If the Pentagon below is to he reflected over the y-axis, which point would not move at all?

In the given graph, the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

To find the equation of the quadratic function, we start by using the vertex form:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:

\(y = a(x - 4)^2 - 2\)

Next, we use the other two points to find two additional equations:

\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)

Simplifying these equations, we get:

\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)

So the equation of the quadratic function is:

\(y = (1/2)(x - 4)^2 - 2\)

Now, we can answer the questions:

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:

\(y = (1/2)(0 - 4)^2 - 2 = 6\)

So the y-intercept is (0,6).

To find the x-intercepts, we set y = 0 in the equation:

\(0 = (1/2)(x - 4)^2 - 2\)

Simplifying, we get:

\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)

So the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

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Answer:

Look in explanation

Step-by-step explanation:

for each k(x) value, plug the x into the given equation

-4: 1/2 (-4) -1 = -2-1=-3

all are solved this way

-2: -2

0: -1

2: 0

4: 1

ordered pair will be (x, (k(x))

for example (-4, -3)

do this for all other points

slope can be found by taking the change in y over change in x

so -2- -4 divided by -2 - - 3 = 2/1 = 2

slope = 2

hope that makes sense

Answer:

\(h \:(x) = 30 \: {x}^{2} - 54x + 10\)

Answer:

Step-by-step explanation:

The value that would have the most dots on a line plot is given as follows:

4.25.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

A line plot is built from the dot plot, in which:

Hence the value 4.25 is the value in this problem that would have the most dots in a line plot, as it is the value that appears the most times in the data-set (only value to appear three times).

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Answer:

e

Step-by-step explanation:

The factors of a quadratic polynomial are:

where x1 and x2 are the roots (or zeros) of the polynomial

Using the quadratic formula, we get:

Then, the factor are: (x - 4) and (x + 6)

Answer:

y = 6h  h = hour

Step-by-step explanation:

9514 1404 393

Answer:

  (x +3) -14

Step-by-step explanation:

The total of a number and 3 will be represented by (x +3). Fourteen less than that is ...

  (x +3) -14  or  -14 +(x +3)

The interest Raymond will pay this month is $54.98

What does APR mean?

APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate

monthly interest=21.99%/12

What is the monthly interest amount in dollars?

The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month

monthly interest=$3,000*21.99%/12

monthly interest=$54.98

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Answer:

A=-2 and B=7

Equation is -2x+7y=3

Step-by-step explanation:

The number of farms whose land and building values are between $1,200 and $1,400 is given as follows:

50 farms.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Considering the mean of $1,300 and the standard deviation of $100, measures between $1,200 and $1,400 are within one standard deviation of the mean, hence the percentage is of 68%.

The total amount is of 74 farms, hence the amount relative to 68% of 74 is of:

0.68 x 74 = 50 farms. (rounded).

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Answer:

this is hard

Step-by-step explanation:

is it trigonometry?

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

14w -29x

Step-by-step explanation:

-4w -6(4x -3w) -5x

= -4w -6(4x) -6(-3w) -5x (expand)

= -4w -24x +18w -5x

(grouping like terms together,)

= 18w -4w -24x -5x

= 14w -29x

Answer:

Step-by-step explanation:

17:3 is already in lowest terms. 17:3 = 34:6, 51:9, etc.

15:60 = 1:4

Answer:

2 × 3^2 × 7

Step-by-step explanation:

hope this works for you :)

Answer:

They are collinear if they are on the same line

Answer:

12 1/2 gallons

Step-by-step explanation:

Answer: So, the sales tax on the item is $49.

Step-by-step explanation:

The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:

Sales tax amount = $350 * 14% = $350 * 0.14 = $49

So, the sales tax on the item is $49.

Answer:

Step-by-step explanation:

divide length by 100

Answer:

2700pi \(m^{3}\)

Step-by-step explanation:

The radius of cylinder is 15 meters and the height is 12 meters.

