A rock is dropped into a pond, creating a circular ripple. The radius of the ripple increases steadily at 6 cm/s. A toy boat is floating on the pond, 2.00 m east and 1.00 m north of the spot where the rock is dropped. How long does the ripple take to reach the boat?

The answer is  X= 3, -2

Answer:

k = 4

Step-by-step explanation:

g(x) higher than by 4 units

Answer:

k = 4

Step-by-step explanation:

'k' represents the vertical translation

Answer:

y = -5/6x + c

Step-by-step explanation:

line equation is:

y = mx + c

y = -5/6x + c

sub in values:

1 =-5/6(6) + c

1 = -5 + c

6 = c

equation of line:

y = -5/6x + 6

Triangle B is a reflection of triangle A across the axis y=-1

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

The graph A is the original graph and it is transformed to B. Triangle B is a reflection of triangle A across the axis y=-1

Hence  Triangle B is a reflection of triangle A across the axis y=-1

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Answer:

5.48

78.541

97

42.111...

(all of above)

Step-by-step explanation:

because a rational number is a number that can be written as a fraction

a decimal number that ends can be written as a fraction (ex: 5/4 = 1.25)

a decimal number that has a repeating number after the decimal point can also be written as a fraction (ex: 10/3 = 3.33...)

Answer:

[tex]\textsf{1.} \quad 3x^2-4x+12[/tex]

[tex]\textsf{2.} \quad 3x^2-8x+4[/tex]

[tex]\textsf{3.} \quad 6x^3-8x+32[/tex]

[tex]\textsf{4.} \quad \dfrac{3x^2-6x+8}{2x+4}[/tex]

[tex]\textsf{5.} \quad 12x^2+36x+32[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x^2-6x+8\\g(x)=2x+4\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

The composite function (f + g)(x) means to add function f(x) and g(x):

[tex]\begin{aligned}\implies (f+g)(x) & = f(x)+g(x)\\&=(3x^2-6x+8)+(2x+4)\\ &=3x^2-6x+2x+8+4\\ &=3x^2-4x+12\end{aligned}[/tex]

The composite function (f - g)(x) means to subtract function g(x) from function f(x):

[tex]\begin{aligned}\implies (f-g)(x) & = f(x)-g(x)\\&=(3x^2-6x+8)-(2x+4)\\&=3x^2-6x+8-2x-4\\ &=3x^2-6x-2x+8-4\\ &=3x^2-8x+4\end{aligned}[/tex]

The composite function f(x) · g(x) means to multiply functions f(x) and g(x):

[tex]\begin{aligned}\implies f(x)\cdot g(x) & =(3x^2-6x+8)(2x+4)\\ &=3x^2(2x+4)-6x(2x+4)+8(2x+4)\\&=6x^3+12x^2-12x^2-24x+16x+32\\&=6x^3-8x+32\end{aligned}[/tex]

The composite function f(x)/g(x) means to divide function f(x) by function g(x):

[tex]\begin{aligned}\implies \dfrac{f(x)}{g(x)} & = \dfrac{3x^2-6x+8}{2x+4}\\\end{aligned}[/tex]

The composite function f(g(x)) means to substitute the function g(x) in place of the x in function f(x):

[tex]\begin{aligned}\implies f(g(x))&=3(g(x))^2-6(g(x))+8\\&=3(2x+4)^2-6(2x+4)+8\\&=3(2x+4)(2x+4)-12x-24+8\\&=3(4x^2+16x+16)-12x-16\\&=12x^2+48x+48-12x-16\\&=12x^2+48x-12x+48-16\\&=12x^2+36x+32\end{aligned}[/tex]

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The sum of the values is

[tex]67+85+92+123+147+181+181+196+198+213+252+277+287+325+459=3083[/tex]

Dividing this by the number of values, which is 15, the mean is 3083/15.

The mean is a measure of central tendency, and indicates that people make an average of about $205.53 per month.

Answer:

Use the stemplot to answer the questions.

The mean paycheck is $

✔ 205.53

.

The mean is a

✔ statistic

.

This mean paycheck indicates that

✔ on average, students earned $205.53 per paycheck

.

Step-by-step explanation:

edge 2023

Answer:

29041

Step-by-step explanation:

1995-1990

300×5=1500

27541+1500=29041

Answer:

f= 37 / 4

Step-by-step explanation:

I am using ( / ) to show a fraction

Let's solve your equation step-by-step.

f(4)=7(4+2)−5

Step 1: Simplify both sides of the equation.

f(4)=7(4+2)−5

4f=42+−5

4f=(42+−5)(Combine Like Terms)

4f=37

4f=37

Step 2: Divide both sides by 4.

