The graph of a cubic polynomial function
has horizontal tangent lines at (1, −2) and (−1, 2). Find
an equation for the function and sketch its graph.

Because the ratios between each set of numbers are equal, and the graph passes through the point, the linear relationship is proportionate (0,0).

Proportional connections are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportional relationship. The "constant of proportionality" is the name given to this variable.

The origin, points (2,14.5), (4,29), and (6,43.5) are provided (0,0).

We are aware that the ratios are equivalent in a proportional connection, i.e.

So,

⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25

The linear relationship is a proportionate relationship since the ratios are equal.

The given situation's graph has been drawn, and it is evident that the graph passes through its origin, or "zero," which is (0,0)

Since the ratios between each set of data are equal, the linear relationship can only be a proportional relationship because the graph passes through the point (0,0).

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Answer:

The equation [tex]\frac{csc x -1}{cot x} = \frac{cot x}{csc x + 1}[/tex] can be simplified by cross-multiplying the fractions and then solving for x. This will result in the equation [tex]csc^2 x - 1 = 0[/tex], which can be simplified to [tex]csc x = 1[/tex], and thus [tex]x = \frac{\pi}{2} + n\pi[/tex], where n is any integer.

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Hey there!

If you are solving for x, then your final solutions are [tex]x=\sqrt{-y},-\sqrt{-y}[/tex].

Hope this helps!

The z-score for the given values is - 0280, -1.08, 0.49, 0.147 respectively.

The z-score of a data point defines this precise distance in terms of standard deviations above or below the mean.

This formula is used to determine a z-score:

mean standard deviation for each data point

Means of the data points with a standard deviation of z

Below is the same equation in symbol form:

z= x−μ / σ

Here are some noteworthy z-score details:

When the z-score is high, the data point is.

A negative z-score indicates that a data point is below average.

If the z-score is close to 0.00, the data point is thought to be around average.

For the given data set,

14 9 19 18 5 8

Mean of the data =sum of observations / no. of observations =  73/6 = 12.16

Mean of the data is 12.16

Standard deviation = √∑(x - μ)² / n-1

= ​5.70

a) The z- score of 12 is

z=  x−μ / σ

z = 12 - 12.16 / 5.70

z = - 0280

b) x = 6,

z = 6 - 12.16/5.70

z = -1.08

c) x = 15

z = 15 - 12.16/5.70

z = 0.49

d) x = 13

z = 13 - 12.16 / 5.70

z = 0.147

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The equation for the graph will be

[tex]y=1 cos(3x)[/tex]

The function y = cos(2x + π/4) is a cosine function where the independent variable x is multiplied by 2 and then has π/4 added to it before the cosine is applied. The amplitude of this function is 1 and the period is π.

In this question

[tex]we assume, \\y=acos(bx)\\\\when x=0y=1\\\\y=acos(bx)\\\\1=acos0\\\\a=1\\so y=cos(bx)\\\\when x=\pi/3 y=-1\\y=cos(b.\pi/3)\\-1=cos1b.pi/3=cos(pi)\\b=3[/tex]

[tex]y=acosbx[/tex]

[tex]so, y=1.cos(3x)[/tex]

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The gauge pressure, or the difference between the inner pressure and the external pressure p0, is what the pressure gauge on a gas cylinder measures. Give the gauge pressure the letter pg.

The gas in the cylinder weighs mi at pgi gauge pressure when it is full. We can apply the ideal gas formula, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, assuming the cylinder's temperature stays constant.

We can assume that the product nRT is constant because the temperature is constant. Consequently, we can write:

(pgf + p0) = (pgi + p0)(Vi) (Vf)

where Vi is the cylinder's initial volume and Vf is the cylinder's final volume when the pressure is pgf.

We also know that the gas's mass, m, is determined by multiplying the number of moles, n, by the molar mass, M, or m = nM.

The ideal gas law can be used to express the number of moles in terms of volume and pressure:

m/M = P(V/RT) = n

Thus, mf = pgf(Vf/RT).

M equals (pgf + p0)(Vf/RT).

(Vi/RT) Mi (pgi + p0)

where mf is the mass of gas still present in the cylinder at pgf pressure.

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Any square-free integer can be expressed as the product of a square-free integer (which has no square  factors) and a perfect square (which has only square factors). This product is unique for any given square-free integer.

Any square-free integer can be expressed as the product of a square-free integer and a perfect square. This is because a square-free integer has no square factors, so the product of a square-free integer and a perfect square would have only square factors, and thus be square-free. To show that this product is unique for any given square-free integer, we can use the fact that any integer can be expressed as the product of its prime factors and that a square-free integer has no square factors. This means the prime factors of the square-free integer are all distinct, and thus the product of the square-free integer and the perfect square can be expressed as the product of the prime factors of the square-free integer and the prime factors of the perfect square. Since the prime factors of the perfect square are all the same, the product is uniquely determined by the prime factors of the square-free integer. Thus, the product of a square-free integer and a perfect square is unique for any given square-free integer.

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The measure of the angle represented by the expression (7x+12) is 61°.

The measure of the angle represented by the expression (7x+12) is determined as follows:

The same-side interior angles are supplementary and their sum is 180°.

7x + 12 and 17x are same-side interior angles and are, therefore, supplementary.

7x + 12 + 17x = 180°

solving for x by summing similar terms:

24x + 12 = 180

24x = 168

Dividing both sides by 24

x = 7

Therefore,

7x + 12 = 7 * 7 + 12

7x + 12 = 61°

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Answer:

3.53%

Step-by-step explanation:

annual 3.5%

So half a year =1.75% and compound twice a year.

equivalent annual rate is (1+1.75%)^2 -1 =.0353 =3.53%

Answer:

Train 1: 130 km/h

Train 2: 108 km/h

Step-by-step explanation:

Let train 1 be the faster train.

Train 1:

distance = d

speed = s

time = 2 hours

Train 2:

distance = 476 - d

speed = s - 22

time = 2 hours

speed = distance/time

distance = speed × time

Train 1:

d = 2s

Train 2:

476 - d = 2(s - 22)

d = 2s

476 - d = 2s - 44

d = 2s

476 - 2s = 2s - 44

520 = 4s

s = 130

s - 22 = 108

Train 1: 130 km/h

Train 2: 108 km/h

The change in height divided by the change in time yields the firework's average speed from t=1 to t=3 seconds.

Average change speed is equal to (h(3) – h(1)) (3 - 1)

h(3) = 16*32 + 105*3 + 10 = 536

h(1) = 16*12 + 105*1 + 10 = 126

Average speed = (536 - 126)/(3 - 1) = 410/2 = 205 ft/sec

h(t) = 16r2 + 105t + 10 models the height of a firework t seconds after it is released. We must determine the change in height divided by the change in time in order to get its average speed between t=1 and t=3 seconds.

By entering t = 3 into h(t), we can determine the height at 3 seconds, which gives us h(3) = 16*32 + 105*3 + 10 = 536. We can figure out the height.

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Answer:  We can start by using algebra to represent the information given in the problem. Let x be the number of gallons consumed by the first car and y be the number of gallons consumed by the second car.

We know that:

x + y = 45 (the total number of gallons consumed by both cars)

15x + 30y = 975 (the total number of miles driven by both cars, given the fuel efficiency of each car)

We have two equations and two unknowns, so we can use these equations to solve for the value of x and y.

From the first equation, we can solve for x:

x = 45 - y

We can substitute this expression of x into the second equation:

15(45 - y) + 30y = 975

Simplifying the left side of the equation:

675 - 15y + 30y = 975

Subtracting 675 from both sides:

15y = 300

And finally divide both sides by 15:

y = 20

So the second car consumed 20 gallons of gas that week.

We can substitute this value of y back into the equation x = 45 - y to find the value of x

x = 45 - 20 = 25

So the first car consumed 25 gallons of gas that week.

Step-by-step explanation:

Span(u,v) is the set of all linear combinations of u and v, including scalar multiples of both. It does not include the origin.

Span(u,v) is the set of all linear combinations of u and v, meaning any combination of u and v multiplied by scalars. This includes scalar multiples of both u and v, but does not include the origin. To calculate Span(u,v), first write u and v as vectors u = (u1,u2,...,un) and v = (v1,v2,...,vn). Then, any linear combination of u and v can be written as c1u + c2v, where c1 and c2 are scalars, and the set of all such linear combinations is Span(u,v). For example, if u = (1,2) and v = (3,4), then Span(u,v) = {(1,2), (3,4), (4,6), (5,8), (7,10), ...}. In other words, Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v.

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Answer:

Diagonals are perpendicular

1 diagonal bisects the other

Opposite angles are congruent

If two friends shop for fresh fruit. Jaxson buys a watermelon for $8.25 and 3 pounds of cherries. The expression to represent how much more Jaxson spent is :5.1 +p.

P = price of the cherries per pound

Price of cherries bought by Jaxson= $3p

Total amount spent by Jaxson =  $8.25 + $ 3p

Price of cherries bought by Tim = $2p

Total amount spent by Tim = $3.15 + $ 2p

Now let find how much more Jaxson spent.

8.25 + 3p - 3.15 + 2p

5.1 + 3p - 2p

Combine like terms

5.1 +1p

Multiply by 1

5.1 + p

Therefore the expression to represent how much more Jaxson spent is :5.1 +p.

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The break-even points at which the sum of the fixed and variable costs (40,800 + (1/3)·x + 222) is equivalent to the revenue (1946·x - (2/3)·x²) are; x = 21, 2897

The break-even point in cost accounting is the point where the total cost of production is equivalent to the total revenue from the sale of the products.

The fixed cost of the company = $40,800

The variable cost = (1/3)·x + 222 Dollars

x = The total number of units sold

The selling price of the product = 1946 - (2/3)·x Dollars

A possible question, obtained from a similar question is the value of the number of units sold at break even point

The break even point where the cost and revenue are equivalent, can be found as follows;

Revenue = Selling price × Number of units sold, therefore;

Revenue = (1946 - (2/3)·x) × x = 1946·x - (2/3)·x²

At the break even point, we get;

Sum total of the cost = Revenue

Therefore;

Fixed cost + Variable cost = Revenue

40,800 + (1/3)·x + 222 = 1946·x - (2/3)·x²

1946·x - (2/3)·x² - (40,800 + (1/3)·x + 222) = 0

(-2·x² + 5837·x - 123066)/3 = 0

x = (-5837 ± √(5837² - 4×(-2)×(-123066)))/(2×(-2))

x = (-5837 ± √(33086041))/(-4)

x ≈ 21 or x ≈ 2897

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Answer: 1,200. None of the above.

Step-by-step explanation:

200 revolutions per minute times 60 feet. 1,200

The typical increase in speed from 40 to 70 seconds The magnitude is lower than the initial acceleration and is positive.

The velocity change's average acceleration is referred to as this. To calculate any object's average acceleration, we divide the change in velocity by the amount of time that has passed. As a result, it is clear that the average acceleration is defined as the ratio of the change in velocity to the change in time over a certain interval.

The average acceleration is the velocity change divided by the time that has passed. A marble's average acceleration is 20 cm/s, for instance, if its velocity increases from 0 to 60 cm/s in three seconds. The marble's speed will increase by 20 cm/s every second as a result. The ball will therefore have an upwards-moving terminal velocity of 20 m/s after two seconds.

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The probability  that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child  is 12/25 , 1/ 6  respectively.

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes  and number of total outcomes.

Given in the table ,

Probability that a randomly chosen person is a child

= 48 / 100

= 12/25

Probability that a randomly chosen person prefers running and is a child

= 6/48

= 1/8

Probability that a person prefers running given that the person is a child

= 6/48

=1/8

Therefore, The probability  that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child  is 12/25 , 1/ 6  respectively.

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Answer:

slope: 2 , y-int: (0, -5)

Step-by-step explanation:

The rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

Oil is spilled onto a kitchen floor. The function A, where A(t) is measured in square centimeters and t is measured in seconds, gives the area covered by the oil at time t.

Given that the region that was covered in oil at time t = A(t)

We must differentiate A(t) with respect to time t in order to calculate the rate of change in the area covered by the oil over time.

By differentiation:

[tex]\frac{dA}{dt}=A'(t)[/tex]

The rate at which the oily area is transforming is t = 10

[tex]\frac{dA}{dt}|_{t=10}=A'(t)|_{t=10}[/tex]

[tex]\frac{dA}{dt}=A'(10)[/tex]

Hence, the rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

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The equation of a sphere with center (a, b, c) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 + (z - c)^2 = r^2[/tex]

Given the center (2,-6,4) and radius 5, we can substitute these values into the equation to find the equation of the sphere:

[tex](x - 2)^2 + (y + 6)^2 + (z - 4)^2 = 5^2[/tex]

So, the equation of the sphere is:

[tex](x-2)^2 + (y+6)^2 + (z-4)^2 = 25[/tex]

The sphere will intersect each of the coordinate planes in circles.

Intersection with the XY-plane:

The sphere intersects the XY-plane when z = 4.

Then, the equation of the circle on the XY-plane is [tex](x-2)^2 + (y+6)^2 = 5^2[/tex]

Intersection with the XZ-plane:

The sphere intersects the XZ-plane when y = -6.

Then, the equation of the circle on the XZ-plane is [tex](x-2)^2 + (z-4)^2 = 5^2[/tex]

Intersection with the YZ-plane:

The sphere intersects the YZ-plane when x = 2.

Then, the equation of the circle on the YZ-plane is [tex](y+6)^2 + (z-4)^2 = 5^2[/tex]

The sphere with center (2,-6,4) and radius 5 intersects each of the coordinate planes at circles.

These circles are defined by the equations [tex](x-2)^2 + (y+6)^2 = 25[/tex] on the XY-plane, [tex](x-2)^2 + (z-4)^2 = 25[/tex]  on the XZ-plane, and  [tex](y+6)^2 + (z-4)^2 = 25[/tex]  on the YZ-plane.

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Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.

A quadrilateral is a four-sided closed shape, where sum of the interior angles equals 180°.

Here,
For the quadrilateral there are only two quadrilaterals where diagonals bisect each other at 90° and will be of equal length of measure are square and rhombus.

Thus, Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.

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Answer:

A

Step-by-step explanation:

Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].

The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].

When 62.5 pairs of jeans are sold, the price is $112.50.

Based on the information, the store should discount $112.50 from the price to maximize its revenue.

To calculate the amount of discount that the store must make to maximize its profits we must perform the following mathematical operation:

First we have to analyze the available data which are:

According to the above information, the problem could be answered with the following mathematical formula:

(175 - x)(40 + 0.8x)

x = 175

x = -50

x = 62.50.

According to the above, the correct answer is $112.50 (option A).

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The first diagram of the triangle DEF correctly represents the transformation.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The preimage of the triangle is ABC and the image is DEF.

Therefore, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F>

A 90° rotation counterclockwise will rotate the vertex C one-quarter left of a complete circle.

Therefore, The first triangle represents the correct transformation.

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Answer: One way to calculate the percent increase in Robin's monthly bill is to use the following formula:

% increase = (new amount - original amount) / original amount x 100

In this case, the original amount is $120 and the new amount is $150. So, the calculation would be:

% increase = (150 - 120) / 120 x 100 = 30 / 120 x 100 = 0.25 x 100 = 25

Therefore, the percent increase in Robin's monthly bill is 25%.

Another way to calculate the percent increase is to use the formula:

(New amount - original amount) / original amount

In this case: (150-120)/120 = 0.25, and multiply by 100 to get 25%

So, both formula gives the same answer 25%

Step-by-step explanation:

Answer:

answer is B) 8 240 000

(: have a nice day

Answer:

B 8,240,000

Step-by-step explanation:

your welcome