I need help with this question

Answer:

To find the coordinates of the vertex of the graph of the function -3x^2+12, we can use the formula x = -b/2a to find the x-coordinate of the vertex, and then substitute it back into the function to find the y-coordinate.

In this case, the function is in the form f(x) = -3x^2+12, so we can see that a = -3 and b = 0.

Using the formula x = -b/2a, we get:

x = -0/(2*(-3)) = 0

So the x-coordinate of the vertex is 0.

To find the y-coordinate of the vertex, we can substitute x = 0 into the function:

f(0) = -3(0)^2+12 = 12

So the y-coordinate of the vertex is 12.

Therefore, the coordinates of the vertex of the graph of the function -3x^2+12 are (0, 12).

Step-by-step explanation:

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If a relay lasts 5.92 miles and there are 4 runners on the team, we can divide the total distance by the number of runners to find the distance each person runs.

5.92 miles / 4 runners = 1.48 miles per runner

Therefore, each person on the relay team would run a distance of 1.48 miles, assuming that each runner runs in the same direction in the race.

It's important to note that in a relay race, each runner usually runs a specific distance that is predetermined by the race organizers. This distance may be different from the total distance of the race, and it may also be different for each runner on the team. However, if all runners on the team are running equal distances, as in this case, then we can simply divide the total distance by the number of runners to find the distance each person runs.

1. (x - 3)(x + y + z) = x² + xy + xz - 3x - 3y - 3z. This product is not a sum or difference of two cubes. 2. (3x - 4y)(2x - 3y - 4) = 6x² - 17xy + 12y² + 4y. This product is not a sum or difference of two cubes.

An equation in mathematics is a claim made regarding the equality of two expressions. It comprises of two expressions that express the same value or amount and are joined by an equal sign. The objective is to solve for the unknown value by modifying the equation in accordance with predetermined rules and principles when one side of the equation is typically unknown. From straightforward arithmetic operations to intricate differential equation systems, equations are used to model and solve a wide range of issues in many branches of mathematics, science, and engineering.

1. (x - 3)(x + y + z) = x² + xy + xz - 3x - 3y - 3z. This product is not a sum or difference of two cubes.

2. (3x - 4y)(2x - 3y - 4) = 6x² - 17xy + 12y² + 4y. This product is not a sum or difference of two cubes.

3. (6x + 3)(x - y + 4) = 6x² - 15xy + 18x + 3y - 12. This product is not a sum or difference of two cubes.

4. (x² - 2)(x² + 3x - 1) = x⁴ + 3x³ - x² - 6x - 2. This product is a difference of two cubes: x^6 - 2^3.

5. (x - 3)(3x + 1) (4x (2)) = 12x⁴ - 32x³ - 9x² + 27x. This product is not a sum or difference of two cubes.

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Answer:

a. The London population data cannot be accurately modeled by a linear function because the population growth is not constant over time. A quadratic function may be able to fit the data, but it is unlikely to accurately model the population growth in the long term. An exponential function is a more suitable choice because it can model exponential population growth, which is common in real-world scenarios.

b. Using a logistic growth equation, we can determine if the London population data can be accurately modeled by a logistic equation. We can use a regression analysis to find the values of a, b, and c that best fit the data, and then compare the predicted values to the actual population data to determine the accuracy of the model.

c. The logistic growth equation P(t) = 1 / (a + be^(-b(t-c))) produces an S-shaped curve, which represents the growth of a population that is initially slow, then accelerates, and finally levels off as it approaches a carrying capacity. The value of a represents the initial population size, b represents the growth rate, and c represents the time at which the population growth rate is highest. As a increases, the curve shifts upwards, indicating a larger initial population size. As b increases, the curve becomes steeper, indicating faster population growth. As c increases, the curve shifts to the right, indicating a later time at which the population growth rate is highest.

Based on the information given, the histogram is attached

A histogram is a graphical representation of data points organized into user-specified ranges. Similar in appearance to a bar graph, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.

From the information, the range of the dataset will be:

= 68 - 32

= 36

The number of classes will be:

= 36 / 10

= 3.6

= 4 approximately.

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We are given an equation that models the distance an object has fallen after t seconds.

