ArithmeticBrains1234

The largest possible size is just the GCF of the two numbers:

1575 = 3² * 5² * 7

1485 = 3³ * 5 * 11

GCF = 3² * 5

         =  45

Therefore, the maximum team size is 45 people.

Let p represent the number of people that signed up for programming class.

Math class = 9p

Total students = 9p + p = 10p

We also know that 45 students are wanted in each class, therefore there are 45*2=90 total students.

Now:

10p = 90

p = 9

45 - 9 = 36 students that needed to be moved.

One such line tangent to both circles is the line x = 3, as both circles intersect point (3,0).

I'm not sure if this is what you are asking for, as the instruction is a bit unclear.

I assume you would want me to answer in terms of a, b, and c.

The key realization is  FG/GH=1 - this means FG = GH.

This also implies that if a line were to be drawn between the two points, point G would be the midpoint - meaning that the coordinates of point G are the averages of the endpoints of the line(point F and H).

The average of a and 7a is 4a.

The average of b and c is (b+c)/2

Therefore the coordinates of point G are (4a,(b+c)/2).

There are a total of 6 + 5 = 11 marbles in the bag.

The chance of not getting a red marble is 6/11 for one try.

With the second try, the chance of not getting a red marble is again 6/11.

Therefore, the probability of not getting a red marble on either try is 6/11 * 6/11 = 36/121

From here, the chance of getting a red marble on either try is 1 - (36/121) = 85/121.

Let x represent the length of DB.

AC =  √(16² + 12²) = √400 = 20

CB = √(x² + 12²)

AB = x + 16 

Note that △ABC is right, meaning that AC² + CB² = AB².

Substituting values for AC, CB, and AB, we get:

20² + [√(x² + 12²)]² = (x + 16)²

400 + x² + 12² = x² + 32x + 256

544 + x² = x² + 32x + 256

544 = 32x + 256

288 = 32x

x = 9

Therefore the length of DB is 9.

Note that the decrease from FD to GH is proportional to the decrease from ED to EG.

Since GH is 1/2 of FD(6 is 1/2 of 12), we can deduce that  EG is 1/2 of GD:

1/2(ED) = EG

1/2((x+5)+9) = x+5

1/2(x+14) = x + 5

x + 14= 2x + 10

4 = x

Since HF is also 9, we can apply the same logic to EH, meaning that EH = x+5

EH = x + 5

EH = (4) + 5

EH = 9

I assume you meant odd numbers rather than odd-digit numbers.

For a number to be odd, it has to end with an odd digit; in your case, it has to end with either 1 or 3.

If the number ends with a 1, that leaves 2, 3 and 4 to "fill up" the first three spots of a four-digit number.

2, 3, and 4 can be arranged in 6 distinct ways, meaning there are 6 numbers that fit your criteria when the number ends with 1.

The same applies when the number ends with 3, for which exist another 6 distinct numbers that fit your criteria.

6+6 = 12 total numbers that fit your criteria.

The Area of the bottom-most rectangle is 60 * 20 = 800 u².

The Area of the "ring" is simply the difference of the two circles with the inner and outer radii.

Inner radius = 50 - 20 = 30u

Outer radius = 50u

Area = πr_outer² - 30πr_inner²

Area = π50² - π30²

Area = 2500π - 900π 

Area = 1600π u²

The Area of the "V" in the center can be simply divided up into two congruent parallelograms and a trapezoid.

Area_parrellogram= bh = 30*10 = 300 u²

Since we have 2 of these, the total is 300*2 = 600 u²

Area_trapezoid= h(a+b)/2 = 15(10+20)/2 = 15*30/2 = 225 u²

Area_"V"= 600 + 225 = 825 u²

Now the total area is the sum of the areas of the "V", the ring, and the rectangle. (Sum of everything underlined)

825 + 1600π + 800 = 1600π + 1625 u²

From above, we can deduce that a = 1600, and b = 1625.

Therefore a+b = 3225 u².

Since NQ bisects ∠MNP, ∠MNQ = ∠QNP.

Considering that ∠NMQ≅∠NPQ, we can create the following diagram:

Notice that △MNQ and △PNQ share a side; meaning that we can use the ASA similarity rule to deduce that △MNQ≅△PNQ.

Angle LMN is 180 - 90 - 30 = 60°.

Therefore, triangle LMN is a 30-60-90 triangle.

LM = 20/2 = 10 ft

NL = 20/(√3/2) = 10√3

Area = bh/2 = 10 * 10√3 = 100√3 ≈ 173.2 ft²

Let x be the number of peaches Babken originally bought.

We can now represent the situation with an equation:

\({\frac {1} {3}}(x-{\frac {1} {3}}x-1)=3\)

The -1/3x and -1 comes from giving 1/3 and one extra to his sister.

The 1/3 at the front of the first bracket comes from the 1/3 he was left with after giving 2/3 to his brother.

Solving:

\({\frac {1} {3}}(x-{\frac {1} {3}}x-1)=3\)

\(x-{\frac {1} {3}}x-1=9\)

\(x-{\frac {1} {3}}x=10\)

\({\frac {2} {3}}x=10\)

\(x=15\)

Therefore Babken originally bought 15 peaches.

(2x)(3y) = 6xy

6xy = 46656

xy = 7776

So, essentially we are looking for two numbers(x and y) whose product is 7776.

Factor set of 7776: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776} 

For any of the factors of 7776, there is another number in that same factor set that when multiplied by the first factor, gives 7776.

Eg. 2*3888 = 7776

Thus the sum of the factor set of 7776 is your answer.

Sum of the factor set = 22932

Solved! :)

Let c represent the number of child tickets sold;

Let a represent the number of adult tickets sold.

We know:

c + a = 450

a = 450 - c

and

6a + 4c = 2450

3a + 2c = 1225

Now, using substitution:

3a + 2c = 1225

3(450 - c) + 2c = 1225

1350 - 3c + 2c = 1225

-c = -125

c = 125

a = 450 - c

a = 450 - (125)

a = 325

Therefore 125 child tickets and 325 adult tickets were sold.

There are 3 triangles in the diagram.

The second smallest triangle has a 90° and 30°, meaning the last angle is 60°; thus the triangle is a 30-60-90 triangle.

The smallest triangle is a 30-60-90 triangle as it has a 90° angle, and a 90 - 60 = 30° angle. The last angle is therefore 60°, meaning the triangle is also a 30-60-90 triangle.

The large triangle has a 90° and 45° angle, meaning the last angle is 45°, indicating a 45-45-90 triangle.

The side opposite of the 30° angle is:

7*2 = 14

The vertical side of the largest triangle is:

14*2 = 28

Therefore x =

28 * √2 = 28√2

There are 3 times the dogs as children.

So, let's say that there are 5 children.

Based on the statement, there are 3 times 5 children number of dogs.

- That's 15 dogs; or 3* the number of children(5).

In other words, the expression is 3c.

You can solve the question using the law of sines:

(sin A)/a = (sin B)/b = (sin C)/c

A, B and C are angles in the triangle; a, b, and c are the side lengths opposite to their respective angles.

Plugging this in we get:

sin(120)/15 = sin(S)/9

sin(120) = sin(S) * 5/3

sin^-1{[sin(120)]/(5/3)} = S

S ≈ 31.3°

Solved! :)