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)
I need help plz with this
Answer:
a) 390
b)108
I hope this answer was helpfull for you
pls help i will give brainliest for answer and explanation.
Answer:
36
Step-by-step explanation:
girls:boys=2:3
2units=24
1unit=24÷2=12
boys have 3 units
3units=12 x 3 =36
There are 36 boys
Can someone please help me
Answer:
- 3Step-by-step explanation:
As,
- 0.0084
When estimated,
= - 0.008
[tex] = \frac{ - 8}{1000} [/tex]
Then,
[tex] - 8 \times \frac{1}{1000} [/tex]
[tex] = - 8 \times {10}^{ - 3} [/tex]
Here,
Power of ten as observed is -3
An airplane flies a distance of 800km from A to B. If its average speed is 600km/h, how long does it take to cover that distance?
Answer:
1 hour 33 minutes
Step-by-step explanation:
distance/speed= time
d =800/600
d=1.33
The aeroplane takes 1.33 hours to traverse a distance of 800 km.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: An airplane flies a distance of 800 km with an average speed of 600 km/h
Thus the time taken by the aeroplane to cover that distance is
t=800/600
t=4/3
t=1.33 hours
Hence, The aeroplane takes 1.33 hours to traverse a distance of 800 km.
Learn more about the speed of an object here:
https://brainly.com/question/28224010
#SPJ2
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
is it a,b,c or d?
Answer:
5
5 1/2
6 1/2
Step-by-step explanation:
Let n=1
a1 = 5+(1-1)*(1/6)
a1 = 5
Let n=4
a4 = 5+(4-1)*(1/6)
a4 = 5 +3(1/6)
a4 = 5+1/2 = 5 1/2
Let n=10
a10 = 5+(10-1)*(1/6)
a10 = 5 +9(1/6)
a4 = 5+3/2 = 5 + 1 1/2 = 6 1/2
if sinA=4/5 and cosB=12/13 find the value of:
Sin2A
Answer:
24/25
I hope this will help you.
A water bottling company has purchased the rights to bottle 960 liters of spring water a month from the local spring.
How many 4-liter bottles can they produce a month?
Answer:
becouse 4×960 will give you
3840
Please help me solve this problem fast!!
Answer:
12.53
Step-by-step explanation:
√(11²+(10-4)²)
= √157
= 12.53 (rounded to two decimal places)
Answered by GAUTHMATH
Which of the following is true about the sequence graphed below? (and Why)
Options:
• The sequence is arithmetic because the terms have a common difference.
• The sequence is arithmetic because the terms do not have a common difference.
• The sequence is not arithmetic because the terms have a common difference.
• The sequence is not arithmetic because the terms do not have a common difference.
Answer:
Step-by-step explanation:
a₂ = 9
a₃ = a₂-1.5
a₄ = a₃-1.5
a₅ = a₄-1.5
etc.
The terms have a common difference of -1.5, so the sequence is arithmetic.
Answer:
Step-by-step explanation:
The common difference is a y-thing. It looks like the difference in the y-values of each of these points is -1.5. That means that this is an arithmetic sequence because the common difference is consistently -1.5. In fact, the whole equation can be determined to be
[tex]a_n=-1.5n+12[/tex]
PLZZZZZZ HELPPPPPP!!!!!!!!!
Answer:
1 3/8 ft. tall.
Step-by-step explanation:
First, we need to find a common denominator between the two fractions.
8 is already a common denominator of 2, so convert 1/2 into 4/8.
Then add 7/8 and 4/8 to get 1 3/8 ft. tall.
Hope this helps.
If there is something wrong, just let me know.
Write an equation of a circle given the center (-4,4) and radius r=5
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y - k)² = r² where (h,k) is the center.
