Point R has coordinates of (5.-6). What the coordinates of R' after being reflected across the y-axis?

Answer:

Step-by-step explanation:

2005 AMC 8 Problems/Problem 20

Problem

Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$

Solution

Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.

See Also

2005 AMC 8 (Problems • Answer Key • Resources)

Preceded by

Problem 19 Followed by

Problem 21

1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Answer:

17$

Step-by-step explanation:

Answer:

$17

Step-by-step explanation:

Since the discount is 15%, and 100% would be the full price, 100 - 15 = 85. You are paying 85% of the price. 20 * .85 = 17.

Answer:

i need help too

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

x = - 3 is a vertical line parallel to the y- axis.

A line perpendicular to it will therefore be a horizontal line parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (6, - 4 ) with y- coordinate - 4 , then

y = - 4 ← equation of perpendicular line

[tex]\large\huge\green{\sf{Answer:-}}[/tex]

[tex] \red {\mathbb{ \underline { \tt By \: using \: Pythagoras \: theorm}}}[/tex]

[tex]h {}^{2} = p {}^{2} + b {}^{2} \\ x {}^{2} = (7 {}^{2} + 6 {}^{2} )ft {}^{2} \\ x {}^{2} = (49 +3 6)ft {}^{2} \\ x {}^{2} = 85 ft\\ x = \sqrt{85 } ft \\ [/tex]

the length of missing side= √85=9.2 ft

Answer:

The constant of proportionality is thus 1

Step-by-step explanation:

Note that the green line passes through (6, 6) and has a y-intercept of 0.  Thus, the equation of the line is y = (6/6)x + 0, or y = x, or y = 1x.

The constant of proportionality is thus 1, which is also the slope of this line.

Answer:

The inverse of subtracting 24 is adding 24.

Step-by-step explanation:

The inverse of subtraction is addition.

Answer:  

2 hours:  3968  [I don't understand the $ sign in the answer box]

At midnight:  12137

Step-by-step explanation:

The bacteria are increasing by 15% every hour.  So for every hour we will have what we started with, plus 15% more.  

The "15% more" can be represented mathematically with (1 + 0.15) or 1.15.  Let's call this the "growth factor" and assign it the variable b.  b is (1 +  percent increase).

Since this per hour, in 1 hour we'll have (3000)*(1.15) = 3450

At the end of the second hour we're increased by 15% again:

(3450)*(1.15) = 3968.

Each additional hour add another (1.15) factor,  If we assign a to be the starting population, this can be represented by:

P = a(1.15)^t for this sample that increase 15% per hour.  t is time, in hours.  

If a represents the growth factor, and P is the total population, the general expression is

P = ab^t

Using this for a = 3000 and b = 1.15, we can find the total population at midnight after starting at 2PM.  That is a 10 hour period, so t = 10

P = (3000)*(1.15)^10

P = 12137

The required equivalent expression for  [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex] is [tex]2 \ log_{5}\ x-2\ log_{5}\ 4[/tex].

Given expression,

[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex].

We have to find the Equivalent fraction of  [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex].

We know that from the properties of logarithm, the following identities

[tex]log\ m^{n} =n\ log\ m[/tex] .....(1)

[tex]log\ \frac{m}{n} = log\ m- log\ n\\[/tex].......(2)

Now, [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5} \ \frac{x}{4}[/tex] ( using 1 identity)

Again using 2 identity, we get

[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2[ log_{5}\ x-log_{5}\ 4 ][/tex]. (using 2 identity)

[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5}\ x-2\ log_{5}\ 4[/tex]

Hence the required equivalent expression for  [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex] is [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5}\ x-2\ log_{5}\ 4[/tex].

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Answer:

C on edge

Step-by-step explanation:

Answer:

[tex]y=-\frac{5}{4} x-3[/tex]

Step-by-step explanation:

Use the slope formula equation to plug in values. Slope formula equation is y=mx+b. The known values are y=2, m=-5/4, x=-4. [tex]2=(-\frac{5}{4} )(-4)+b[/tex]. Multiply -5/4 times -4 to get 5. 2=5+b. Subtract 5 from each side to isolate b. b=-3.

The correct roots of the equation are (a) 9 and 1

From the complete question, their mistakes are:

Anu

Aji

A quadratic equation is represented as:

[tex]ax^2 + bx + c = 0[/tex]

Where:

[tex]\alpha\beta = \frac ca[/tex] --- product of roots

[tex]\alpha + \beta = -\frac ba[/tex] --- sum of roots

Anu made a mistake in the constant term, so we consider the sum of roots

[tex]Sum = 8 + 2[/tex]

[tex]Sum = 10[/tex]

Aji made a mistake in the coefficient, so we consider the product of roots

[tex]Product = -9 \times -1[/tex]

[tex]Product = 9[/tex]

The possible equations from the above sum and products are:

Of all the above equations, the most likely equation is [tex]x^2 - 10x + 9 =0[/tex], and it has a root of 9 and 1

Hence, the correct roots are (a) 9 and 1

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Answer:

The line representing the number of ounces of chicken required to serve x people is steeper than the line representing the number of ounces of fish required to serve x people.

Step-by-step explanation:

I took the test

Comparing the two graphs, we can conclude that: the graph representing the number of ounces of chicken required to serve x people has a steeper slope than the graph representing the number of ounces of fish that will serve x people

Recall:

Given the following:

Graph representing the number of ounces of chicken required to serve x people: y = 7x

The slope is 7.

