Sunny runs at a steady rate, and Moonbeam runs m times as fast, where m is a number greater than 1. If Moonbeam run to overtake Sunny a head start of h meteres, how many meters must Moonbeam run to overtake Sunny? ( Give your ansewr as an expression in terms of h and m.)

Hint : Let s be Sunny's rate. In terms of m and s, at what rate does Moonbeam catch up to Sunny?

Answer:

3x - 5y = 11

5(x + y) = 5

Expand the second equation:

5x + 5y = 5

Add both equations:

3x - 5y = 11

5x + 5y = 5

8x = 16

Solve for x:

8x = 16

x = 2

Input x in any equation and solve for y:

3(2) - 5y = 11

6 - 5y = 11

-5y = 5

y = -1

The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is the m:n ratio, finding the mid-point of the line, etc.

Make an opposite bisector of the Stomach muscle and mark the convergence point of line E. To check your outcome, measure AE and EB and the points between the bisector and Stomach muscle.

The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.

The diagram is given below.

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On Thursday when the correct time is 5:00h, watch shows 4:24h.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The watch is set at 11:00 h on Sunday.

Also, the watch loses 8 seconds in every hour.

To determine the time in watch on Thursday,

In one day total hours = 24 hours.

from Sunday 11:00 to Thursday 11:00

Total hours = 24 x 4 = 96 hours

And 11:00 to 5:00, total = 6 hours

Total hours = 96 + 6 = 102 hours

Since, watch loses 8 seconds in 1 hour

So in 102 hours watch losses = 102 x 8 = 816 seconds

816 seconds = 816/60 minutes = 13.6 minutes

The watch loses 13.6 minutes in 102 hours.

So the exact time will be, 4 : 24.

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The graph of the equation, y = -50x + 300, is given in the attachment below.

The equation of a line, where m is the slope or unit rate, and b is the y-intercept or starting value, is expressed as y = mx + b in the slope-intercept form.

Given the situation above, first determine the value of the starting value / y-intercept (b) and that of the slope / unit rate (m).

The starting value / y-intercept is b = 300.

The slope / unit rate is m =  - 50 [this is negative because the distance from home reduces as she drives at the speed of 50 mph]

To write the equation, substitute m = -50 and b = 300 into y = mx + b:

y = -50x + 300.

Thus, the graph of this equation, y = -50x + 300 is shown in the mage attached below.

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The line has a 17/5 slope and y has a value of 51 which will be (15, 51).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

The general equation for every straight line is y = MX + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).

So, the water level rises by 17 cm in 5 minutes.

Then in 15  minutes, the water will rise by:

15 * 17/5

3*17

51

Then (x, y) will be (15, 51).

Obtaining the slope as follows:

Formula: m = y1 - y2/x1 - x2

m = y2 - y1/x2 - x1

m = 17  - y/5 - x

m = 17/5

Therefore, the line has a 17/5 slope and y has a value of 51 which will be (15, 51).

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Answer:

3

Step-by-step explanation:

this problem we need to subtract

There is 6 1/2 grape juice and 3 1/3 orange juice

6 1/2 3 1/3

We get common denominators and one is 6

6 3/6 3 2/6

And now we subtract

3 1/6

And rounded down is 3

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Sales Tax added to the cost of the computer is 178.34 pounds

What is sales tax?

Sales tax is a tax imposed by the government on the price of a commodity for the sale of that commodity. Imposing sales tax on a product increases the price of the product. Nowadays, sales tax has been replaced by Goods and Service Tax (GST).

Here, sales tax is added to increase the price of the computer.

Cost of a computer = 964 pounds

Rate of tax added = 18.5 %

Tax added = [tex]\frac{18.5}{100} \times 964[/tex]

                  = 178.34 pounds

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By using the concept of function, it can be seen that the given table represents a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values under x represents the domain and the values under y represents the Range.

From the table it can be seen that

Every point of the domain maps to unique point on the range.

So this is a function.

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Answer:

15

Step-by-step explanation:

15

He walked 15

The change in the temperature after 4 1/4 hour is -6.8 C.

Given :

A freezer in a lab is set so that the temperature changes at a rate of –1.6 C every hour.

Temperature :

Temperature is the degree of hotness or coldness of an object.

The degrees must contain any units like kelvin , centigrade etc .

Change in temperature after 4 1/4 hours = change rate for hour * number of hours.

= -1.6 C * 4 1/4

= -1.6 C * 4.25

= -16 / 10 C * 425 / 100

= -16 * 425 / 10 * 100 C

= -6800 / 1000 C

= -68 / 10 C

= -6.8 C

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The estimate expected mean time for the given activity E from the give table data is equal to 101days.

