A turtle and a rabbit are in a race to see who is first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continues at a constant speed of 40 feet per minute for the last 50 feet. Determine which animal won the race and by how much time.

The coordinates of the point M' is (-6,2) when the point M was reflected across x =-2.

Here, assume that there is a point A(a, b). This point is reflected across the line x = -2. When reflected across this line, the value of the y coordinate of this point A will not change, only the value of the x coordinates of the point A will change.

Here, the point M(1,2) is reflected across the line x = -2.

The coordinates of the reflected point M' are (a, b).

The value of will b will remains same as that of the point M.

Now, the location of a,

the distance between the line x = -2 and a will be same as that of the distance between 2 and x =-2 which is 4 units,

So, the location of a will be fours units away from x =-2 and in the opposite direction so, a = -6

So, the Point M' is (-6,2)

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If He rides back home, taking the same route, on a bus that travels at a rate of 40mi/hr. The entire trip takes 3.5 hrs. How far along this route is Terrence’s house from the theater is : 50 mile.

Movie time = 2hrs and 15mins

Let convert the movie time

2hrs and 15mins = 2 15/60 h = 2 1/4 h = 2.25 h

Now let calculate the bus time and the distance

Bus time = Entire time - Walking time

Bus time = 3.5 h - 2. 25 h

Bus time =  1.25 h

Now let calculate the distance

Distance = Speed × Time

Distance =  40mi/hr ×  1.25 h

Distance = 50 mile

Therefore the distance is 50 mile.

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Answer:

  z = 134°

Step-by-step explanation:

You want to know the measure of exterior angle z given remote interior angles of the triangle are 77° and 57°.

The exterior angle of a triangle is equal to the sum of the remote interior angles of the triangle. (It is useful to remember this.)

  z = 77° +57°

  z = 134°

__

Additional comment

As you know the value of the interior angle at C will be the supplement of the value of z: (180° -z). Then the sum of the interior angles is ...

  77° +57° +(180°-z) = 180°

Add (z -180°) to both sides of this equation and you get ...

  77° +57° +(180°-z) +(z -180°) = 180° +(z -180°)

  77° +57° = z . . . . simplified

Answer:

The place value of 5 is HUNDREDTH

Explanation:

From the right-hand side, the place value of:

8 is Hundred

2 is Ten

6 is Unit

1 is Tenth

and finally, what we are required to tell,

5 is Hundredth.

Answer:

-6.3 is your slope.

Step-by-step explanation:

Hello, there! Nice to meet you.

This is a pretty easy question, as it's written in y = mx + b form.

When it's written like this, the m in replacement is your slope value.

So, in this case, -6.3 is your slope.

If I had y = 3x + 6, then 3 would be the slope, but that's just an example.

Once more, the m value is your slope.

Hope this helped, and best of luck with the rest of your assignment! (:

Best fit quadratic equation is: y = 77x + 140

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. An example of a quadratic equation is x² + 2x + 1. Here, an is greater than zero because if it equals zero, the equation will cease to be quadratic and change to a linear equation, such as bx+c=0. As a result, we cannot refer to this equation as a quadratic equation.

Given,

A shot-putter throws a shot and its height is noted every 20 feet

Best fit quadratic equation is:

y = 77x + 140

As after this equation, feet above ground is decreasing.

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Answer: C. Both are correct. Gregory's definition can be simplified to get Felipe's definition.

Step-by-step explanation:

-1, 6, 13

[tex]a_n=a_1+(n-1)d\\\\d=a_2-a_1\\\\d=6-(-1)\\\\d=6+1\\\\d=7[/tex]

Hence,

[tex]a_n=-1+7(n-1)\\\\a_n=-1+7(n)-7(-1)\\\\a_n=-1+7n-7\\\\a_n=7n-8[/tex]

4 tickets----------------------------->$40

8 tickts------------------------------->$x

Using cross multiplication:

8 tickets cost $80

Answer:

20 pencils for $2.50 has the lesser price per pencil.

Step-by-step explanation:

$0.13 compared to $2.50 ÷ 20 = $0.125

$0.13 > $0.125

Answer: y = -3x + 1

Step-by-step explanation:

Find the slope, rise/run:

-5 - (-17) / 2 - 6

-12/4 or -3

Find the y-intercept by substitution:

y = mx + b

-5 = -3(2) + b (Using the first coordinate)

1 = b

Answer:

Step-by-step explanation:

the first one

Given the expression:

The first step to solve it using the square root property, is moving the coefficient on the right side of the equation to the left side, changing it's sign:

Now, remember the rule for conjugates:

in this case we have the following:

therefore, we can factor the expression like this:

Finally, we have that the only values that make true the expression are:

The most appropriate choice for cube and cube root of a number will be given by-

8000 is a perfect cube number because cube root of 8000 is an integer.

Second option is correct.

What is cube and cube root of a number?

Let the number be p. If we multiply p three times with itself ([tex]p \times p \times p[/tex]), then we get the cube of p.

If we take [tex]\frac{1}{3}[/tex] power of p ([tex]p^{\frac{1}{3}}[/tex]), we will get the cube root of p.

[tex]8000 = 2^6 \times 5^3[/tex]

On taking the cube root of 8000, we get

[tex]\sqrt[3]{8000} = 2^2 \times 5[/tex]

          [tex]= 20[/tex]

which is an integer.