4f / 4 = 37 / 4

f= 37 / 4

Answer:

f= 37 / 4

Hope this helps! :)

Using linear function concepts, the interpretation of the slope of the model is:

The slope indicates that the Fuel Efficiency decreases by an amount of 0.15 mpg for every 1 mile per hour increase of speed.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For this problem, the model is given as follows:

Fuel Efficiency = 32 - 0.15Speed.

The slope is of m = -0.15, meaning that for each mph that the average velocity increases, the fuel efficiency decays by 0.15 mpg.

The model is missing, and is given as follows:

Fuel Efficiency = 32 - 0.15Speed.

The units are as follows:

It asks for the interpretation of the slope.

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Answer: 12.5 pounds

Step-by-step explanation:

How many times greater, 75=6x

divide by 6

It is to be noted that the height of the bread is 5 centimeters. The hint given is in the information about the surface area. See the explanation below.

In this case, the surface area of bread is the total sum of the area of the base and perimeter. The surface area of the bread is given below.

That is:

A = 2 x b + p x H,

Where b is the area of the base,  p is the perimeter of the base and h is the height.

Recall that it is stated that 50% of the surface area of the bread is the crust.

The implication is that the surface area of both sides of the base is equivalent to the surface area of its perimeter.

That is:

2 x b = p x h

We can compute the perimeter of the bread as:

P = 4 x length
p = 4 x 10
p = 40cm

The area of the base is:

b = 10 x 10
b = 100cm²

Substituting the values in the above formula,
2 x 100 = 40 x h
200 = 40h
h = 200/40

h= 5cm.

Hence the height of the bread is 5cm.

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Answer:

y = 15x - 35

Step-by-step explanation:

STANDARD PLAN information:

Define the variables:

If it costs $40 for the first 5GB then y = 40 when 0 ≤ x ≤ 5.

It costs $15 per GB after the first 5GB. Therefore:

Therefore:

⇒ y = 40 + 15(x - 5)

⇒ y = 40 + 15x - 75

⇒ y = 15x - 35

Answer:

6, -2, and-1

Step-by-step explanation:

f(2) means that x is 2, so looking in the left column find x as 2, and then find the corresponding number beside it.

f(x)=0 so look for 0 in the right column and find the number corresponding to it in the left.

Answer:

#8 is equal to 6

#9 is equal to -2

#10 is equal to -1

Step-by-step explanation:

If you look in the x column for 2 the outcome is 6

If you look in the f(x) column for 0 the income is -2

If you look in the f(x) column for 1.5 the income is -1

Using a proportional relationship, it is found that:

a) The independent variable is x.

b) The dependent variable is y = 12x.

c) The domain is of 0 ≤ x ≤ 25.

d) The range is of 0 ≤ y ≤ 300.

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as shown below:

y = kx

In which:

For this problem, Jennifer makes $12 an hour, hence the constant is of k = 12 and the equation is:

y = 12x.

She can work between 0 and 25 hours, hence:

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Jeweler needs 144 inches of silver chain to make the necklaces and 108 inches of silver chain to make the bracelets.

For the given question;

The total length of silver chain jeweler had = 36 inches.

Length of silver chain required to make necklaces = 4 times.

So, multiply 36 with 4 to get the result;

36 x 4 = 144.

Thus, the silver chain required to prepare the necklaces is 144 inches.

For the making of bracelets = 3 times the length of silver chain.

So, multiply 36 with 3 to get the result.

36 x 3 = 104

Thus, the length of silver chain required to prepare bracelets is 104 inches.

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Answer: None

Step-by-step explanation: Trick question the total is 110 and none took both math and physics

Answer:

Explanation below:

Step-by-step explanation:

So basically x is the diameter - so is the radius times by 2

The radius is the length from the center of the circle to the edge which in this case is 7.9 + 8.9 = 16.8

So from this we have worked out the radius which is 16.8

But x is the diameter so we have to times 16.8 by 2 which gives 33.6

Answer: :( I don’t know how to solve the problem

Step-by-step explanation:

The population of the city next year, after decreasing, will be 359,778

Here, we are given that the population of a city decreases by 1.7 percent per year.

This, means that the city's population will decrease by 1.7% in 1 year, (1.7 × 1.7)% in 2 years and so on.

The population of the city this year is given to be 366,000.

Thus, next year, the population will decrease by-

1.7% of 366,000

= 1.7/100 × 366,000

= 17/10 × 3,660

= 17 × 366

= 6,222

Thus, the city's total population next year will be-

366,000 - 6,222

= 3,59,778

Hence, the city's population to the nearest individual comes out to be 359,778.

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2a + 3b = 7
-> 3(2a + 3b) = 21
6x + 10y = 40
-> (6x+10y)/2 = 20

Therefore, 6a + 9b = 21 ; 3x + 5y = 20.

