Find the number of all the 2-digit numbers satisfying the
following congruences x = 3(mod7), x = 2(mod5).
OLEASE HELP

Answers

Answer 1

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)


Related Questions

How do I solve this problem: 6c - 8 - 2c = -16

Answers

Answer:

c = -2

Step-by-step explanation:

6c-8-2c = -16

4c -8 =-16

4c = -16 +8

4c = -8

4c/4 = -8/4

c = -2

Answred by Gauthmath

The solution of the equation 6c - 8 - 2c = -16 is -2 calculated by combining like terms and isolating the variable then dividing the equation by coefficient of the c variable.

To solve the equation 6c - 8 - 2c = -16, isolate the variable c on one side of the equation.

Combine like terms on the left side of the equation:

6c - 2c = 4c

The equation now becomes:

4c - 8 = -16

Take constant term on the right side of the equation by adding 8 to both sides:

4c - 8 + 8 = -16 + 8

The equation simplifies to:

4c = -8

To find the value of c, divide both sides of the equation by 4:

4c / 4 = -8 / 4

c = -2

Hence, the value of c is -2 in the equation  6c - 8 - 2c = -16.

To learn more on Equation:

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(cos^2x-sin^2x)-sin4x+sin^22x=0

Answers

Answer:

x=22.5

Step-by-step explanation:

(there's a correction in the question since the I did this one before, so I know)

(cos²x-sin²x)²-sin4x+sin²2x=0

or, cos²2x-sin4x+sin²2x=0

or, 1-sin4x=0

or, sin4x=1

or, 4x=90

or, x=22.5

Phoebe took a survey of her classmates' favorite sport. The results are in the table below:

What is the relative frequency of survey members who prefer football?

Answers

Answer:

.14

Step-by-step explanation:

The relative frequency that favors football is around 0.14, or 14%.

Given that Phoebe took a survey of her classmates' favorite sport.

We need to find the relative frequency of survey members who prefer football,

Preferred sports =

Football    baseball     basketball    tennis       others     total

     4              5                     8                 7              4          28

To calculate the relative frequency of survey members who prefer football, you need to divide the number of people who prefer football by the total number of survey respondents.

According to the table, the number of people who prefer football is 4, and the total number of respondents is 28.

Relative Frequency = Number of people who prefer football / Total number of respondents

= 4 / 28

≈ 0.14

Therefore, the relative frequency of survey members who prefer football is approximately 0.14 or 14%.

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I need help there should be a picture that pops up on the screen if not then it might be a link if it is a like press on it THANK YOU SO MUCH!!!

Answers

Answer:

ans is b hope I helped you

Determine the quotient of .     ​

Answers

of what?? the hamburgler??

An electricity post is supported by a 12 m long strut(wire). If the strut makes an angle of 53° with the ground level, how far from the post is the strut attached to the ground?

Answers

Step-by-step explanation:

I do hope that you understand through the steps in the attachment, if not kindly reach out!

Can somebody help me with this problem. And make sure that u can explain how to do it don't just give me the answer.

Answers

Answer:

x=50

Step-by-step explanation:

Look at the triangle as a whole. This is a 30-60-90 triangle by speculation. You can see that the hypotenuse is equal to 100. By using sine (you can use cosine as well) , you get the expression, "(sin 30 degrees) = x/100" since sin is the opposite side over the hypotenuse. Do some basic trigonometry to get "1/2 = x/100". By now, you should know that 50/100 is the same as 1/2.

An executive for a large company is considering a change to health insurance plans offered to the employees. To
assess employee satisfaction with the current plan, the executive sends an email to all company employees asking
their opinion of the current plan. A summary of the results received shows that 27% of company employees are
"highly satisfied" with the current health insurance plan. Which statement about the results is most likely to be true?

Answers

Answer:

not D

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

rs 20736 was distributed to as many rupees as there were. how many students were there​

Answers

This question is solved by proportions

Doing this, we found that there were 144 students.

20736 was distributed. The number of rupees for each student is the number of students.

Considering n students, the amount each student receives is:

[tex]A = \frac{20736}{n}[/tex]

Considering each student received n rupees:

[tex]n = \frac{20736}{n}[/tex]

Applying cross multiplication:

[tex]n^2 = 20736[/tex]

[tex]n = \sqrt{20736}[/tex]

[tex]n = 144[/tex]

Thus, there were 144 students.