[tex]\Rightarrow d=13x^2[/tex]

And are asked to find the objects average speed over the interval,[tex]a\leq x\leq a+h[/tex].  

Take the derivative of the "d" function, which is a function of position, to get a function for velocity.        

[tex]\Longrightarrow d=13x^2 \Longrightarrow d'=26x \Longrightarrow \boxed{v=26x}[/tex]

[tex]average \ speed = \boxed{ \bar v=\frac{d'(a)+d'(a+h)}{2}}[/tex]

[tex]\Longrightarrow \bar v = \frac{26a+26(a+h)}{2} \Longrightarrow \bar v = \frac{26a+26a+26h}{2} \Longrightarrow \bar v = \frac{52a+26h}{2} \Longrightarrow \bar v = \frac{52a}{2}+\frac{26h}{2}[/tex]

[tex]\Longrightarrow \boxed{ \bar v=26a+13h} \therefore Sol.[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Alternative way (without derivatives):

[tex]average \ speed = \bar v=\frac{d(a+h)-d(a)}{a+h-a} = \boxed{\frac{d(a+h)-d(a)}{h} }[/tex]

[tex]\Longrightarrow v = \frac{d(a+h)-d(a)}{h} \Longrightarrow \frac{13(a+h)^2-13a^2}{h}\Longrightarrow \frac{13(a^2+h^2+2ah)-13a^2}{h}[/tex]

[tex]\Longrightarrow \frac{13a^2+13h^2+26ah-13a^2}{h} \Longrightarrow \frac{13h^2+26ah}{h} \Longrightarrow \frac{13h^2}{h}+\frac{26ah}{h}[/tex]

[tex]\Longrightarrow \boxed{\bar v = 13h+26a} \therefore Sol.[/tex]

The limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

To find the limit of (x + x²)/(2 − 3x²) as x approaches infinity, we can use l'Hospital's Rule.

First, we need to check if the limit is in the indeterminate form 0/0 or ∞/∞. As x approaches infinity, both the numerator (x + x²) and the denominator (2 - 3x²) approach infinity.

Therefore, the limit is in the indeterminate form ∞/∞, and we can apply l'Hospital's Rule.

l'Hospital's Rule states that if the limit is in the indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately, and then find the limit of the ratio of their derivatives.

Numerator's derivative: d/dx(x + x²) = 1 + 2x Denominator's derivative: d/dx(2 - 3x²) = -6x

Now, we'll find the limit of the ratio of their derivatives as x approaches infinity: lim (1 + 2x)/(-6x) as x→∞

We can use l'Hospital's Rule again, as this limit is also in the indeterminate form ∞/∞. Numerator's second derivative: d/dx(1 + 2x) = 2

Denominator's second derivative: d/dx(-6x) = -6

Now, we'll find the limit of the ratio of their second derivatives as x approaches infinity: lim (2)/(-6) as x→∞ Since the limit involves constants only, it does not depend on x, and we can directly compute the limit: 2 / (-6) = -1/3

Therefore, the limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

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Answer:

The correct answer is: a translation of 3 units down.

Step-by-step explanation:

To identify the transformation that occurred after the dilation, we can compare corresponding points on both parallelograms.

The point (-4,0) on parallelogram P was dilated to the point (3,0) on parallelogram P'. This means the x-coordinate was multiplied by 2, since 3 = -4 x 2.

Similarly, the point (-2,0) on parallelogram P was dilated to the point (7,0) on parallelogram P', indicating again that the x-coordinate was multiplied by 2 since 7 = -2 x 2.

Therefore, the dilation was a scale factor of 2 in the x-direction about point P.

To transform parallelogram P' from its position after the dilation to its final position, we can see that corresponding points have been translated 3 units down. For example, the point (3,0) was transformed to (3,-3), and the point (1,-6) was transformed to (-4,-6).

Thus, the transformation that occurred after the dilation was a translation of 3 units down.

Therefore, the correct answer is: a translation of 3 units down.

Let's first write out the proportionality statement based on the information given:

distance ∝ time^2

We can then write an equation for the relationship between the distance and time:

distance = k(time^2)

where k is the constant of proportionality. We need to solve for k in order to use this equation to answer the question.

