Find the number of all the 2-digit numbers satisfying the
following congruences x = 3(mod7), x = 2(mod5).
OLEASE HELP
Use the Chinese remainder theorem.
Start with x = 3×5 + 2×7 = 15 + 14 = 29. Now,
• 29 ≡ 15 ≡ 1 (mod7)
• 29 ≡ 14 ≡ 4 (mod5)
Adjust for this by multiplying the first term in x by 3, and the second term by 3 (because 4×3 ≡ 12 ≡ 2 (mod5)).
So now x = 3×5×3 + 2×7×3 = 45 + 42 = 87, and
• 87 ≡ 45 ≡ 3 (mod7)
• 87 ≡ 42 ≡ 2 (mod5)
The CRT then says that x ≡ 87 (mod(7×5)) ≡ 87 (mod35), which is to say any number x = 87 + 35n satisfies both congruences (where n is any integer).
So there are 3 possible 2-digit numbers that work: {17, 52, 87}.
To confirm:
• 17 ≡ 15 + 2 ≡ 2 (mod5) and 17 ≡ 14 + 3 ≡ 3 (mod7)
• 52 ≡ 50 + 2 ≡ 2 (mod5) and 52 ≡ 49 + 3 ≡ 3 (mod7)
• 87 ≡ 85 + 2 ≡ 2 (mod5) and 87 ≡ 84 + 3 ≡ 3 (mod7)
Write equations for the vertical and horizontal lines passing through the point (5,-9).
Answer:
the vertical line is:
x = 5
The horizontal line is:
y = -9
Step-by-step explanation:
A vertical line has a fixed x-value, while a horizontal line has a fixed y-value.
Then we can write a vertical line as:
x = a
and a horizontal line as
y = b
Then, if we want a vertical line that passes through the point (5, -9), remember that the x-vale will be fixed, then we fix the x-value at the same x-value of the point, which we know that is 5, then the vertical line that passes through the point (5, -9) is:
x = 5
While the horizontal line that passes through the point (5, -9) will be a line with the y-value fixed at the y-value of the point, which we know is -9
Then the horizontal line is:
y = -9
Rewrite using exponents
AxAxAxAxAxAxA
need answer quick!!! please
Answer:
A^7
Step-by-step explanation:
Best answer gets brainliest and 5 stars
Answer:
A
Step-by-step explanation:
pgt states if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Answer:
Does the answer help you?
Answer my question
im being timed
Answer:
the third one
Step-by-step explanation:
Help me, please
I really need
Answer:
answrr
yes ok
Step-by-step explanation:
4+4-4#_44
Correct answer get brainliest and 5 star
Answer:
B
Step-by-step explanation:
(Slant height)^2= (Radius)^2+(Height)^2
(20)^2= (12)^2+(Height)^2
Height=16
Answer:
B. pls mark me at brainliest and like my answer.
Step-by-step explanation:
⩥ɓeŋʝ⩤
If s = 6 and t = 4, find the value of x.
x = 4 + s - t
Answer:
x = 6
Step-by-step explanation:
s = 6
t = 4
x = 4 + s - t
Substituting s and t in equation,
x = 4 + 6 - 4
x = 6
Answer:
6
Step-by-step explanation:
s=6
t=4
x= 4+6-4
x=10-4
x=6
Therefore; the final result is 6
Debt is a result of spending more than you make.
True
False
The perimeter of a rectangle is 74 inches. If the length is five more than the width, what are the rectangle's measurements?
Answer:
P=2(74)+2(5)
148+10=158
HELP ASAP KHAN NEED HELP NOW ITS KHAN
Answer:
[tex]{ \bf{ \green{line \: B}}}[/tex]
It's a direct proportionality
what is |x-4| if x>4
Answer:
x-4
Step-by-step explanation:
If x>4, |x-4|>0 which means |x-4|=x-4
-2z² + 4z + 2z² = ?
Anyone know this?
Answer:
4
Step-by-step explanation:
Let's simplify step-by-step.
−2z2+4z+2z2
Combine Like Terms:
=−2z2+4z+2z2
=(−2z2+2z2)+(4z)
=4z
Answer:
4z
Hope this helps <3 Need thanks?
Comment /hearthelp
[tex]\\ \sf\longmapsto -2z^2+4z+2z^2[/tex]
Combine like. variables[tex]\\ \sf\longmapsto -2z^2+2z^2+4z[/tex]
[tex]\\ \sf\longmapsto (-2+2)z^2+4z[/tex]
[tex]\\ \sf\longmapsto 0z^2+4z[/tex]
[tex]\\ \sf\longmapsto 4z[/tex]
pls explain me i will make u as brainlist
Answer:
hope this help you
have a great day
Any help would be nice
Answer:
11. angles on a straight line add up to 180
so 180 -133 equal to b.b=47
12.Vertical opposite angles are equal.
therefore b=50
an obtuse angle is an angle which is _______
Answer:
an obtuse angle is an angle that is more than 90 degrees
Step-by-step explanation:
Laura brought some fish; salt water ($2 each) and fresh water ($1 each). If she has 15 fish - how many of each did she buy?