A similar question can be found at https://brainly.com/question/23843273

Jim removed 27 gallons of water from a rainwater storage tank. There are 59 gallons left in the tank. What equation can Jim use to find how much water was in the tank earlier? Use x to represent the amount of water originally in the tank.

Answers

Answer: X = 86 gallons

Step-by-step explanation:

X-27=59

X=59+27

convert f(x) = 5x(x – 6) to standard form

Answers

Answer:

[tex]5x^{2} - 30x[/tex]

Step-by-step explanation:

Find all complex numbers z such that z^4 = -4.

Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.

Answers

26 and yeah just need points ignore this answer so sorry

Plz help similarity theorems

Answers

Answer:

b is the answer bro and try first then ask questions

equivalent expression: 3 + 4(2z - 1)

Answers

Answer:

8z - 1

Step-by-step explanation:

Given

3 + 4(2z - 1) ← multiply each term in the parenthesis by 4

= 3 + 8z - 4 ← collect like terms

= 8z - 1

Answer:

-1 + 8z

Step-by-step explanation:

First use the distributive property of multiplication (Just multiply 4 with all numbers in the parenthesis):

3 + 4(2z - 1)

3 + 8z - 4

Group like terms:

3 + 8z - 4

-1 + 8z

The answer is -1 + 8z

Hope this helped.

Which of these products is negative? Select all that apply.
-8 ÷ (-3)
-2 ÷ 8
0 ÷ (-2)
15 ÷ (-5)
-8 ÷ (-9)

Answers

Answer:

Positive/negative = negative

Negative/positive = negative

So -2 ÷ 8 and 15 ÷ (-5) are going to have negative quotients.

Let me know if this helps!

Can someone help me out

Answers

Answer:

17.6 mi

Step-by-step explanation:

I know you are using Windows 10 OS or something because of the cortana thingie and task bar option, and you can do Windows Key + Shift + S to take a screenshot.

This gives much better quality than a third party device and lets us evade the terrible pixel green line rippley thingies that form. Plus it is more efficient and faster.

Circumference formula is Diameter * Pi.

I assume the 5.6 mi. is the diameter since the line segment is going completely through the circle.

Pi is something of the lines of 3.141592653 blah blah blah and goes on forever, but the point is, we take it to be 3.14 when doing circle stuff so we don't die from old age trying to figure out a question of a 1 x 1 circle.

So 5.6 * 3.14 is 17.584 which is your answer.

It says to round to the nearest tenth though, so you round and get

17.6 since the 5 in 17.584 is the tenths place, the 8 is the hundredths place, the 4 is the thousandths place and so on and so forth.

(The "  *  " symbol represents multiplication and is in use all the time when going to higher levels of education.)

NEED HELP ASAP!!!!!!!

Answers

Letter b because you need to multiply

Geometry, please answer question ASAP

Answers

Magnitude of angle D = 170
Because,
Sum of interior angles of a pentagon = 540 degree
That is,
Angle A + angle B + angle C + angle D + angle E = 540 degree
87degree + 125 degree + 63 degree + 95 degree + angle D = 540 degree

So that gives angle D = 170 degree

Hope this helps.
ArmyCee:)

Answer:

m<D = 170°

Step-by-step explanation:

In a pentagon, the angles add up to 540°. This means the sum of <A, <B, <C, <D, and <E add up to that, and we can write an equation:

m<A + m<B + m<C + m<D + m<E = 540°

We are already given the measures of all the angles except D, so we can substitute them in:

87° + 125° + 63° + m<D + 95° = 540°

Now, we can simplify and solve for <D:

m<D + 370° = 540°

m<D = 170°

Which angles are adjacent to each other?

Angle CHG and Angle HDL
Angle AEB and Angle DEA
Angle CHG and Angle HCE
Angle JCH and Angle CHG


Please make sure it's correct because one person once tried it and got it wrong..lol.​

Answers

Answer:

B

Step-by-step explanation:

Adjacent angles must have the same vertex, so if the middle letter of the three letters used to name each of the angles in a pair are not the same, the angles cannot be adjacent.

That eliminates choices A, C, and D.