As given in the question,

Let optimistic time be represented by [tex]T_{o}[/tex]

Most like time be represented by [tex]T_{m}[/tex]

And Pessimistic time be represented by [tex]T_{p}[/tex]

Optimistic time for activity E is equal to  [tex]T_{o}[/tex] = 91

Most likely time for activity E is [tex]T_{m}[/tex] = 100

Ans Pessimistic time for activity E is [tex]T_{p}[/tex] = 115

Estimated expected mean time

= [tex]( T_{o} + 4T_{m} + T_{p} ) / 6[/tex]

= [ 91 + 4(100) + 115 ] / 6

= 606/6

= 101

Therefore, option d. 101days represents the estimated expected mean time for the given activity E.

The complete question is:

From the given table:

                                                         { Time estimates (days)}

Activity   Predecessor             Optimistic       Most likely       Pessimistic

A              A, B, C                         30                   50                          62

B                  D                              90                    99                        108

C                  E                              85                   105                         115

D                  End                         19                      25                         31

E                    F                             91                     100                        115

F                   End                          62                    65                          68

What is the estimated expected (mean) time for activity E?

Multiple choice

a. 91 days        b. 100 days          c.  99 days       d. 101 days        e.115 days

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The registration fee is $60.

Given,

Sale Price = $5400

The value of the registration:

Registration fee = 0.9% of $5,400

                          = (0.9/100) * 5,400

                          = 60

Therefore, the registration fee is $60.

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The rate of change in the attendance of students between 2018 and 2021 is 1.24.

The term "rate of change" (ROC) describes the rate at which something changes over time.

Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).

The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.

Divide the change in y-values by the change in x-values to determine the average rate of change.

Identifying changes in measurable values like average speed or average velocity calls for the knowledge of the average rate of change.

So, according to the given table:

The rates of change between 2018 and 2021 are:

2018/2021

93/75

1.24

Therefore, the rate of change in the attendance of students between 2018 and 2021 is 1.24.

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Answer:

$60

Step-by-step explanation:

Let x = the original cost

x - .25x = 45

.75x = 45  Divide both sides by .75

x = 60

If its half-life is 93 minutes, then the amount left after 279 minutes will be equal to 164 grams.

In radioactivity, the half-life is the amount of time needed for half of a radioactive sample's atomic nuclei to spontaneously decay (convert into different nuclear species by emitter particles and energy) or, alternatively, the amount of time needed for the radioactive material's disintegration rate to drop by half.

As per the given information given in the question,

Initial amount, N₀ = 1312 grams

Time elapsed, t = 279 min

Half-life, [tex]t^1^/^2[/tex] = 93

Then, use the formula of half-life:

N(t) = N₀[tex](\frac{1}{2})^t^/^(^t^)^1^/^2[/tex]

Substitute the values in above equation,

N(t) = 1312[tex](\frac{1}{2})^2^7^9^/^9^3[/tex]

N(t) = 1312(1/2)³

= 1312 × 0.125

N(t) = 164 grams.

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Answer: 164 grams

Step-by-step explanation: I got the answer right on my ixl

Answer:

To find the change in temperature per ice cube, you need to divide the total change in temperature by the number of ice cubes. In this case, you would divide -15F by 5 ice cubes to get -3F per ice cube. The negative sign indicates that the temperature of the tea decreased.

Step-by-step explanation:

Answer:

domain=5,12,3

range=0,4,-3

Answer:

Step-by-step explanation:

You want to know if 5x²y²z +10x²y²z is monomial, binomial, or trinomial, and what its degree is.

The degree of a term is the sum of the degrees of the variables in the term:

  degree = 2 + 2 + 1 = 5

Two terms are shown. However, the terms are like terms, so can be combined into one term:

  15x²y²z

This tells us the expression is a monomial.

__

Additional comment

The terms of a binomial must be unlike. That is, they don't count as separate terms if they can be combined.

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Using distance, rate and time the answer is 155093.3.

Distance is the total movement of an object without any regrad to direction. It is the length of the space between two points .

Given question are-

D=rt where d represent distance.

R represent= Rate

T represents= Time

Based on the given conditions formulate :

A dolphin swims= 465,280

Time = 3hour

=465280/3

Evaluate the expression/equation we can get -

155093.3

Thus the answer is

155093.3

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The slope of the line is  1/2 or 0.5

The slope of a line characterizes the direction of a line.

