which is better to buy 5 pack for 9.98 or 7 pack for 14.14

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

In this problem, we have:

Then:

a = -1

b = -6

We write now:

For this part, we need to find the x-intercepts. This is, when y = 0:

To solve this, we can use the quadratic formula:

And solve:

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

To find the y intercept, we need to find the value of y when x = 0:

The y-intercept is at (0, -13)

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

The two points are:

(1, -20)

(-1, -8)

Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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Answer:

235

Step-by-step explanation:

Answer:

sue.

Step-by-step explanation:

sue paid 1.25 per book while Joliet paid 1.27. hope that helps

Answer:

22.0

Step-by-step explanation:

Similar triangles have proportional side lengths, so:

\(\frac{KL}{49}=\frac{13.9}{31} \\ \\ KL \approx 22.0\)

Answer:

x=13

Step-by-step explanation:

3(x-10)=x+4

3x-30=x-4

3x=x+26

2x=26

x=13

Answer:

Group the like terms together:

4x²y + 6x²y + 12z² - 2z

Simplify:

10x²y + 12z² - 2z

The simplified expression is 10x²y + 12z² - 2z.

Step-by-step explanation:

Answer:

The simplified expression is 10x²y + 12z² - 2z

Step-by-step explanation:

To simplify the expression, we combine like terms, which are terms that have the same variables raised to the same powers. In this case, we have two terms with the variable 4x²y and two terms with the variable -2z. We can combine these like terms by adding their coefficients:

4x²y + 6x²y = 10x²y

-2z + (-2z) = -4z

So the expression simplifies to:

10x²y + 12z² - 4z

We can further simplify this expression by combining the terms with the variable z:

12z² - 4z = 4z(3z - 1)

Therefore, the final simplified expression is:

10x²y + 4z(3z - 1)

We can also write this expression as:

10x²y + 12z² - 2z

which is the answer provided.

Answer:

7 1\68

Step-by-step explanation:

all i did was look up a fraction calculator

calculator soup is the one i used :)

Answer:

answer

Step-by-step explanation:

step by step explanation

a. The polyhedron is a triangular prism

b. The polyhedron a pentagonal pyramid

From the question, we are to determine the names of the given polyhedra.

a. The given polyhedra is a three-dimensional geometric shape that consists of two congruent parallel triangles as the base and three rectangular faces that connect the corresponding sides of the triangles.

This shape is known as a triangular prism.

b. The polyhedra is a three-dimensional geometric shape that consists of a pentagonal base and five triangular faces (also known as lateral faces) that meet at a common vertex point above the base. The lateral faces connect the corners of the pentagonal base to the apex, forming five triangular sides that taper upwards to meet at a single point.

This shape is known as a pentagonal pyramid.

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If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer: 14%

Step-by-step explanation: To find the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade, we divide the number of members who meet both criteria (14) by the total number of members (100) and multiply by 100 to get a percentage. Therefore, the probability is approximately 14%.

- Lizzy ˚ʚ♡ɞ˚

Answer:

caca water

Step-by-step explanation:

True. Summarizing allows you to focus on the important information by finding the introduction, topic sentence and conclusion.

Summarizing is a technique that helps to distill the main points of a text by identifying the introduction, topic sentence, and conclusion. It involves condensing the information to focus on the most important aspects and omitting unnecessary details.

This process enables the reader to grasp the core message of the text quickly and efficiently.

By summarizing, one can communicate the key ideas in a concise and clear manner, making it easier for others to understand and engage with the information presented.

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the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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The distance between the points (-6, 4) and (5, 4) is 11 units.

To find the distance between two points in a Cartesian coordinate system, we can use the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Given the two points (-6, 4) and (5, 4), we can plug in the coordinates into the distance formula:

Distance = √[(5 - (-6))² + (4 - 4)²]

        = √[(5 + 6)² + 0²]

        = √[11² + 0]

        = √[121]

        = 11

Therefore, the distance between the points (-6, 4) and (5, 4) is 11 units.