The volume of cylinder is

V = \(\pi r^{2} h\)

Where, r is radius and h is height.

Substitute r = 15 and h = 12 in the volume formula.

V = \(\pi (15)^{2} (12)\)

V = 2700\(\pi\)

The volume of the cylinder is 2700\(\pi\) m³.

Answer:

the answer should be 2700pi

Step-by-step explanation:

Using the Poisson distribution, it is found that there is a 0.5414 = 54.14% probability that a randomly chosen school in Samarkand will close for 1 or 2 days next month.

We have the mean in an interval, hence, the Poisson distribution is used.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

Average of 24 days each year, considering that a year has 12 months, the monthly mean is of \(\mu = \frac{24}{12} = 2\)

Then:

\(P(1 \leq X \leq 2) = P(X = 1) + P(X = 2)\)

In which

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 1) = \frac{e^{-2}2^{1}}{(1)!} = 0.2707\)

\(P(X = 2) = \frac{e^{-2}2^{2}}{(2)!} = 0.2707\)

\(P(1 \leq X \leq 2) = P(X = 1) + P(X = 2) = 0.2707 + 0.2707 = 0.5414\)

0.5414 = 54.14% probability that a randomly chosen school in Samarkand will close for 1 or 2 days next month.

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Answer:

Step-by-step explanation:

Part A:

Let's assume that the velocity of the runner changes linearly over time. We can use the slope-intercept form of a linear equation, y = mx + b, to describe the velocity of the runner at different times. In this case, the y-axis represents the velocity in km/h and the x-axis represents time in hours. We can define:

y = velocity of the runner in km/h

x = time in hours

The velocity of the runner changes by -2/3 km/h for every hour that passes. This gives us a slope of -2/3. We can use the point-slope form of a linear equation to find the equation of the line:

y - 5 = -2/3(x - 1)

Simplifying this equation, we get:

3y - 15 = -2x + 2

Rearranging to standard form, we get:

2x + 3y = 17

So the equation in two variables in standard form that can be used to describe the velocity of the runner at different times is 2x + 3y = 17.

Part B:

To graph the equation obtained in Part A for the first 5 hours, we can simply plot points for different values of x and y. For example, we can use x = 0, 1, 2, 3, 4, and 5 to find the corresponding values of y using the equation 2x + 3y = 17. Then we can plot these points on a graph and connect them with a straight line.

Here are the values of y for different values of x:

x = 0, y = 17/3

x = 1, y = 5

x = 2, y = 13/3

x = 3, y = 3

x = 4, y = 7/3

x = 5, y = 1

Plotting these points and connecting them with a straight line, we get the graph of the equation 2x + 3y = 17 for the first 5 hours:

|

6.0 -| .

| .

5.5 -| .

| .

5.0 -| .

|.

4.5 -|

|

4.0 -| .

| .

3.5 -| .

| .

3.0 -| .

|.

2.5 -|

|

2.0 -| .

| .

1.5 -| .

| .

1.0 -|.

|

0.5 -|

|

--------------

0 1 2 3 4 5

The y-intercept of the line is 17/3, which represents the initial velocity of the runner at time 0. The slope of the line is -2/3, which represents the rate of change of the velocity over time.

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Part A:

Let v be the velocity of the runner in km/h and let t be the time elapsed in hours. We can use the two given data points to form a system of two equations:

v = 5 when t = 1

v = 3 when t = 3

To find the equation in standard form, we can first use point-slope form:

v - 5 = m(t - 1) (using the point (1, 5))

v - 3 = m(t - 3) (using the point (3, 3))

Simplifying both equations:

v - 5 = m(t - 1)

v - 3 = m(t - 3)

v = mt + (5 - m)

v = mt + (3m - 3)

Setting the right-hand sides equal to each other:

mt + (5 - m) = mt + (3m - 3)

Simplifying and rearranging:

-m = -2

m = 2

Substituting m = 2 into one of the equations above:

v = 2t + 3

This is the equation in two variables in standard form that describes the velocity of the runner at different times.