The value of 6a + 9b is 21 and the value of 3x + 5y is 20

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equations are,

2a + 3b = 7                  (1)

and 6x + 10y = 40        (2)

To find the value of 6a + 9b,

Multiply equation (1) with 3,

3(2a + 3b) = 7 x 3

6a + 9b = 21

To find the vale of 3x + 5y,

Divide equation (2) by 2,

1/2(6x + 10y) = 40/2

3x + 5y = 20

The required values are 21 and 20.

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The value of the exponential form (-15)³ is -3375.

The  f(x)= exp (x) or eˣ are used to represent the exponential function in mathematics (where the argument x is written as an exponent).

We know that any exponential form such as (-15)³ can be written as

-15×-15×-15 = -3375

Therefore the solution of the exponential form is -3375 .

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Answer:

Step-by-step explanation:

(a+6)(a-3)

A line of best fit (linear equation) to model this data is y = 27x + 699.43

A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the game would be plotted on the x-axis of the scatter plot while the attendance would be plotted on the y-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that a linear equation for the line of best fit is given by:

y = 27x + 699.43

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By using percentage, we conclude that the total cost of the stereo equipment is $114.8.

The worth of stereo equipment is $112 and there is a 2.5% processing fee for using a credit card.

Whenever we purchase anything with a credit card we have to pay a processing fee that a Bank charges.

To find the total cost of the stereo equipment, we have to add the worth of the stereo equipment and processing fee for using a credit card.

And to find the processing fee for using a credit card, we have to calculate 2.5% of the worth of the stereo equipment.

So, 2.5/100 x 112 = 2.8

Therefore, the required processing fee for using a credit card is $2.8.

The total cost of the stereo equipment = $112 + $2.8 = $114.8

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The angle between the line PV and the plane PTWS is 29.4°

In this question we have been given a cuboid PQRSTUVW

We need to find the angle between the line PV and the plane PTWS.

First we find the length of the line PW which is diagonal of rectangular surface PTWS.

In right triangle PWS by Pythagoras theorem,

PW² = PS² + SW²

PW² = 19² + 16²

PW² = 361 + 256

PW² = 617

PW = 24.84 cm

now, consider a right triangle PWV.

Consider tangent of angle VPW

tan(∠VPW) = VW / PW

tan(∠VPW) = 14 / 24.84

∠VPW = tan^{-1}(0.5636)

∠VPW = 29.4°

Therefore, the angle between the line PV and the plane PTWS is 29.4°

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Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.

What is Average speed?

The average speed is the total distance traveled by any object in a particular time interval.

Given that;

Distance covered by Roger = 13.2 miles

Time is taken by Roger = 1.6 hours

Distance covered by Ana = 10.85 miles

Time is taken by Ana = 1.4 hours

Now, Calculate the speed of Roger and Ana as;

Speed = Distance / Time

For Roger,

Speed = 13.2/1.6 = 8.25 mph

For Ana,

Speed = 10.85/1.4= 7.75 mph

Hence, Roger has a faster speed at 8.25 miles per hour compared to Ana who ran with a speed of 7.75 mph.

Answer:

20

Step-by-step explanation:

280 divided by 14 is 20

Area= (length)(width)

280= (14)(x)

280=14x

divide by 14

20=x

The highest common factor of N and 500 is 2²x5² and The lowest common multiple of N and 500 is [tex]2^{3}[/tex]x[tex]5^{3}[/tex]x7.  p, q and r is p =2 , q =2 , r =1

Prime factorization is the technique of expressing a number as the product of prime numbers. The only two components in prime numbers are the number itself and the number itself. Prime numbers include, for instance, 2, 3, 5, 7, 11, 13, 17, 19, and so forth. Any number can be represented as a sum of prime numbers by "prime factorizing" it.

Given that : Written as product of their prime factors N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex] and 500= 2² x 5³ The highest common factor of N and 500  is 2² x 5³? The lowest common multiple of  N and 500 is  2²x5²x7.

N= [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]

500= 2² x 5³

highest common factor of N and 500  is 2²x5²

p ≥ 2

q = 2

r ≥ 0

The lowest common multiple of  N and 500 is  2²x5²x7.

HCF x LCM = N * 500

=> 2²x5²  x 2²x5²x7 =  [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]  x 2² x5³

=>  2²x5x7 = [tex]2^{p}[/tex] x[tex]5^{q}[/tex]x[tex]7^{r}[/tex]

p = 2

q = 1  but q = 2 as per HCF

r = 1

There is mistake in data

As LCM should have [tex]5^{3}[/tex] atleast as 500 has 5^2

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