So 8000 is a perfect cube number.

so, 8000 is a perfect cube number because cube root of 8000 is an integer.

Second option is correct.

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Answer:

f ( 5, 2 )

h ( 4, -2 )

a ( 1,0 )

d ( -3, 5 )

Step-by-step explanation:

Assuming every point is one space.

We can find this by counting how far away it is form the origin for example f is 5 place right of the origin so x=5 and is above the origin two places so y=2. So (5,2) is the answer.

Answer:

6/3x=30 = x= 15

Step-by-step explanation:

2x=30

(divide) ^

simplify, x=15

Answer: 34.196 x 10^6

The quota sampling produces the same advantages for convenience sampling that stratified random sampling produces for probability sampling.

Sampling:

Sampling is defined as the process in statistical analysis where researchers take a predetermined number of observations from a larger population.

Given,

Here we need to find the type of sampling that produces the same advantages for convenience sampling quota sampling.

Before, move on to the result, first we have to know the details about quota sampling and the probability sampling.

Probability sampling defined as the selection of a sample from a determined number of population, when this selection is based on the principle of randomization, that is, random selection or chance.

In contrast to probability sampling, Quota sampling means a non-probability sampling method in which researchers create a sample involving individuals that represent a population.

Based on these definition we have identified that the method that is best suitable answer for this one is stratified random sampling.

Because the stratified random sampling means, is a probability sampling technique in which the total population is divided into homogenous groups to complete the sampling process.

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He got a 61.5% Discount

Maximum volume through the concept of maxima is 564.22 cm3.

What are maxima?

Volume of box=(50-2x)(10-2x).x

=4x^3-120x^2+500x

for maximum volume,

dv/dx=0

⇒12x^2-240x+500=0

⇒3x^2-60+14=0

x=17.63,2.36

d2v/dx2=24x-240

at x=2.36

d2v/dx2<0

∴x=2.36

v will be maximum

Maximum volume through the concept of maxima is 564.22 cm3.

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The quotient is  [tex]x-1+\frac{9}{x+6}[/tex]

The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder. Here, The dividend is the number, which is being divided. The divisor is the number, which divides the number (dividend) into equal parts.

Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. For example, dividing 15 by 3 means splitting 15 into 3 equal groups of 5.

In the above question we simply have to divide the dividend that is [tex]x^2+5x+3[/tex] with x + 6

and then we will get the quotient as x - 1 and remainder 9 .

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Solution

Where

Now,

Therefore, V = 150

The required equation is g(x)=x+6

What is an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. A polynomial equation is the most common sort of equation. A mathematical equation is akin to a weighted scale. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal. To keep the scale in balance, if grain is withdrawn from one pan of the balance, an equal amount of grain must be removed from the other pan. In general, if the identical operation is done on both sides of an equation, it stays balanced.

The required equation is g(x)=x+6, when the parent function is 6 units up

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The slope of the line between the two points defined in the graph is 1/2.

Slope of the line:

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

m = Δy/Δx

Where the net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line

Given,

There is a graph presented here.

Through the graph we have identified two points,

They are (3,0) and (-3, -3).

Now we need to find the slope of the line between these points.

Here we consider the values of (x1,y1) as (3,0) and the value of (x2,y2) as (-3,-3).

Through the values we have to identify the slope of the line.

For that, we have to apply the values on the formula,

Then we get,

m = (-3 - 0)/(-3-3)

m = -3/-6

m = 1/2

Therefore, the slope of the line is 1/2.

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Answer:

1,560 miles

Step-by-step explanation:

[tex]\frac{130}{5} = \frac{x}{60}[/tex]

Solve for x.  Multiply both sides by 60 to get 1,560.

Answer:

32 feet

Step-by-step explanation:

See attached worksheet

In February, Robbins and Myers, Inc. executed a 2-for-1 split, then the

(a) . The shares did she hold after the split is 940 shares.

(b) . The post-split price per share is $34.74

(c) . Janine didn't gain or lose any money during the event.

Based on the given conditions,

In February, Robbins and Myers, Inc. executed a 2-for-1 split.

That means,

2 - for - 1 stock split.

= 2 / 1

= 2

(a) . How many shares did she hold after the split?

Then,

Janine had 470 shares before the split.

Each share was worth $69.48.

= 470 shares * 2

= 940 shares

Hence,

The shares did she hold after the split is 940 shares.

(b) . What was the post-split price per share?

Each share was worth $69.48.

Then,

= $69.48/2

= $34.74

Hence,

The post-split price per share is $34.74

(c) . Show that the split was a monetary non-event for Janine

We can write,

After the split, Janine had 940 share worth $34.74.

Since they doubled the amount of share, but decrease the amount of each share.

So,

Janine didn't gain or lose any money during the event.

Therefore,

Robbins and Myers, Inc. executed a 2-for-1 split,

(a) . The shares did she hold after the split is 940 shares.

(b) . The post-split price per share is $34.74

(c) . Janine didn't gain or lose any money during the event.

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solution

For this case we can use the following proportion rule:

Then we can solve for f on this way and we got:

Answer:

25%

Step-by-step explanation:

5/20 = 1/4

1/4 x 100 = 100/4 = 25

(1 x 25)/(4x100) = 25/100

25%

Answer:

25%

Step-by-step explanation

5/20 = 1/4

1/4 x 100 = 100/4 = 25

(1 x 25)/(4x100) = 25/100

25%                                   Therefore They have lost 25% of there games