In this case, since the y-coordinates of both points are the same (4), the distance between them only considers the difference in their x-coordinates. As the x-coordinate of the second point is 11 units greater than the x-coordinate of the first point, the distance between them is simply the absolute value of the difference, which is 11.

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So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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The equation of the polynomial equation is P(x) = -12(x + 3))(x + 1)(x - 2)

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of each zero is 1

The equation of the polynomial is then calculated as

P(x) = Coefficient * (x - zero)^ multiplicity

So, we have

P(x) = -12(x - (-3))(x - (-1))(x - 2)

This gives

P(x) = -12(x + 3))(x + 1)(x - 2)

Hence, the equation of the polynomial equation is P(x) = -12(x + 3))(x + 1)(x - 2)

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Answer:

To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.

First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.

Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.

Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.

However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.

Answer:

standard form, real nums

Step-by-step explanation:

To find the volume of the solid, you need to calculate the area of each cross-section and then multiply that by the thickness of the section (which is the distance along the y-axis).

(a) Squares: The cross-sections are squares with sides of length y. The area of a square is side^2, so the area of each square is y^2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the square cross-sections is y^2 * y

(b) Semicircles: The cross-sections are semicircles with radii of length y. The area of a semicircle is (pi * r^2) / 2 , so the area of each semicircle is (pi * y^2) / 2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semicircular cross-sections is (pi * y^2) / 2 * y

(c) Equilateral triangles: The cross-sections are equilateral triangles with side length of y. The area of an equilateral triangle is (s^2 * √3)/4. so the area of each equilateral triangle is (y^2 * √3) / 4. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the equilateral triangle cross-sections is (y^2 * √3) / 4 * y

(d) Semi-ellipses: The cross-sections are semi-ellipses whose heights are twice the lengths of their bases. The area of a semi-ellipse is πab/2, where a and b are the lengths of the semi-major and semi-minor axes respectively. Therefore the area of each semi-ellipse will be (πy^2)/2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semi-ellipse cross-sections is (πy^3)/2

It is important to note that this is a theoretical volume calculation, as the shape of the solid does not have a closed form representation by these functions, but rather, these are an approximation.

Also, for any of these volumes to be meaningful, we have to integrate over the range of the variable y, since it is bounded by the equations y=x, y=0 and x=1, the variable y is limited.

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Answer:

No

Step-by-step explanation:

x = -3 is a vertical line at x= -3

Tow points on the line are

(-3,1) and (-3,2)

This means one x value goes to 2 different y values so it is not a function

Answer: No

Step-by-step explanation: The line x = -3 is a vertical or straight up and down line that is parallel to the y-axis. On the vertical line x = -3, when x = -3, y can be 0, 1, 2, -5, or any other number, there are in infinite number of possibilities.

The technical definition of a function is written as "a relation in which each element in the domain is paired with one and only one element in the range."

The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:

b = 10.

The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.

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Answer:

y=-x+1

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Answer:

Vhjaakkjvvkllmn aar

Step-by-step explanation:

Vbkisavn

Vhikjsqiol

NG Jill quolk

Hill s njknbn

The maximum revenue, to the nearest whole dollar, is $180,625 (option c).

To find the maximum revenue, we need to determine the vertex of the quadratic function represented by the revenue equation.

The revenue equation is given as:

R(p) = -4p² + 1700p

The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:

x = -b / (2a)

For the given revenue equation, a = -4 and b = 1700. Plugging these values into the formula, we have:

p = -1700 / (2 × -4)

p = -1700 / -8

p = 212.5

The maximum revenue occurs at p = 212.5.

To find the maximum revenue, we substitute this value back into the revenue equation:

R(p) = -4(212.5)² + 1700(212.5)

R(p) = -4(45256.25) + 361250

R(p) = -181025 + 361250

R(p) = 180625

Therefore, the maximum revenue, to the nearest whole dollar, is $180,625 (option c).

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