We know that when the egg falls for ½ second, it falls 8 feet. Plugging in these values, we get:

8 = k(0.5^2)

8 = 0.25k

k = 32

Now that we have k, we can use the equation to find the time it takes the egg to fall 200 feet. We rearrange the equation to solve for time:

distance = k(time^2)

time^2 = distance/k

time = sqrt(distance/k)

Plugging in the values, we get:

time = sqrt(200/32) = 2.5 seconds

Therefore, it will take the egg 2.5 seconds to fall 200 feet.

Answer:

The top right graph. I have circled this one in the attached figure to avoid confusion

Step-by-step explanation:

The solution to the system of equations will be the value of x and y where both lines in the graph intersect

The two equations are
y = (1/3) x   (1)

and

x + 3y = 6  (2)

Substitute y = (1/3) x   in the second equation:
x + 3y = 6

=> x + 3 · (1/3)x = 6

=> x + x = 6

=> 2x = 6

=> x = 6/2 = 3

At x = 3, y = (1/3) ·3 = 1

So the solution is (3, 1)

The second graph(top right) has lines intersecting at x = 3, y = 1 i.e. point(3, 1)

So this graph represents the solution to the system of equations

If the original price of the football is $22.00, and the store is offering a 20% discount, then the new price of the football before tax would be:

New price before tax = Original price - Discount

= $22.00 - (20% x $22.00)

= $17.60

Now, we need to calculate the price of the football after adding the sales tax of 5%. To do this, we can calculate the amount of sales tax first, and then add it to the new price before tax:

Sales tax = 5% x $17.60

= $0.88

Price after tax = New price before tax + Sales tax

= $17.60 + $0.88

= $18.48

Therefore, the cost of the discounted football after tax is $18.48.

1. Yearly total dividends paid are $151,250.

2. The dividends per share are $1.25 for common stockholders

3.  The dividends per share are $4 for preferred stockholders.

We must calculate amount of dividends paid to the preferred stockholders in order to get dividends per share for common and preferred stockholders.

The per dividends paid to the preferred stockholders is:

= $50 par value x 8% guaranteed rate of return

= $4 per share

The total dividends paid to preferred stockholders:

=  $4 per share x 5,000 shares

= $20,000

The per dividends paid to those stockholder is calculated as:

= Common stock + Preferred stock

= $1.25 per share + $4 per share

= $5.25 per share

The total dividends paid to common stockholders:

= $5.25 per share x 25,000 shares

= $131,250.

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The solution to the equation -6 - 10log₇(x - 1) = 4 is x = 8/7.

Given the equation in the question;

-6 - 10log₇(x - 1) = 4

To solve for x in the equation -6 - 10log₇(x - 1) = 4,

we can follow these steps:

Add 6 to both sides of the equation to isolate the logarithmic term

-6 + 6 - 10log₇(x - 1) = 4 + 6

-10log₇(x - 1) = 10

Divide both sides of the equation by -10

-10log₇(x - 1) / -10 = 10 / -10

log₇(x - 1) = -1

Rewrite the equation in exponential form

7⁻¹ = x - 1

Simplify and solve for x

7⁻¹ + 1 = x

x = 1 + 7⁻¹

x = 1 + 1/7

x = 8/7

Therefore, the solution is x = 8/7.

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Answer:

-6-10log(7)(x-1)=4

Answer:

The answer is c. 1/12

The conditional relative frequency of having more than one dog given there is a flea infestation is equal to 0.464.

The conditional relative frequency of having more than one dog with the condition there is a flea infestation.

Use the formula,

P(more than one dog | flea infestation)

= P(more than one dog and flea infestation) / P(flea infestation)

Looking at the two-way relative frequency table.

The probability of having more than one dog and a flea infestation is 0.032.

And the probability of a flea infestation regardless of the number of dogs is 0.069.

The conditional relative frequency is,

P(more than one dog | flea infestation)

= 0.032 / 0.069

= 0.464 (rounded to the nearest thousandths place)

Therefore, the conditional relative frequency representing there is more than one dog along with there is a flea infestation is 0.464.

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The above question is incomplete , the complete question is:

attached question.

The volume of the canister is 339.1 cubic inches.