Answer: B

Look in the picture first below. Each pair of angles with the same vertex marked in blue is a pair of adjacent angles. For two angles to be adjacent angles, they must be next to each other, have the same vertex, and one cannot be inside the other.

Now look in the second picture below. Each pair of angles marked in red is not a pair of adjacent angles. Some of them are not next to each other. Others have one angle inside the other.

Find the area of the bolded outlined sector.

Answers

Outlined sector:

2 πr x 225/360 +2r

=2x3.14x10 x 225/360 +20

=59.25 cm

Hope this helped!

Date: Pages The recent price of a car is Rs. 10.00,000: If its price reduces by to1 yearly after how many year its price will be Rs 7, 29,000?​

Answers

Answer:

729000 year it's price will Rs 729000

Pressure varies inversely as volume. When the pressure is 8 Pascals, the volume is 22 liters. What would the volume be if the pressure were increased to 16 pascals?

Answers

Answer:

we can use 2 formule to solve your question: One is P*V=n(mol)*R*T(KELVIN)

Step-by-step explanation:

And other is P(first)*V(first)=P(last)*V(last)

8*22=16*?

the ?=11

the polygons in each pair are similar. find the scale factor of the smaller figure to larger figure.​

Answers

Answer:

Scale factor = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

From the picture given in the question,

If the larger figure is dilated to form the smaller figure,

Scale factor by which a figure is dilated with is determined by the expression,

Scale factor = [tex]\frac{\text{Measure of one side of the smaller figure}}{\text{Measure of the corresponding side of the larger figure}}[/tex]

                    = [tex]\frac{3}{6}[/tex]

                    = [tex]\frac{1}{2}[/tex]

When a shape is dilated, the _________ of the lengths in the image to the corresponding lengths in the pre-image are equal to the scale factor.

A. ratios
B. lengths
C. scale factors
D. proportions

Answers

when a shape is dilated the RATIOS of the lengths in the image to the corresponding lengths in the preimage are equal to the scale factor

Please Help !


Which of the following describes point D? (-4, 0) (0, -4) (0, 4) (4, 0)

Answers

Answer:

D(0 , 4)

Step-by-step explanation:

Point D is on the y axis. So, x-coordinate  = 0

y- coordinate is the vertical length from origin which is 4

Answer:

D(0 , 4)

Step-by-step explanation:

plz give me this ans by explaining​

Answers

Answer:

I don't know what to do so I just answered the volume of this tell me if I am wrong

Step-by-step explanation:

radius : 3.5 cm

volume : ?

now,

volume (v) : π × r (2)

: 22/7 × 3.5(2)

:22×3.5×3.5 by 7

therefore,

the volume is 38.5

help me plzzzzzz tyyyyyyyyyy​

Answers

Answer:

your answer is B.

Step-by-step explanation:

mode is 76, mean is 79, the median is 76.

Instructions: Find the missing side. Round your answer to the nearest tenth

Answers

Answer:

x≈64.3

Step-by-step explanation:

since we already know the measures of 2 of the 3 angles in the triangle, we can find the 3rd angle:

180°-90°-25°=65°

now, we can use the law of sines to find the missing side:

sin25°/30=sin65°/x

x sin25°=30sin65°

x=(30sin65°/sin25°)

x≈64.33520762

rounded to the nearest 10th:

x≈64.3

find the missing length indicated​

Answers

Answer:

x = 240

Step-by-step explanation:

Apply the leg rule to find the value of x.

Leg rule is given as:

Hypotenuse/leg 1 = leg 1/part 1

Hypotenuse = 400

Leg 1 = x

Part 1 = 144

Plug in the known values into the formula

400/x = x/144

Cross multiply

x*x = 144*400

x² = 57,600

Take the square root of both sides

√x² = √57,600

x = 240

Solve 4 sinx + 9 cosx=0 for 0° ​

Answers

4 sin(x) + 9 cos(x) = 0

4 sin(x) = -9 cos(x)

tan(x) = -9/4

x = arctan(-9/4) + … … … (in radians)

or

x = arctan(-9/4) + 180n ° … … … (in degrees)

where n is any integer.

I'm guessing you're solving for x over some domain, probably 0° ≤ x < 360°. In that case, you would have two solutions for n = 1 and n = 2 of

x ≈ 113.96°   and   x ≈ 293.96°

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