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See here for solution: https://web2.0calc.com/questions/system_33729. Let me know if that answer is incorrect.

The answer is P(6,4) = 6!/2! = 30.

Incorrect, the answer is 118.

Incorrect, the answer is 7.

We have that f(2) = 2/21 = 1/14. Since 2 is not a multiple of 3 or 7, we have that f^a(2) = 2 + 3 = 5. Therefore, we need to find the smallest value of a such that 1/14 = 5. This is never true, so the smallest value of a is 2​.

Why is it 2*1/5*1/4 instead of 1/5*1/4 (which would make the answer 1/20).

Hello! \(\frac{3}{7} \cdot \frac{5}{3} \cdot \frac{7}{11} = \frac{3\cdot5\cdot7}{7\cdot3\cdot11} = \frac{105}{231} = \frac{105\div21}{231\div21} = \boxed{\frac{5}{11}}\)

Hello! The answer is $30.

We can form two equations with two variables based upon the given facts where x is the amount of money I have and y is the amount of money my brother has:

  x-5=y

-

  x+25=2y

---------------

    -30 = -y

Using system of equations, we find y = 30.

So your brother currently has 30 dollars.

Sorry, some of the LaTeX isn't rendered. Can you please post the question again?

Your answer is incorrect. Can you please try again?

7 / 12 ==0.58333.......==58.33% percentage of people who are bored by cable news.

280 / (7/12)==280  x  12/7 ==480 - total number of people at the Math Convention.

480  -  280 ==200 people who are NOT bored by the cable news.

Since your question says "A temperature, x, that differs from normal by at least 2°F is considered unhealthy", then how do you write " at least" in the 4 choices given to you?

I would say "C" and ≥ 2, because that means "equal to or greater than 2". In other words it says "at least".

Divide the first by the second and should get:

a≈82.4194     and      b≈0.87358

Let the number of pages in the scrapbook when they will be equal==P

47 + 1P ==9 + 2P

47 - 9 ==2P - 1P

P ==38 pages - when the 2 srapbooks will be equal

Sub P into one of equations above:

47  + 38 ==$85 - the cost of the scrapbook.

The probability is 2*1/5*1/4 = 1/10.

Hello,

In an equilateral triangle, the angle bisector and perpendicular bisector are the same line. Since triangle PQR is an equilateral triangle with all sides equal to 9, we can conclude that XY is also equal to 9.

Like this:

What is Sophie's favorite number XY ?

10y + x = 10x + y - 45

Two possibilities:

a) y = (2x - 1)   or  b) x = (2y - 1)

a):

10y + x = 10x + y - 45

10(2x - 1) + x = 10x + (2x - 1) - 45

20x - 10 = 12x - 46

8x = 36

x = 4.5   \(\to\)  So it must be b).

b):

10y + x = 10x + y - 45

10y + (2y - 1) = 10(2y - 1) + y - 45

12y - 1 = 21y - 55

9y = 56

y = 6.22

Unfortunately not solvable.

  !

To multiply the numbers 12121 (base 3) and 1222 (base 3) in base 3, we can perform the multiplication as we would with decimal numbers, but considering the base 3 digits.

1 2 2 2 <- Multiplicand (1222) × 1 2 1 2 <- Multiplier (12121) ______________ 2 2 2 2 <- Partial product (1222) + 2 2 2 2 0 <- Partial product (1222, shifted 1 place to the left) + 1 2 2 2 0 0 <- Partial product (1222, shifted 2 places to the left) + 1 2 2 2 0 0 0 <- Partial product (1222, shifted 3 places to the left) _______________ 1 1 2 2 0 2 0 <-

Therefore, the product of 12121 (base 3) and 1222 (base 3) in base 3 is 1122020.

Let's call the radius of the circle R. Since X is the circumcenter of triangle OYZ, it lies on the perpendicular bisectors of all three sides of the triangle. This means that XY = XZ = R, and YZ = 2R/sqrt(3), which is the diameter of the circle.

Now let's find the area of triangle XYZ. We can use the formula for the area of an equilateral triangle:

Area of XYZ = (sqrt(3)/4) * XY^2

Substituting XY = R, we get:

Area of XYZ = (sqrt(3)/4) * R^2

To find the area of the circle, we use the formula:

Area of circle = pi * R^2

Substituting the given area, we get:

pi * R^2 = 

Solving for R, we get:

R = sqrt() / pi

Substituting this value of R into the formula for the area of XYZ, we get:

Area of XYZ = (sqrt(3)/4) * (sqrt() / pi)^2
Area of XYZ = (3 / 4pi) * 

Simplifying, we get:

Area of XYZ = (3sqrt(3)) / 4

Therefore, the area of triangle XYZ is (3sqrt(3)) / 4. 

To find the output when the input is n, we need to determine the rule or equation that generates the outputs from the inputs. Since the function is linear, we know that it has a constant rate of change or slope. 

To find the slope, we can use any two points on the line. Let's use the first and last points:

slope = (output at last input - output at first input) / (last input - first input)
slope = (2 - (-4)) / (4 - 1)
slope = 6/3 = 2

So the slope of the function is 2. Now we can use the point-slope form of the equation of a line to find the output when the input is n:

y - y1 = m(x - x1)

where y is the output, x is the input, m is the slope, and (x1, y1) is any point on the line. Let's use the first point (1, -4):

y - (-4) = 2(x - 1)

y + 4 = 2x - 2

y = 2x - 6

Now we can substitute n for x to find the output when the input is n:

output when input is n = 2n - 6

Therefore, the output when the input is n is 2n - 6.

A circle is centered at the origin and has a radius of square root 130. Work out the coordinates of the two points on the circle where x=7  

The first answer made a mistake.  

Used 130 for r instead of sqrt(130).  

The numbers got really big after that.  

The equation of a circle centered at the origin is x² + y² = r²   

We already know the x coordinate is 7, because the problem tells us that, 

so we only have to solve for y.  So plug the 7 in for x and sqrt(130) in for r  

into the equation.  

                                                                       x² + y²  =  r²   

                                                                       7² + y²  =  [sqrt(130)]²  

                                                                       49 + y²  =  130  

                                                                               y²  =  130 – 49  

                                                                               y²  =  81  

                                                                               y   =  +9  

So the coordinates are                                  (7, 9) and (7, –9)  

_.

The ball will hit the ground when y = 0. Solving for t in the equation y = -6t^2 - 10t + 56, we get:

-6t^2 - 10t + 56 = 0

We can factor this equation as:

(2t - 7)(3t - 8) = 0

Solving for t, we get:

t = 7/2 or 8/3

The smaller of these two values is 7/2. Therefore, the ball will hit the ground in \(\boxed{3.50}\)​ seconds.

1. Start by multiplying both sids of the equation by \(64a^3+7\) to get rid of the fraction. From there just do some regrouping to get the variable terms on one side and constant terms on the other.

2. Same here get rid of the fractions by multiplying the whole equation by the common denominator \(3a\), and from there just rearrange it and solve 

First, combine like terms on the right hand side: \(3a+4b=2a-6b+24\)

Then we rearrange the equation so that all the terms with \(b\) in it are on one side, and the rest (\(a\) terms and constants) are on the other side. So now we have \(-10b=a-24\)

Since we want to get b on its own, we divide by \(-10b\).

Thus \(b=-\frac{a-24}{10}\)

Hope that helped!