What is (6 + 6 + 6) · (6² + 1²)?

Please don't tell the answer is the devil number.

Answers

Answer 1

Answer: (6+6+6)(36+1) = (18)(37) = 666. ... If you don't want an answer posted, there's a simple solution ... don't post the question ! And if it still mysterously somehow appears, then for heaven's sake, don't offer points as a reward for an answer. ... Finally ... devil's numbers belong in the Old Wives' Hooey category, not in the Mathematics one. They're not real.

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Given the following scenario, decide if it is a permutation or combination. Then calculate the number of possibilities. (Please write Permutation/Combination ; answer)A committee must choose 4 finalists from 15 candidates. How many ways can the committee choose the four finalists.

The three sides of a triangle are tangent to a unique circle called the incircle. On the coordinate plane, the incircle of ABC has its center at the origin. The lines whose equations are x+4y=6s(qrt17), 2x+(sqrt5)y=-18, and 2(sqrt2)x=y+18 contain the sides of ABC. What is the length of the radius of the incircle?sqrt= square root

A. 2 units
B. 3 units
C. 6 units
D. 8 units

Answers

We are looking for the length of a radius.

If we can find the coordinates of the two endpoints of a radius, then we can find its length.

A tangent to a circle intersects the circle at a single point.

A radius of the circle drawn to the point of tangency is perpendicular to the tangent.

We know the center of the circle is the origin. That means we know one endpoint of every radius.

We use one side of the triangle which is given as an equation.

We find its slope. Then using that slope and the coordinates of the origin,

we can find the equation of the radius that is perpendicular to that side.

We then solve the equations simultaneously to find the coordinates of the point of tangency. The point of tangency is the other endpopint of the radius.

Knowing two endpoints of a radius, we can find its length. That will give us the answer since we are looking for the length of the radius.

Let's use the first given equation.

Find its slope.

$x + 4y = 6 √(17)$

$4y = -x + 6 √(17)$

$y = -(1)/(4)x + (3√(17))/(2)$

The slope of the side of the triangle is -1/4.

The slope of the radius perpendicular to that side is 4.

The equation of the line that contains the radius is

$y - y_1 = m(x - x_1)$

We are told the circle is centered at the origin, so one point on the line containing the radius is (0, 0).

$y - 0 = 4(x - 0)$

$y = 4x$

The line containing the radius is y = 4x.

Now we use the equation of the line containing the side of the triangle and the equation of the line containing the radius as a system of equations to find their point of intersection. That point is the other endpoint of the radius.

$x + 4y = 6 √(17)$

$y = 4x$

Multiply the first equation by 4 and subtract the x-term from both sides.

$16y = -4x + 24 √(17)$

$y = 4x$

Add the equations and solve for y.

$17y = 24 √(17)$

$y = (24 √(17))/(17) = (24)/(√(17))$

Now replace y with the value we found, and solve for x in the second equation.

$(24 √(17))/(17) = 4x$

$(6 √(17))/(17) = x$

$x = (6 √(17))/(17) = (6)/(√(17))$

The coordinates of the point of intersection are

$((6)/(√(17)), (24)/(√(17)))$

This point of intersection is one endpoint of the radius.

The other endpoint of the radius is the origin.

Now we need to find the the length of the radius.

$r = √((x_2 - x_1)^2 + (y_2 - y_1)^2)$

$r = \sqrt{((6)/(√(17)) - 0)^2 + ((24)/(√(17)) - 0)^2}$

$r = \sqrt{(36)/(17) + (576)/(17)}$

$r = \sqrt{(612)/(17)}$

$r = √(36)$

$r = 6$

Answer: The radius is 6 units long, choice C.

Answer:

Step-by-step explanation:

edge21

There are 3 times as many pears are oranges. If a group of children receive 5 oranges each,there will be no left over.If the same group of children receive 8 oranges each, there will be 21 pears left over. How many oranges are there?

Answers

There are 15 oranges

Solution:

Let "x" be the number of oranges

Let "y" be the number of pears

Let "c" be the number of children

There are 3 times as many pears are oranges

Number of pears = 3 times the number of oranges

y = 3x -------- eqn 1

If a group of children receive 5 oranges each, there will be no left over

So, "c" children receives 5 oranges each, there will be no left over

number of oranges = 5(number of children)

x = 5c ------- eqn 2

If the same group of children receive 8 oranges each, there will be 21 pears left over

number of pears = 8 oranges(number of children) + 21

y = 8c + 21

Substitute eqn 1

3x = 8c + 21 ---- eqn 3

Substitute eqn 2

3(5c) = 8c + 21

15c - 8c = 21

7c = 21

c = 3

Substitute c = 3 in eqn 2

x = 5(3)

x = 15

Thus there are 15 oranges

Answer:

15 orangs

Step-by-step explanation:

There are 15 oranges

Solution:

Let "x" be the number of oranges

Let "y" be the number of pears

Let "c" be the number of children

There are 3 times as many pears are oranges

Number of pears = 3 times the number of oranges

y = 3x -------- eqn 1

If a group of children receive 5 oranges each, there will be no left over

So, "c" children receives 5 oranges each, there will be no left over

number of oranges = 5(number of children)

x = 5c ------- eqn 2

If the same group of children receive 8 oranges each, there will be 21 pears left over

number of pears = 8 oranges(number of children) + 21

y = 8c + 21

Substitute eqn 1

3x = 8c + 21 ---- eqn 3

Substitute eqn 2

3(5c) = 8c + 21

15c - 8c = 21

7c = 21

c = 3

Substitute c = 3 in eqn 2

x = 5(3)

x = 15

Thus there are 15 oranges

Perform the following computations. retail price of steel-belted radial tire = $89.50 discount offered = 10% federal tax = 12% local sales tax = 5% selling price = _____. 66.86 94.24 95.76 112.15

Answers

For the answer to the question above
Retail price of steel-belted radial tire = $89.50
Discount offered = 10% = $8.95
Value before federal tax = $89.50 - $8.95 = $80.55
Federal tax = 12%=$80.55(0.12) =$9.67
Local sales tax = 5% =$80.55(0.05)=$4.03

Selling price = $80.55 +$9.67+$4.03 =$94.25
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

Answer:

94.25

Step-by-step explanation:

Find the slope given (2,-7) and (-1,6)

Answers

Answer:

$-(13)/(3)$

Step-by-step explanation:

$5,000 is invested at 3% interest. How much money must be invested at 5% interest so that the total interest from the two investments is $275 after one year?

Answers

$Part \ of\ 5000\ should\ be\ invested\ at\ 3\%\ and\ part\ at\ 5\%.\n\n x-\ part\ of\ 5000\ invested\ at \3\%\nx*3\%+(5000-x)*5\%=275\n 0,03x+0,05(5000-x)=275\n 0,03x+0,05*5000-0,05x=275\n -0,02x=275-250\n -0,02x=-25\ |:-0,2\n\ x=125\n 5000-125=4875\n 125 \$\ should\ be\ at\ 3\%\ and\ 4875\ at \ 5\%.$

Every month, Carmine's savings account pays 0.049% interest on the amount in the account. Ifshe has $1,100.00 in the account at the beginning of the month and doesn't withdraw any of it,
what will be the interest payment for this month?

$53.90

$49.00

$0.54

S0.49