The volume of a cylinder is calculated by using the formula V=πr²h, where r is the radius of the cylinder and h is the height of the cylinder.

The radius of the cylinder is half of the diameter, so the radius of the canister is 3 inches.

Using the formula, we can calculate the volume of the canister as follows:

V = π×3²×12

V = 108×3.14

V = 339.1 cubic inches

Therefore, the volume of the canister is 339.1 cubic inches.

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The total surface area of tumbler designed like cube with cylindrical hole is 700.48cm² and cost of glass to make tumbler is $3 (round off).

Shape of the tumbler is cube.

Side length of the edges = 10cm

Radius of the cylindrical hole = 4cm

Depth of the cylindrical hole = 8cm

Total surface area of the tumbler = surface area of the cube and the surface area of the cylinder - (surface area of the cylindrical hole ).

The surface area of a cube with edge length 10 cm is,

6 × (10 cm)² = 600 cm²

The surface area of a cylinder with radius 4 cm and height 8 cm is,

2π(4 cm)² + 2π(4 cm)(8 cm) = 96π cm²

Surface area of the cylindrical hole is the lateral area of a smaller cylinder with radius 4 cm and height 8 cm,

2π(4 cm)(8 cm) = 64π cm²

So the total surface area of the tumbler is,

= 600 cm² + 96π cm² - 64π cm²

= 600 cm² + 32π cm²

≈ 700.48 cm²

Total volume of the tumbler = volume of the cube - volume of the cylindrical hole.

The volume of a cube with edge length 10 cm is,

(10 cm)³ = 1000 cm³

The volume of the cylindrical hole is,

π(4 cm)²(8 cm) = 128π cm³

So the total volume of the tumbler is,

= 1000 cm³ - 128πcm³

≈ 598.08 cm³

The cost of the glass needed to make the tumbler

= cost of one cubic centimeter of glass × total volume of the tumbler.

Since one cubic centimeter of glass costs half a cent.

The cost of the glass needed to make the tumbler is,

= 0.5 cents/cm³ × 598.08 cm³

≈ 299.04cents

≈ $3

Therefore, total surface area of tumbler is 700.48cm² approximately and  cost of glass needed to make tumbler is approximately $3.

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The percentage of 120 which gives the value 72 is 60%.

The given number is 120.

We have to find what percent of 120 gives the value as 72.

Let x be the percent for which the value gives 72.

The using the definition of percentage,

120 × x% = 72

120 × x/100 = 72

1.2x = 72

x = 60%

Hence 60% of 120 gives 72.

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I'm sorry, but the question you provided is unclear and incomplete. It mentions Jordan and Taylor and going to the movie theater, but it does not provide enough information about the distances they will travel or the context of the problem. Please provide a clear and complete question so I can assist you in a better way.

Answer:

TSA of a cone = πrl+πr²

22/7*7/2*10+22/7*7/2*7/2

=22*5+11*7

187

ans

The length of the arc defined by a central angle of 270 degrees in a circle with a radius of 1 unit is 3.141592653589793 units.

The statement the area of bottom of round pan is greater than area of bottom of rectangular pan by about 8.5 square inches is correctly describes how the area of the bottom of the round pan compares to the area of the bottom of the rectangular pan.

What is a area of a surface?

In mathematics, the area of a surface refers to the measurement of the size of a two-dimensional region enclosed by a closed boundary or surface. It is typically expressed in square units such as square inches, square meters, or square feet. The concept of area is used in various fields such as geometry, physics, engineering, and many others to calculate the amount of material needed to cover a surface, to determine the capacity of a container, or to estimate the amount of paint required to paint a wall. The formula for calculating the area of a surface varies depending on the shape and complexity of the surface, but typically involves finding the product of two or more dimensions of the surface or using integration techniques in calculus to calculate the area under a curve.

To find the relation we have to find the areas of the pans.

Area of round pan nr 3.14 x 52 78.5 square = 78.5 inches.

Area of the rectangular pan = length x breadth = 10 x 7 = 70 square inches.

Difference between the area of the circular pan from rectangular pan = 78.5 - 70 = 8.5 square inches.

Hence option 1 is the correct answer.