Answer:
are you sure there is no further info
Step-by-step explanation:
A point is chosen randomly on KN. Identify the probability that the point is on KL or MN.
Answer:
11/18
Step-by-step explanation:
KL + MN = 11
Total = 18
Probability of KL or MN = 11/18
Write an equation
in slope y-intercept form A(2,6),m=0
Solve for b:
y = 0x + b
6 = 0 + b
b = 6
The answer is y = 0x + 6
value of the pronumeral and describe the rule.
4,1,-2,p,-8,-11
Answer:
p = -5
every element in the sequence is created by subtracting 3 from the pervious element.
Step-by-step explanation:
I am not sure you put every necessary information here.
but I'd the visible information is truly everything, then it's is trivial.
the difference between 4 and 1 is ... well, -3. meaning we subtract 3 from 4 to get 1.
we suspect this is the rule and keep trying.
1 -3 = -2
hey it works.
and -8 -3 = -11
hey, also correct.
and the difference between -2 and -8 is -6, and when we place another item in between (p), we cut that in half again to -3. so, it is all consistent.
therefore,
p = -2 -3 = -5
the rule is
an = an-1 - 3
help pls pls pls pls pls pls
Warren has money to go see a movie after he pays $8 for the MOVIE he will have $14 left right and solve an equation to show how much money Warren has before paying for the movie
Answer:
$(8+14)
Step-by-step explanation:
Amount of money Warren has at first=$8+$14=$22
What is the value of x in the equation 1/5x - 2/3y
=
30, when y = 15?
Answer:
x = 200
Step-by-step explanation:
Plug in 15 as y into the equation and solve for x:
1/5x - 2/3y = 30
1/5x - 2/3(15) = 30
1/5x - 10 = 30
1/5x = 40
x = 200
So, when y = 15, x = 200
Find the measure of b.
please help!
=======================================================
Explanation:
The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.
------------
A slightly longer alternative path would be to do this:
The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...
20+20+c = 180
40+c = 180
c = 180-40
c = 140
Then angle b is supplementary to this
b+c = 180
b+140 = 180
b = 180-140
b = 40
This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.
In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.
X = [?]°
Dr.
X Х
As
140°
B
C
Answer:
40°
Step-by-step explanation:
x+140=180°(angle on a straight line)
x=180-140
x=40°
∠DBA and ∠DBC are making linear pair.
Linear pair of angles are formed when two lines intersect each other at a single point.
The sum of angles of a linear pair is always equal to 180°[tex] \rm \large\longrightarrow \: \: x \: + \: 140 \degree \: = \: 180 \degree[/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 140 \degree \: [/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 40 \degree[/tex]
What is 15.4624 divided by 0.32
Answer:
48.32
Step-by-step explanation:
Find the Measure of one interior angle for each polygon
Answer:
5 corners : 108 degrees
6 corners : 120 degrees
Step-by-step explanation:
there are (at least) 2 different views to get the result :
officially (usually the teachers' preferred method) you consider a polygon as a combination of non-overlapping triangles. a polygon with n corners or edges we can split into n-2 such triangles.
each triangle has an angle sum of 180 degree.
so, the polygon angle sum is (n-2)×180 degrees.
and each (internal) angle is then (n-2)×180/n
n = 5 : (5-2)×180/5 = 3×36 = 108 degrees
n = 6 : (6-2)×180/6 = 4×30 = 120 degrees
the second approach (I prefer) goes after the external angles of the polygon.
the sum of all external angles in any polygon is 360 degrees (a full circle).
for n corners/edges each external angle is 360/n.
and the internal angle is then the complement to 180 degrees = 180 - 360/n
n = 5 : 180 - 360/5 = 180 - 72 = 108 degrees
n = 6 : 180 - 360/6 = 180 - 60 = 120 degrees
ABCD is a parallelogram, AE=16, AB=24, EC=2y-4, DE=67, and EB = 2x+7. Solve for x. (Round your answer to one decimal place, if necessary.) Plz help will give brainliest
Answer:
x = 30
Step-by-step explanation:
The diagonals are bisected so DE =EB
67 = 2x+7
Subtract 7
67-7 = 2x+7-7
60 =2x
Divide by 2
60/2 =2x/2
30 = x
8 ÷ -2 · 42 + 9 i need help please
You and six friends play on a basketball team. A sponsor paid $100 for the league fee, x dollars for each player’s T-shirt, and $68.25 for trophies. Write an expression for the total amount paid by the sponsor
Answer:
Total amount paid by the sponsor = 175 + 6d
Step-by-step explanation:
You and 5 friends = 6 people
Cost of renting a bus = $75
Team entry fee = $100
Cost of each student t shirts = $d
Cost of 6 student t shirts = $d × 6= $6d
Write an expression for the total amount the sponsor paid.
Total amount paid by the sponsor = Cost of renting a bus + Team entry fee + Cost of 6 student t shirts
= $75 + $100 + $6d
= $175 + $6d
Total amount paid by the sponsor = 175 + 6d
Where,
d = cost of each student t shirts