Center( -4 , 4) and r = 5
(x -[-4])² + (y - 4)²= 5²
(x + 4)² + (y-4)² = 25
x² + 2*4*x +4² + y² - 2*y*4 + 4² = 25
x² +8x + 16 + y² - 8y + 16 = 25
x² + 8x + y² - 8y + 16 + 16 -25 = 0
x² + 8x + y² - 8y +7 = 0
We have that the an equation of a circle given the center (-4,4) and radius r=5 is mathematically given as
(x-4)^2+(y-4)^2=5^2
Equation of a circle
Question Parameters:
Given the center (-4,4) and radius r=5
Generally the equation for the Equation of a circle is mathematically given as
(x-x')^2+(y-y')^2=r^2
Therefore, The resultant equation will be
(x-x')^2+(y-y')^2=r^2
(x-4)^2+(y-4)^2=5^2
Hence,an equation of a circle given the center (-4,4) and radius r=5 is
(x-4)^2+(y-4)^2=5^2
For more information on Equation visit
https://brainly.com/question/2263981
A fish tank is in the shape of an open glass cuboid 30 cm deep with a base 16 cm by 17 cm, these measurements being external. If the glass is 0.5 cm thick and its mass is 3 g/cm3, find a the capacity of the tank in litres, and the mass of the tank in kg.
Answer:
3.24 kg
Step-by-step explanation:
internal Vol = (30-0.5)(16-1)(17-1) = 7080 cm^3 = 7.08ltrs
external Vol= 30* 16* 17 = 8160cm^3 = 8.16ltrs
Vol of thickness = 8160 - 7080 = 1080cm^3
Mass of the tank= density * volume = 3*1080 = 3,240g = 3.24 kg
x+x+y+y+z+z=24
b+x+x+y+z=21
b+b+y+y=28
x+x+x+y+z=23
ASAP PLEASE
what numbers do the variables stand for
all x’s have the same numbers
all b’s have the same numbers
all y’s have the same numbers
all z’s have the same numbers
Answer:
b = 7/2
x = 11/2
y = 21/2
z = -4
Step-by-step explanation:
2x + 2y + 2z = 24
x + y + z = 12
b + 2x + y + z = 21
2b + 2y = 28
b + y = 14
3x + y + z = 23
we can start anywhere by transforming these equations in a way that always one variable is excised by others.
so, e.g.
b = 14 - y
14 - y + 2x + y + z = 21
2x + z = 7
z = 7 - 2x
3x + y + 7 - 2x = 23
x + y = 16
16 + z = 12
z = -4
-4 = 7 - 2x
-11 = -2x
11 = 2x
x = 11/2
11/2 + y = 16
y = 16 - 11/2 = 32/2 - 11/2 = 21/2
b = 14 - 21/2 = 28/2 - 21/2 = 7/2
One of the angles of a triangle is 110° and the other two angles are equal.What is the measure of each of these equal angles?
Answer:
x = 35
Step-by-step explanation:
Let x be the one of the other angles
X is also the third angle since we know they are equal
The sum of the angles of a triangle is 180
110+x+x = 180
110 +2x= 180
2x = 180-110
2x= 70
Divide by 2
2x/2 = 70/2
x = 35
Answer:
[tex]x = 35 \degree[/tex]
Step-by-step explanation:
Let the unknown angle be x
Unknown Angles are equal to each other so,
[tex]x + x + 110 = 180[/tex]
sum of the interior angles in a triangle is 180°
[tex]2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ \frac{2x}{2} = \frac{70}{2} \\ x = 35 \degree[/tex]
Please hurry I will mark you brainliest
What is the equation of the line through the point (2, 3) with slope -2?
Answer:
y = -2x+7
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -2x+b
Using the point
3 = -2(2)+b
3 = -4+b
3+4 = b
7=b
y = -2x+7
A flag has a perimeter of 5 metres. The length of the flag is 600 mm more than the
width of the flag. The length is represented by L and the width is represented by W.
Which of the linear systems in the choices represents the description?
O2L + 2W = 5
L - 600 = W
O2L + 2W = 5000
L - 600 = W
OL+W = 5000
W + 600 = L
O L x W = 5000
L + 600 = W
Answer:
The first two.
Step-by-step explanation:
See that L is 600mm MORE than W.
From there, you can note that L = W+600
or rearrange the formula and get W= L-600
Then, see that the perimeter of a flag is 2L + 2W
(Because there are two four sides to a rectangle, 2 width, 2 length)
It must total to be 5 meters, or 5000mm
Thus,
2L + 2W = 5000
What is 12% and 22% of 600 added together?