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The interval of convergence for the power series is the set of all values of x for which the series converges. The table mentioned in your question likely shows the values of x for which the series converges or diverges.

The interval of convergence for a power series is determined by finding the values of x for which the series converges absolutely. The convergence or divergence of a power series can be determined using various tests, such as the ratio test or the root test.
Once the interval of convergence is found, it can be summarized as a range of values for x. For example, if the interval of convergence is (-3, 5], then the series converges for all values of x between -3 and 5, inclusive.

Hence, the interval of convergence for a power series is the set of all values of x for which the series converges, and it can be determined by finding the values of x for which the series converges absolutely.

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Answer:

If the area of the square office is 148 ft², then the length of one side can be found by taking the square root of the area: √148 ≈ 12.17

So the length of one side of Joseph's office is closest to B.) 12 feet

Answer:

12 ft

Step-by-step explanation:

Area of square = S²

We Know

He used a 148 ft² carpet.

Which length of one side of Joesph's office is in feet?

We take

√148 ≈ 12 ft

So, the answer is 12 ft

The measure of the angle C is 58.99 degrees

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

The triangle

The measure of angle C is calculated using

c² = a² + b² - 2ab * cos(C)

So, we have

20² = 22² + 18² - 2 * 18 * 22 * cos(C)

Evaluate

400 = 808 - 792 * cos(C)

Subtract and divide

cos(C) = 0.5152

Take the arc cos

C = 58.99 degrees

Hence, the angle is 58.99

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The graph of g(x) is the graph of f(x) shifted 8 units to the left and 4 units up.

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

f(x) and we have

g(x) = f(x+ 8) + 4

The +8 in g(x) = f(x+ 8) + 4 means that the function is shifted left by 4 units

The +4in g(x) = f(x+ 8) + 4 means that the function is shifted up by 4 units

Hence, the statement is (a)

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Answer:

30 bc he did 20 m and healf way after

A system of inequalities can be used to determine the number of packages of hamburgers, x, and the number of packages of hot dogs, y, that Natalia should buy are;

x + y ≤ 5

4x + 2y ≥ 18

In order to write a system of inequalities to describe this situation, we would assign variables to the number of packages of hamburgers and the number of packages of hot dogs respectively, and then translate the word problem into a linear equation as follows:

Since Natalia needs to buy no more than 18 pounds of meat for a cookout, and hamburgers are sold in 4-lb. packages, and hot dogs are sold in 2-lb. packages and she plans to buy at least 5 packages of meat, a linear inequality that models the situation is given by;

x + y ≤ 5

4x + 2y ≥ 18

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The values of x and y in the right triangle are 24.3 and 12.14 respectively.

We have to find the values of x and y in the right triangle

We know that the sine is a ratio of opposite side and hypotenuse

Sin 60 = 21/x

√3/2 = 21/x

√3x = 42

x=42/√3 = 42/1.73

x=24.3

Now let us find value of y

the cosine is a ratio of adjacent side and hypotenuse

cos 60 = y/x

1/2 = y/(42/√3)

42/√3 = 2y

21/√3 = y

12.14 = y

Hence, the values of x and y in the right triangle are 24.3 and 12.14 respectively.

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The slope of the line which parallel to the given lines are as follow,

Slope of x+ y=-7 is -1.

Slope of -7x +y=-7 is 7.

Equation of the lines are ,

x+ y= -7

and -7x+y=−7

Standard slope-intercept form y=mx + b

The equation x+ y=-7 can be rearranged to slope-intercept form y=mx + b by solving for y,

x+ y= -7

⇒ y = -x-7

The slope of this line is -1, since the coefficient of x is -1.

Similarly, the equation -7x+y=-7 can be rearranged to slope-intercept form,

-7x+y=-7

⇒ y=7x-7

The slope of this line is 7, since the coefficient of x is 7.

A line parallel to the first line x + y=-7 will have the same slope of -1.

A line parallel to the second line -7x+y=-7 will have the same slope of 7.

Therefore, the slope of a line parallel to,

x+ y=-7 is -1.

-7x +y=-7 is 7.

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The above question is incomplete , the complete question is :

Find the slope of a lines parallel to the line whose equation is x+ y= -7 and -7x+y=−7. Fully simplify your answer