Graph representing the number of ounces of fish required to serve x people: y = 5x.

The slope is 5.

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Answer:

the answer is 14.04

...............

25 % of pizzas were mushroom pizzas.

Percentage is a measurement to find value of given number out of hundred.

Given that,

Number of mushroom pizzas = 19,

And number of pepperoni pizzas = 57.

Total number of pizzas = 19 + 57 = 76.

To find the number of percentage of pizzas of mushroom,

Use percentage property,

= (Number of mushroom pizzas / total pizzas) x 100

= (19 / 76) x 100

= 100/ 4

= 25 %

The required percentage of mushroom pizzas = 25 %.

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Answer:

3m + 5

Step-by-step explanation:

uhmm i think 2n is i cant solve here hope it helps

Answer:

D -1

Step-by-step explanation:

[tex]-6(3a+4)=3a-3[/tex]

[tex]-18a-24=3a-3[/tex]

[tex]-18a-3a=-3+24[/tex]

[tex]-21a=21[/tex]

a = [tex]\frac{21}{-21} =-1[/tex]

Hope this helps

Answer:

£100.32

Step-by-step explanation:

An increase of 14% on the original amount (100%) is

100 + 14 = 114% = [tex]\frac{114}{100}[/tex] = 1.14 , then

£88 × 1.14 = £100.32

Answer:

  3 ft

Step-by-step explanation:

The formula for the volume of a cone is ...

  V = 1/3πr²h

Solving for r, we find ...

  r = √(3V/(πh))

  r = √((3×94.2)/(π×10)) ≈ √9 = 3 . . . . ft

The radius of the cone is 3 ft.

Therefore, 2x³ - 8x units³ is the volume of a rectangular prism.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

(2x³ - 8x) is the volume of a rectangular prism.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, a rectangular prism with a length of 2x, a width of (x−2), and a height of (x + 2)

Volume: L x B x H

= (2x) × (x - 2)(x + 2)

= (2x) × (x² - 4)

= 2x(x² - 4)

= 2x³ - 8x units³

Hence, 2x³ - 8x units³ is the volume of a rectangular prism.

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Answer:

  A, D, F

Step-by-step explanation:

It is convenient to let a calculator or spreadsheet evaluate the function for you. Reflection over the y-axis means x is replaced by -x in the original function definition.

The values that show up on the reflected graph are ...

  (-7, -10.206)

  (0.5, -0.221)

  (9, -0.003)

Answer:

9 cm

Step-by-step explanation:

[tex]\sqrt{81} = 9[/tex]

Answer:Let Y = height

Let X = time

Height is a linear function of time, so Y = mX + b, where m is the slope and b is the y-intercept.  

We can calculate the slope from the given values (8,20.4) and (19,18.2)

Slope = (y2 - y1) / (x2 - x1) = (18.2 - 20.4) / (19 - 8) = -2.2 / 11 = -0.2

This means that the height of the candle is going down by 0.2 cm per hour

Since 16 hours is 8 hours after the first data point of (8,20.4), the height will go down by 8 * (-0.2) = -1.6 cm in the 8 hours between hour 8 and hour 16.  

So the height of the candle after 16 hours = 20.4 - 1.6 = 18.8 centimeters

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

b. d>-3/5

Step-by-step explanation:

L.C.M=5

5×1/5>5×d+4/5×5

1>5d+4

1-4>5d

-3>5d

-3/5>5d/5

-3/5>d

Answer: 7

Step-by-step explanation: if it's so easy, why do you need brainly? (not judging, just confused why you'd waste points)

Answer: Your mom

Step-by-step explanation:

HEHEHEHA

Answer:

To get 6 1/3 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction. Here are the detailed math steps we use to convert 6 1/3 mixed number to decimal form: Step 1:Multiply the whole number by the denominator: 6 × 3 = 18

Step-by-step explanation:

The value of the expression 6 - 1/3 will be 17 / 3.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The numbers are given below.

6 and 1/3

Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have

⇒ 6 - 1/3

⇒ (18 - 1) / 3

⇒ 17 / 3

The value of the expression 6 - 1/3 will be 17 / 3.

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Answer:

The Equation for lyft is:

4.50x

The Equation for uber is

2.50x+5

Step-by-step explanation:

If you want to determine which one is better then you can just plug in the distance in place of x. For example if it asked you which one was better for 5 miles, uber or lyft you could plug 5 into the equation.

It would look like this

Lyft: 4.50 (5)= 22.5

Uber

2.50 (5) +5= 17.5

If the distance were 5 miles uber would be the better option.

[tex]\huge\boxed{\sf{Hello\:there!}}[/tex]

First of all, we should add 34 and 32:

34+32=66

Now, let's divide both sides by 9:

66÷9=7.3333...

[tex]\huge\boxed{\sf{Hope\:it\:helps.\:Please\:mark\:Brainliest.}}[/tex]

[tex]\huge\bold{Good\:luck!}\\\huge\mathfrak{LoveLastsAllEternity}[/tex]

Answer:

6 hours.

Step-by-step explanation:

deal: 135-(60+12.5h)=y

let h= # of hrs

135-60=75.

75/12.5=6 hours.

Answer:

a) 512 cm^3

b) 469.125 cm^3

Step-by-step explanation:

8*8*8 = 512 cm^3

or

8^3 = 512 cm^3

3.5^3 = 42.875

512 - 42.875 = 469.125 cm^3

You can round the second answer down