Answer:
204
Step-by-step explanation:
600 * .12 = 72
600 * .22 = 132
72 + 132 = 204
Have a great day!
3+3+3+3+3+3+3+333333
Answer:
333354
Step-by-step explanation:
Simplify the expression.
Answer:
333,354
Step-by-step explanation:
First, we add the 3's. And get 21.
333,333 + 21 = 333,354
can somene explain this to me please?
Answer:
10/3
Step-by-step explanation:
rate of change = gradient
(17-7)/(6-3) = 10/3
basically difference of y values / difference of x values
How do I do this question it is really hard
Answer:
Step-by-step explanation:
What is the slope of a trend line that passes through the points (1, 3) and (10, 25)?
Negative StartFraction 15 Over 2 EndFraction
Negative one-half
StartFraction 22 Over 9 EndFraction
StartFraction 24 Over 7 EndFraction
Answer:
[tex]\displaystyle m = \frac{22}{9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (1, 3)
Point (10, 25)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{25 - 3}{10 - 1}[/tex]Subtract: [tex]\displaystyle m = \frac{22}{9}[/tex]Answer:
c
Step-by-step explanation:
1.
Write a function rule for the table.
Answer:
Step-by-step explanation:
If you plot these points on a graph, you would see that this is definitely a line. Let's find the slope of the line first:
[tex]m=\frac{2-1}{6-5}=1[/tex] (I used the last 2 coordinates on the table because I don't like negatives; and since the slope is the same for the whole entire line, it doesn't matter which points you pick to go into your slope formula)
And then use that slope and any other point in the table to write the equation. I am going to use (4, 0), since I like the 0 (less work!)
In point-slope form:
y - 0 = 1(x - 4) and
y = x - 4
That's the function rule (aka equation) for the table.
When 18 divided by a whole number N, the remainder is 4. Is this true for the many different values of N?
Answer:
2
Step-by-step explanation:
18/14 = 1 remainder 4
18/7 = 2 remainder 4
Un alambre de longitud x s3. E dobla en forma de cuadrado exprese su área en términos de la ingitud x
Respuesta:
A = 1/16 × x²
Explicación paso a paso:
Un alambre de longitud x se dobla en forma de cuadrado. Como un cuadrado tiene 4 lados iguales la longitud de cada lado (l) será:
l = 1/4 × x
Para calcular el área de un cuadrado (A) usaremos la siguiente fórmula.
A = l²
A = (1/4 × x)²
A = 1/16 × x²
Describe how to determine the average rate of change between x = 4 and x = 6 for the function f(x) = 2x3 + 4. Include the average rate of change in your answer.
Answer:
152
ΔY = 436 - 132 =304
Δ X = 6-4 = 2
ΔY/X = 304/2 = 152
Step-by-step explanation:
What is the value of y?
A. 55°
B. 850
C. 10°
D. 110°
Solve 2x + 3y = C, for y
Answer:
y= [tex]\frac{c-2x}{3}[/tex]
Step-by-step explanation:
2x+3y=C
isolate y
3y=C-2x
y= [tex]\frac{c-2x}{3}[/tex]
Can u help me solve this
Answer:
V = 5,324 in^3
Step-by-step explanation:
V = 4([tex]\pi[/tex]r^3)/3
= 4(3)(11^3)/3
= 12(11)(11)(11)/3
= 12(1,331)/3
= 15,972/3
V = 5,324 in^3
Answer:
5575.28 or 5,324 depending on use of pie.
Step-by-step explanation
V=4/3πr3=4/3·π·113≈5575.27976
Hope this helps :)!
This is the answer if pie is used as 3.14.
V = 5,324 in^3 if pie used as 3.
V = 5575.28 in^3 if pie used as 3.14.
PLEASE HELP WILL GIVE BRAILNLIEST! Find the value of x
Answer:
x = 14.63
Step-by-step explanation:
Write the sentence as an equation.
351 is 59 subtracted from m
Is means equal to.
59 subtracted from m would be m-59
Answer: 351 = m - 59
