1.5
d= sqrt ( 2 )^ 2 +( 12 )^ 2
Answers
Answer:
d = 146
Step-by-step explanation:
Answer:
d=146
Step-by-step explanation:
the sqrt of 2(2) is 4 which can be simplified to 2 and the 12 raised to the second power is 144 so 2+144 is 146
what cubed is equal to 1000?
Answers
Answer:
10
Step-by-step explanation:
Classify the following triangle
(Chose multiple)
-Equilateral
-Isosceles
-Scalene
-Acute
-Equiangular
-Obtuse
-Right
Answers
Answer:
Scalene
Acute
Obtuse
Step-by-step explanation:
≠ Equailateral because all the sides in the given triangle are not equal nor are the three angles 60°
≠ Isosceles because the triangle doesn't have two equal sides nor two equal angles
= Scalene as all the sides are of different lengths and so are all the angles with different degrees.
= Actue because QPO and PQO are less than 90°, thus they are acute angles
≠ Equiangular because none of the given angles are of the same degree.
= Obtuse as POQ is greater than 90°
≠ Right because the given triangle does not have a right angle
All the numbers round to 7 except
6.61
7.89
6.58
7.37
Answers
7/8 in lowest terms ?
Answers
Answer:
7/8 simplified to lowest terms is 7/8.
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 7 and 8 is 1
Divide both the numerator and denominator by the GCD
7 ÷ 1
8 ÷ 1
Reduced fraction:
7
8
Therefore, 7/8 simplified to lowest terms is 7/8.
y=x−4
y=4x+2
Find x and y
Answers
Answer:
x = -2
y = -6
Step-by-step explanation:
x - 4 = 4x + 2
-4 = 3x + 2
-6 = 3x
x = -2
y = -2 - 4; y = -6
Choose the graph that matches the following system of equations:
x + y = 4
2x + 3y = 18
Picture of coordinate plane with line y equals negative x plus 4 and line y = equals negative 2 thirds x plus 6. They intersect at negative 6, 10.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x plus 6. They intersect at 6, 2.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x minus 6. They intersect at negative 1.2, negative 5.2.
Picture of coordinate plane with line y equals x plus 4 and line y equals negative 2x plus 6. They intersect at 0.67, 4.67.
Answers
Answer:
Line x-intersect: -6
y-intersect: 10
Step-by-step explanation:
X + y = 4
x = 4-y
2(4-y) + 3y = 18 (substitution)
8-2y+3y = 18
y = 18-8
y = 10
x + 10 = 4
x = -6
please help! i need for this to be done.
Solve.
t+7.45=1334
Enter your answer as either a decimal or a mixed number in simplest form in the box.
t =
Answers
Answer:
t = 6.3
Step-by-step explanation:
t + 7.45 = 13 [tex]\frac{3}{4}[/tex] = 13.75 ( subtract 7.45 from both sides )
t = 6.3
Find the slope of the line (-3,-2),(1,-2)
Answers
Answer:
0
Step-by-step explanation:
The y-axis is the same so the slope has to be zero, since the line is not going vetrically anytime on the graph
identify all possible answer for the statement below.
Answers
Answer:
it simple there nothing there Step-by-step explanation:
help please anybody hmm
Answers
Answer:
94.6-18.8=75.8
75.8 is the answer
Step-by-step explanation:
Hope this helps
May i get braineist pls?
3. The sum of the second term and the ninth term of an arithmetic sequence is -5. The sum of the third and fourth terms of the same sequence is 7. Find the first term of the sequence.
Answers
Answer:
First term of the sequence is [tex]11[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be the first term and [tex]d[/tex] be the common difference
We have
The sum of the second term and the ninth term of an arithmetic sequence is [tex]-5[/tex]
[tex]a+(2-1)d+a+(9-1)d=-5\\\\2a+9d=-5---eqn1[/tex]
The sum of the third and fourth terms of the same sequence is [tex]7[/tex]
[tex]a+(3-1)d+a+(4-1)d=7\\\\2a+5d=7---eqn2[/tex]
eqn 1 - eq2
[tex]4d=-12\\\\d=-3[/tex]
Substituting in eqn 1
[tex]2a+9\times -3=-5\\\\2a=22\\\\a=11[/tex]
First term of the sequence is [tex]11[/tex]
3q+3.97=7.57 please help im stuck on ixl
Answers
Answer:
1.2
Step-by-step explanation:
3q+3.97=7.57
3q=7.57-3.97
3q=3.6
q=3.6/3
q=1.2
26=7(g−9)+1226, equals, 7, left parenthesis, g, minus, 9, right parenthesis, plus, 12
Answers
To find g, we expand the brackets first(multiplying every term in the bracket by the term outside it):
26=7g-63+1226
Add the terms on the right hand side:
26=7g+1163
Collect alike terms to left hand side:
26-1163=7g
-1137=7g
Divide equation by 7 to get g on its own:
g= -162.428 (3dp)
Hope this helps!
Hii I would love if anyone would be able to give me the answer to this <3
Answers
Answer:
×=40
Step-by-step explanation:
The total value of all the angles on any line is 180
so x+(4x-20)=180
40+(4×40-20)=180
Answer:
40°
Step-by-step explanation:
The sum of angles x and (4x - 20) is 180°
x + (4x - 20) = 180
5x = 200
x = 40°
Help ME!