To find the slope of a line when the coordinates of the two points are given  you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

Thus if

A ( x1, y1)  and B( x2, y2)

The slope of the line is  y2 - y1 / x2-x1

Calculations

Given ;

A ( -21, -47)

B(-15, -44)

slope = 3/6

           =1/2 or 0.5

The slope of the line is 1/2 or 0.5

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Answer:

30

Step-by-step explanation:

The 45-45-90 Triangle Theorem states that in the isosceles 45-45-90 triangle, if we designate each leg as [tex]a[/tex], the base, or hypotenuse is [tex]a\sqrt{2}[/tex] . Since we know the leg is [tex]15\sqrt{2}[/tex], the hypotenuse would be:

[tex]15\sqrt{2} * \sqrt{2} =\\15 * 2=\\30[/tex]

Answer:

A = -5

Step-by-step explanation:

Answer: 1,235 is your final answer!

Step-by-step explanation:

First we do what's inside the Parentheses always remember PEMDAS

P-Parentheses

E-Exponent

M-Multiplication

A-Addition

S-Subtraction

So first we do what's inside the brackets!

22-(8-2)+ (1230-11)

22-6+1219

16+1219

1235.

Follow the PEMDAS steps to simplify the answer!

The value of P(-3) =-191 if the given polynomial function is

P(x) = 6x³-5x² - 4x + 4

A polynomial is an expression made up of exponents, constants, and variables that are combined using addition, subtraction, multiplication, and division in mathematics, according to the definition of a polynomial. Polynomials are frequently employed in both mathematics and science. For example, they are employed to define polynomial functions, which are present in a range of fields ranging from elementary physics and chemistry to economics and social science. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. In high mathematics, polynomials are used to build algebraic varieties and polynomial rings, which are essential concepts in algebra and algebraic geometry.

Given,

P(x)= 6x³-5x²-4x+4

P(-3)=6(-3)³-5(-3)²-4(-3)+4

=6(-27)-5(9)+12+4

=-162-45+16

=-191

So, the value of P(-3)= -191

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By using the segment method, you handle data in analytics to gain greater insights into our audience's behavior.

Analytics:

Analytic refers the field of computer science that uses math, statistics, and machine learning to find meaningful patterns in data.

Given,

Here we need to find how do you handle data in analytics to gain greater insights into our audience's behavior.

In order to find the solution for this one, we must know the definition for the terms of the following,

Audience's behavior - attitudes that affect the behavior of an audience towards a brand or category.

Data - information that has been translated into a form that is efficient for movement or processing.

Insights - the capacity to gain an accurate and deep understanding of someone or something.

Here we have divide the full question into segment to solve this.

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Solution n(x), where n(x) is the denominator of the function (notice that this only works if t(x) is not zero for the same value of x).When the denominator is equal to zero, you can solve for x to determine the vertical asymptotes.

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Answer:

To solve the quadratic equation 3w^2 - 12w = -12, we can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -12, and c = -12. Plugging these values into the formula, we get:

w = (-(-12) +/- sqrt((-12)^2 - 43(-12))) / (2*3)

Simplifying, we get:

w = (12 +/- sqrt(144 + 144)) / 6

w = (12 +/- sqrt(288)) / 6

w = (12 +/- sqrt(288)) / 6

w = (12 +/- 16.97) / 6

w = (12 +/- 16.97) / 6

w = 28.97/6 or -4.97/6

w = 4.828 or -0.828

Therefore, the solutions to the equation 3w^2 - 12w = -12 are w = 4.828 and w = -0.828.

Answer:

w = 2

Step-by-step explanation:

[tex]3w^{2} -12w=-12\\3w^{2} -12w+12 = 0\\[/tex]

[tex]\frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex]

[tex]\frac{-(-12) + \sqrt{(-12)^{2} - 4(3)(12) } }{2(3)} = 2[/tex]

Answer: x = 25

Step-by-step explanation:

(x-7) = 36/2

x-7 = 18

x = 18 +7

x = 25

Answer: x = 1 and x = 13.

Step-by-step explanation: To solve the equation (x - 7)^2 = 36, we can first rewrite the equation as x^2 - 14x + 49 = 36.

Next, we can rewrite the equation as x^2 - 14x + 13 = 0.

To solve for x, we can then use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a = 1, b = -14, and c = 13.

Substituting these values into the formula, we get:

x = (14 +/- sqrt(14^2 - 4(1)(13))) / 2

x = (14 +/- sqrt(196 - 52)) / 2

x = (14 +/- sqrt(144)) / 2

x = (14 +/- 12) / 2

The values of x are therefore 1 and 13.

Therefore, the correct answer is x = 1 and x = 13.

Answer:

Step-by-step explanation: