Find the domain and range of the function V(x, y) = 9√9y – 45x^2. Indicate the domain of V in equality or inequality notation. Use <= to denote ≤ and >= to denote ≥.
Domain of V = {(2,y) }

There exists at least one c in the open interval (a, b) such that f'(c) = 0.

There are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.

To prove that the given equation has exactly 3 distinct real solutions, let's follow the steps mentioned in the question.

First, consider the polynomial p(x) = (x-a)(x-b)(x-c)(x-d). Since a, b, c, and d are distinct real numbers, p(x) has 4 distinct real roots, namely a, b, c, and d.

Now, let's find the derivative p'(x) using logarithmic differentiation. Taking the natural logarithm of both sides, we have:

[tex]ln(p(x)) = ln((x-a)(x-b)(x-c)(x-d))[/tex]

Differentiating both sides with respect to x, we get:

[tex]p'(x)/p(x) = 1/(x-a) + 1/(x-b) + 1/(x-c) + 1/(x-d)[/tex]

Multiplying both sides by p(x) and simplifying, we have:

[tex]p'(x) = (x-b)(x-c)(x-d) + (x-a)(x-c)(x-d) + (x-a)(x-b)(x-d) + (x-a)(x-b)(x-c)[/tex]

Now, we apply Rolle's Theorem, which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the open interval (a, b) such that f'(c) = 0.

Since p(x) has 4 distinct real roots, there must be 3 intervals between these roots where the function p(x) satisfies the conditions of Rolle's Theorem. Therefore, there are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.

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The congruency statement that describes the figures is:
ΔDEF ≅ ΔRSU

To answer your question, let's first find the image of triangle DEF after reflecting over the y-axis and then translating down 4 units and right 3 units.

1. Reflect ΔDEF over the y-axis:
D'(−6, 4), E'(−5, 8), F'(−1, 2)

2. Translate ΔD'E'F' down 4 units and right 3 units:
D''(−3, 0), E''(−2, 4), F''(2, −2)

Now, we have ΔD''E''F'' with points (−3, 0), (−2, 4), and (2, −2). Comparing this to ΔRSU with points (−2, 4), (−3, 0), and (2, −2), we can see that:

ΔD''E''F'' ≅ ΔRSU
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Answer:

ΔDEF ≅ ΔRSU

Step-by-step explanation:

Por lo tanto, el tercer carro que recibirá boletos de ambos colores ocupará la posición número 18 en la fila.

Hola, entiendo que quieres saber en qué posición de la fila se encontrará el tercer carro que recibirá boletos de ambos colores (verde y azul). Para esto, vamos a analizar la situación:

- La primera persona entrega un boleto verde cada 2 carros.
- La segunda persona entrega un boleto azul cada 3 carros.

Un carro que recibe boletos de ambos colores será aquel que ocupa una posición que es múltiplo común de 2 y 3. El mínimo común múltiplo (MCM) de 2 y 3 es 6. Por lo tanto, cada 6 carros, habrá uno que reciba boletos de ambos colores.

Para encontrar el tercer carro que recibirá boletos de ambos colores, simplemente multiplicamos el MCM (6) por la cantidad de carros que buscamos (3):

6 × 3 = 18

Por lo tanto, el tercer carro que recibirá boletos ición número 18 en la fila.

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To solve the trigonometric equation 2cos^2(x) + cos(2x) = 0 in the interval [0, 2π), we will first use the double angle formula for cos(2x) and then solve for x. Recall that cos(2x) = 2cos^2(x) - 1.

Substitute this into the equation: 2cos^2(x) + (2cos^2(x) - 1) = 0 Combine the terms: 4cos^2(x) - 1 = 0 Now, isolate cos^2(x): cos^2(x) = 1/4 Take the square root of both sides: cos(x) = ±√(1/4) = ±1/2 Now, find the values of x in the interval [0, 2π) that satisfy the equation: For cos(x) = 1/2: x = π/3, 5π/3 For cos(x) = -1/2: x = 2π/3, 4π/3 Combine the answers as a comma-separated list: x = π/3, 2π/3, 4π/3, 5π/3

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Thus, the area of the shaded part is found to be 50 sq. ft.

The shaded region's area is most frequently found in common geometry problems. Such problems always have a minimum of two forms, and you must determine the area for each shape as well as the darkened zone by deducting the smaller shape's area from the larger.

Rectangle's area :

Area has two dimensions: length and width. Square units like square inches, square feet, or square metres are used to measure area.

Length of shaded part = 5 ft

width of shaded part = 10 ft

Area = 5*10

Area = 50 sq. ft

Thus, the area of the shaded part is found to be 50 sq. ft.

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Correct question:

For the given figure find the area of the shaded region.

Length BC = 18 ft

Length CD = 10 ft

The null hypothesis (H0) is that there is no significant difference in mean weight loss between men and women, or μm - μw = 0. The alternative hypothesis (Ha) is that there is a significant difference in mean weight loss between men and women, or μm - μw ≠ 0.

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Answer:

Combining like terms,

(4x - 6) + (5x + 1) = 9x - 5

In a case whereby Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank the statement about the savings plans that is true is B.Maria's way of saving money allows her to earn interest and make her money grow.

An efficient approach to keep your money safe and earning interest is in a savings account. You can keep your savings in a liquid state with a savings account, which allows you to access your money anytime you need to, while also creating some breathing room between your savings and your daily spending requirements.

Because of their safety, liquidity, and potential for collecting interest, savings accounts are a suitable way to put money set aside for future use. These accounts are perfect for saving for short-term objectives like a trip or home repair or for your emergency fund.

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Step-by-step explanation:

Use Pythagorean theorem for right triangles

c^2 = a^2 + b^2      where c = hypotenuse and   a   and b are the legs

8.6^2 = 5^2 + r^2

8.6^2 - 5^2 = r^2

r = ~ 7  units

The value(s) of b that satisfies the given condition is/are 0.506 and 5.327.

We can use the method of setting the integral of f(x) over [0,b] equal to 16 and solving for b.

[tex]\begin{equation}\int 0 b f(x) d x=16\end{equation}[/tex]

Substituting [tex]f(x) = 6x^2 - 38x + 40[/tex], we get:

[tex]\begin{equation}\int 0 b\left(6 x^{\wedge} 2-38 x+40\right) d x=16\end{equation}[/tex]

Integrating with respect to x, we get:

[tex][2x^3 - 19x^2 + 40x]0b = 16[/tex]

Substituting b and simplifying, we get:

[tex]2b^3 - 19b^2 + 40b - 16 = 0[/tex]

Using numerical methods or polynomial factorization, we can find that the solutions to this equation are approximately 0.506 and 5.327.

Therefore, the value(s) of b that satisfies the given condition is/are 0.506 and 5.327.

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The measure of the angle x in the circle is 65 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

On the circle, we have the angle at the vertex of the triangle to be

Angle = 100/2

Angle = 50

The sum of angles in a triangle is 180

So, we have

x + x + 50 = 180

Evaluate the like terms,

2x = 130

So, we have

x = 65

Hence, the angle is 65 degrees

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The length of the straight line between the school and the fire station is 4.6 miles.

We can form a right-angled triangle with the school at the right-angle.

The distance between the school and the fire station is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

h^2 = 4.3^2 + 1.7^2

h^2 = 21.38

h ≈ 4.62

Rounding to the nearest tenth, the length of the straight line between the school and the fire station is approximately 4.6 miles.

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The constant hourly rate using the given data points is  $100 per hour.

To calculate the constant hourly rate, we can use the given data points. For example, let's use the 5-hour rental for $500:

Hourly rate = Total cost / Number of hours
Hourly rate = $500 / 5 hours
Hourly rate = $100 per hour

Now, we can use this hourly rate to find the cost for the missing hour value in the table:

Cost = Hourly rate × Number of hours
Cost = $100 per hour × 9 hours
Cost = $900

So, the table will look like this:

Hours: _______ 5   |   9   |   _______
Cost (in dollars): 500 | 1,250 | 3,500

Now we can calculate the missing hours for the $3,500 cost:

Number of hours = Total cost / Hourly rate
Number of hours = $3,500 / $100 per hour
Number of hours = 35 hours

Now, the completed table is:

Hours: _______ 5   |   9   |   35
Cost (in dollars): 500 | 1,250 | 3,500

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If you randomly select an iphone, The probability that the battery will last more than 10 hours is 0.5000.

Population mean, µ = 10

Population standard deviation, σ = 2

The likelihood that the battery will survive more than 10 hours is equal to

[tex]= P( X > 10)\\= P( (X-\mu)/\sigma > (10 - 10)/2)\\= P( z > 0)\\= 1- P( z < 0)\\[/tex]

Using excel function:

= 1- NORM.S.DIST(0, TRUE)

= 0.5000

The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that describes a large class of phenomena observed in nature, social sciences, and engineering. It is often called the bell curve because of its characteristic shape, which is symmetric and bell-shaped.

The mean and the standard deviation are the two factors that define the normal distribution. The mean is the center of the distribution, and the standard deviation measures how much the data varies from the mean. The normal distribution has several important properties, including that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

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Answer:

Step-by-step explanation:

The cost of 1 pound of peanuts can be found by dividing the total cost of 8 pounds by 8:

Cost of 1 pound of peanuts = $24 / 8 pounds = $3 per pound

The cost of 1 pound of walnuts can be found by dividing the total cost of 6 pounds by 6 and then multiplying by 2 (since the cost of 6 pounds is half that of the peanuts for the same weight):

Cost of 1 pound of walnuts = ($24 / 6 pounds) x 2 = $8 per pound

Therefore, we see that walnuts are more expensive than peanuts by $5 per pound ($8 - $3).

In other words, 1 pound of walnuts costs $5 more than 1 pound of peanuts.

The critical point(s) of the function f(x) = x^3 + x - 3 + 2 are determined to find the x-coordinate(s) of the local minimum or local maximum.

To find the critical point(s) of the given function, we need to first find the derivative of the function and then solve for the value(s) of x that make the derivative equal to zero.

Given function: f(x) = x^3 + x - 3 + 2

Find the derivative of the function f(x) with respect to x.

f'(x) = 3x^2 + 1

Set the derivative f'(x) equal to zero and solve for x.

3x^2 + 1 = 0

Subtract 1 from both sides of the equation.

3x^2 = -1

Divide both sides of the equation by 3.

x^2 = -1/3

Take the square root of both sides of the equation.

x = ±√(-1/3)

Since the square root of a negative number is not a real number, the function f(x) does not have any real critical points. Therefore, the critical point(s) for the function f(x) = x^3 + x - 3 + 2 is DNE (Does Not Exist) in terms of real numbers.

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The number of possible outcomes of the compound event of selecting a card, spinning the spinner, and tossing a coin is B. 72 outcomes.

To determine the number of possible outcomes for the compound event, we need to multiply the number of outcomes for each individual event.

There are 12 cards labeled 1 through 12, so there are 12 possible outcomes for selecting a card. The spinner is divided into three equal-sized portions, so there are 3 possible outcomes for spinning the spinner. There are 2 possible outcomes for tossing a coin (heads or tails).

the total number of possible outcomes for the compound event:

12 (selecting a card) x 3 (spinning the spinner) x 2 (tossing a coin) = 72

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The measurement of angle 2 is 55°, if the measurement of angle 1 and angle 2 equal 180° and measurement of angle 1 is 125° in the drawing of the bridge design.

The measurement of angle 1 is 125°, and the sum of angle 1 and angle 2 is 180°. The relationship between angle 1 and angle 2 is supplementary since their sum is equal to 180°. To find the measurement of angle 2,

Therefore, angle 2 has a measurement of 55°.

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Therefore, the probability that a randomly selected point within the square falls in the red-shaded area is 68%.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event A is denoted as P(A). To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes.

Here,

The area of the red-shaded region is the area of the square minus the area of the white right-angled triangle. The area of the square is the length of one side squared, which is:

Area of square = 5 cm × 5 cm

= 25 cm²

The area of the right-angled triangle is one-half the base times the perpendicular height, which is:

Area of triangle = (1/2) × base × height

= (1/2) × 4 cm × 4 cm

= 8 cm²

Therefore, the area of the red-shaded region is:

Area of red-shaded region = Area of square - Area of triangle

= 25 cm² - 8 cm²

= 17 cm²

To find the probability that a randomly selected point within the square falls in the red-shaded area, we need to divide the area of the red-shaded region by the total area of the square, which is:

Probability = Area of red-shaded region / Area of square

Probability = 17 cm² / 25 cm²

= 0.68 or 68%

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The First derivative: f'(x) = 12x - 15 and the Interval of increasing: (5/4, ∞) and the Interval of decreasing: (-∞, 5/4)

Hi! I'd be happy to help you with your question. Let's compute the first derivative, and then determine the intervals of increasing and decreasing:

Given function: f(x) = 2.3 + 6x^2 - 15x + 3

(a) Compute the first derivative, f'(x):
f'(x) = d(2.3)/dx + d(6x^2)/dx - d(15x)/dx + d(3)/dx
f'(x) = 0 + 12x - 15 + 0
f'(x) = 12x - 15

(c) To find the interval where f is increasing, we need to find where f'(x) > 0:
12x - 15 > 0
12x > 15
x > 15/12
x > 5/4

So, the interval of increasing is (5/4, ∞).

(d) To find the interval where f is decreasing, we need to find where f'(x) < 0:
12x - 15 < 0
12x < 15
x < 15/12
x < 5/4

So, the interval of decreasing is (-∞, 5/4).

Your answer:
- First derivative: f'(x) = 12x - 15
- Interval of increasing: (5/4, ∞)
- Interval of decreasing: (-∞, 5/4)

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Jane is 14 years old, if Sebastian is 12 34 years old. Camden is 1 38 years older than Sebastian and Jane is 1 15 years older than Camden.

To find out how old Jane is, we will first determine the ages of Sebastian and Camden, then add the additional years to find Jane's age.

Sebastian is 12 34 years old, but the correct age should be 12 years old (ignoring the typo).

Camden is 1 38 years older than Sebastian, which should be correctly written as 1 year older. So, Camden's age is 12 (Sebastian's age) + 1 = 13 years old.

Jane is 1 15 years older than Camden, which should be correctly written as 1 year older. Therefore, Jane's age is 13 (Camden's age) + 1 = 14 years old.

So, Jane is 14 years old.

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Answer:

Step-by-step explanation:

If we let M be a number, then 5 times as big as M would be 5M. Not that hard :/

The ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is y=-4x+20.

Now put x=6 and y=4 then,

=> 4=-4(6)+20

=> 4 = -24+20

=> 4 ≠ -4.

Then the coordinate (6,4) dost not satisfy the function.

Put x=0 and y=20 then,

=> 20 = -4(0)+20

=> 20= 0+20

=> 20=20

Hence the coordinate (0,20) satisfy the function.

Now put x=-4 and y=20 then,

=> 20 = -4(-4)+20

=> 20 = 16+20

=> 20 ≠ 36

Hence the coordinate (-4,20) does not satisfy the function.

Now put x=10 and y=-20 then,

=> -20 = -4(10)+20

=> -20 = -40+20

=> -20=-20

Then the coordinate (10,-20) satisfy the function.

Hence the ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).

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No, there is not convincing evidence that p, the true proportion of 17-year-olds at this high school with driver's licenses, is not 0.75.

This is because the P-value of 0.9315 is very large, and the 95% confidence interval contains 0.75 (0.6300, 0.8811). This means that there is not enough evidence to reject the null hypothesis that the true proportion of 17-year olds with driver's licenses is 0.75. The 95% confidence interval also supports this, as it includes 0.75. Therefore, there is no convincing evidence to suggest that the student's claim is incorrect.

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The marginal revenue at 1000 units is 40, at 3000 units is 0, and at 6000 units is -60.

Find the marginal revenue?

To find the marginal revenue for the given production levels, we first need to solve the demand equation for p and then derive the revenue function R(q).

Solve the demand equation for p.
q = 6000 - 100p
100p = 6000 - q
p = (6000 - q) / 100

Find the revenue function R(q) using R(q) = qp.
R(q) = q * ((6000 - q) / 100)

Derive the marginal revenue function MR(q) by taking the derivative of R(q) with respect to q.
MR(q) = dR(q)/dq = d(q * (6000 - q) / 100)/dq

Using the product rule:
MR(q) = (1 * (6000 - q) - q * 1) / 100
MR(q) = (6000 - 2q) / 100

Now, we can plug in the given production levels to find the marginal revenue at each level.

The marginal revenue at 1000 units is:
MR(1000) = (6000 - 2 * 1000) / 100 = (6000 - 2000) / 100 = 4000 / 100 = 40.

The marginal revenue at 3000 units is:
MR(3000) = (6000 - 2 * 3000) / 100 = (6000 - 6000) / 100 = 0 / 100 = 0.

The marginal revenue at 6000 units is:
MR(6000) = (6000 - 2 * 6000) / 100 = (6000 - 12000) / 100 = -6000 / 100 = -60.

So, the marginal revenue at 1000 units is 40, at 3000 units is 0, and at 6000 units is -60.

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The absolute value inequality in form |x-b| < c that has the solution set x<-5 or x>7 is |x-1| < 7

To write an absolute value inequality in the form |x-b| < c, we need to think about what this form means.

The expression |x-b| represents the distance between x and b on the number line. Therefore, |x-b| < c means that the distance between x and b is less than c.

Now, let's consider the given solution set: x < -5 or x > 7. We can see that the midpoint between -5 and 7 is 1, so we choose b = 1. Then, we need to determine c, which is the maximum distance between b and any of the solutions.

If we take x = -6 (which is less than -5), then |x-b| = |-6-1| = 7. Similarly, if we take x = 8 (which is greater than 7), then |x-b| = |8-1| = 7. Therefore, the maximum distance is 7.

Putting it all together, we get the absolute value inequality:

|x-1| < 7

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Answer:

Step-by-step explanation:

Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.

I think sorry if I’m wrong

In ΔMNO, possible values of ∠N are 64.6° and 115.4°.

To find the possible values of ∠N, follow these steps:

1. Since the sum of angles in a triangle is 180°, we first find ∠O by subtracting ∠M from 180°: 180° - 38° = 142°.

2. Next, we use the Law of Sines to find the sine of ∠N: sin(∠N) = (n * sin(∠O)) / m = (88 * sin(142°)) / 60.

3. Solve for sin(∠N), which gives us two possible values: sin(∠N) ≈ 0.8988 and sin(∠N) ≈ -0.8988.

4. Find the inverse sine (arcsin) of both values to get the possible angles for ∠N: arcsin(0.8988) ≈ 64.6° and arcsin(-0.8988) ≈ 115.4° (adding 180° to the negative result).

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Answer:

1.2

Step-by-step explanation:

based on your description the top sides are corresponding pairs, the bottom sides are corresponding sides, the left sides are corresponding sides, and the right sides are corresponding sides between the 2 polygons.

the dilation (scaling) is happening for all points on the polygon with the same scaling factor.

so, we only need to find the scaling factor f between one of these corresponding pairs.

8×f = 9.6

f = 9.6/8 = 1.2

Answer: The answer is 1.2

Step-by-step explanation:

Just trust me.

Answer:

33

Step-by-step explanation:

Pythagorean theorem:

6,5^ - 2.5^2= 36

✓36=6 second leg

3×6=18 square area

0,5×6×2,5=7,5 area of a triangle

2×7,5 + 18= 33