Part B:

To graph the equation v = 2t + 3 for the first 5 hours, we can plot points for different values of t and then connect them with a line. For example:

When t = 0, v = 3, so the point (0, 3) is on the line.

When t = 1, v = 5, so the point (1, 5) is on the line.

When t = 2, v = 7, so the point (2, 7) is on the line.

When t = 3, v = 9, so the point (3, 9) is on the line.

When t = 4, v = 11, so the point (4, 11) is on the line.

When t = 5, v = 13, so the point (5, 13) is on the line.

Plotting these points on a coordinate plane and connecting them with a line, we get the graph of the equation v = 2t + 3 for the first 5 hours:

    |

 15 +-------*

    |       |

 13 +           *

    |           |

 11 +               *

    |               |

  9 +                   *

    |                   |

  7 +                       *

    |                       |

  5 +                           *

    |                           |

  3 +---------------*-----------*

    0   1   2   3   4   5   6   7

The x-axis represents time (t) in hours, and the y-axis represents velocity (v) in km/h. The line starts at (0, 3) and has a slope of 2, indicating that the velocity is increasing by 2 km/h for every hour that passes.

Step-by-step explanation:

Answer: \((-\infty, -3)\)

Step-by-step explanation:

\(2w-2 < -8\\\\2w < -6\\\\w < -3\)

\(4w+3 < 11\\\\4w < 8\\\\w < 2\)

So, the solution is \((-\infty, -3)\)

The table makes it abundantly evident that buying costs less than renting does. Buying a house is therefore better over the course of 15 years. By buying a home instead of renting one, you can save $5,222.4.

Every object's length can be determined using measuring tools like a ruler, measuring tape, etc. For example, a ruler may be utilized to measure the length in inches of a pencil. A foot scale can be used in a classroom to gauge the heights of the students.

Step 1

Buying a home is more advantageous if someone is looking for somewhere to live for an extended period of time. Second, if a person buys the home, it can be sold at a higher price in the future since rental prices after a specified term and after a few years, say 10 or 15, cumulative rental charges become greater than the initial purchase price.

However, according to the above table, renting a property is preferable if the need for the home is for a shorter duration, like fewer then 5 or 10 years, in order to save money.

Step 2

1 year

The cost for Purchasing a house = 30,000 + 1 × 12 × 809.32 = $39,711.84

The cost of renting a house = 1 × 12× 900 = $10,800

So, it is evident that there's a difference between buying and renting a home of $28,911.84. So, renting a home is preferable.

Step 3

5 year

The cost of purchasing the home for five years is listed as $78559.20, whereas the cost of renting the home for five years was $54,900.

Again, renting is more affordable than buying. By renting a home, one could save $23,659.2 (78559.20-54900).

10 years

The cost of purchasing the home over 10 years is shown as $127,118.40, while the cost of renting the home for 10 years was $115,200.

Renting is less expensive than buying. Yet, buying a house is advantageous if it can be bought or rented out; otherwise, leasing one is advantageous.

Step 4

15 years

The table clearly shows that purchasing is less expensive than renting. Over the period of fifteen years, purchasing a home is therefore preferable. You can save $5,222.4 by buying a house instead of renting one.

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Answer:

the experimental probability that the next vase produced at the factory will be chipped is 1/5.

Step-by-step explanation:

Since 5 out of the 13 boats that docked were from North Carolina, the experimental probability of the next boat being from North Carolina is the number of favorable outcomes (i.e., the number of boats from North Carolina) divided by the total number of outcomes (i.e., the total number of boats that docked).

Therefore, the experimental probability that the next boat to dock will be from North Carolina is:

P(North Carolina) = 5/13

For the second question:

Since 2 out of the last 10 vases produced were chipped, the experimental probability that the next vase will be chipped is:

P(chipped) = 2/10 = 1/5

Therefore, the experimental probability that the next vase produced at the factory will be chipped is 1/5.