Question 1: Evaluate the expression:
2+5⋅8
Question 8: 10÷(3−1⋅2)
Option answers for Question 8: 4, 10, 10/4, and 2.5
Answers
Answer:
Q1: 42
Q8: 10
Step-by-step explanation:
PEMDAS
What is the factored form of n3+512 (pleas help fast)
A- (n-8)(n^2+8n+64)
B- (n+4)(n^2-4n+128)
C- (n-4)(n^2+4n+128)
D- (n+8)(n^2-8n+64)
Answers
Answer:
Since both terms are perfect cubes, factor using the sum of cubes formula,
a³+b³=(a+b)(a²-ab+b²) where
a=n and b=8
(n+8)(n²-8n+64)
Answer
(n+8)(n²-8n+64)
hi
have a good day
thank me later
Carryonlearing
Answer:
Step-by-step explanation:
The only one that has a chance of being correct is D. That's because the first term is correct and you have to assume that the second one is as well.
cubrt(512) = 8
The first term is (n + 8)
The second term is (n^2 - 8*n + 8^2) = n^2 - 8n + 64
All the other answers have the wrong first term
A: it should be n + 8 not n - 8
B and C are both wrong because the cube root of 512 is 8 not 4.
Find the area of each figure
Answers
Answer:
flu
Step-by-step explanation:
ugh
which function describes the arithmetic sequence shown -5,-7,-9,-11,-13
Answers
Answer:
[tex]n(x)=x-2[/tex]
Step-by-step explanation:
You can notice that between each of the arithmetic sequence there is a addition of 2. So we know that to add a 2 to get the next value. We can write it as n(x) where n is a function where x is the number:
n is the function and x repersent the number which is givenWe can write this function as: [tex]n(x)=x-2[/tex]So if we input x = -5 we will get -7. If we input -11 we get -13.
Write the converse of the following statement. Then determine its validity.
a. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
b. If a parallelogram is a rectangle, then the diagonals are congruent. TRUE.
c. If a parallelogram is a rectangle, then the diagonals are congruent. FALSE.
d. If the diagonals of a parallelogram are not congruent, then the parallelogram is not a rectangle. FALSE.
d. If a parallelogram is not a rectangle, then the diagonals are not congruent. TRUE.
Answers
The converse and the validity of the statement is:
If a parallelogram is a rectangle, then the diagonals are congruent. TRUE.The statement is given as:
If the diagonals of a parallelogram are congruent, then is the parallelogram is a rectangle
Considering the following statement
If a then b
Its converse is:
If b then a
So, the converse of the given statement is:
If a parallelogram is a rectangle, then the diagonals are congruent.
The diagonals of a rectangle are true.
Hence, the validity is true.
So, the true statement is (b)
Read more about converse statements at:
https://brainly.com/question/4421013
Explanation of approximation, decimal place, significant figure
Answers
Answer:
im not an expert in math but i'll do my best:
1. an approximation is something that is almost, but not exactly something. for example, 5.02 is approximately 5. it's not EXACTLY 5, but it's around 5.
2. decimal place refers to the position of numbers after the decimal point. let's take the decimal number 7.89 for example. there are 2 numbers after the decimal point, which is 8 and 9. hence we say that 7.89 has 2 decimal places.
3. significant figure is kind of hard to explain, so i'll jump into the example straight away.
5.874 to 3 significant figures is 5.87. what i did was count 3 digits: starting from 5 to 7. to round to 3 significant figures, i look at the 4th digit, which is 4 in this case. if it's smaller than 5, i ignore everything past the digit 7, and leave the final answer as 5.87.
if the 4th digit is greater than or equal to 5, i add 1 to the 3rd digit THEN leave out all the numbers after the 3rd digit. (if this were the case, the answer would be 5.88)
lets take a trickier example, 0.064591
in this case i cannot start counting 3 digits starting from 0. i have to count starting from the number 6. the concept in this case is that the 1st significant figure cannot be a 0. in this case the answer to 3 significant figures would be 0.0646.
however, 0 can be a significant figure if it's after another number. for instance 0.90672
the 0 after the 9 would count as a significant figure because it's not the 1st significant figure in the number. however the 0 before the 9 would NOT count as one because 0 cannot be the 1st significant figure. the answer to 3 significant figures would be 0.907.
sorry this was so lengthy, i just hope this answers your question on what these are and how they work. good luck!
What is an equation of the line that passes through the points (4, -1) and (-8, -7)?
Answers
Answer:
y=-1/2x - 3
I think this is it, its been a while though.
y^2 - 19 = 0 find the sum and product
Answers
Answer: Sum of the roots: √19 - √19 = 0
Product of roots: (√19)(-√19) = -19
Step-by-step explanation:
y2 - 19 = 0
add 19 to both sides
y2 = 19
take square root of both sides
y = ±√19
So y = √19 or y = -√19
round 0.006772 to 1 significant figure
Answers
Answer:
0.007
Step-by-step explanation:
0's before other numbers are non-significant. Then you just round your number.
Hope that helps
Can someone help me with this please?