The Gomez’s deck is shown below. The deck is a regular hexagon. It has a perimeter of 45 units. What is the are of the deck

The vertical shape of the graph will be the same as that of the first rocket, assuming both rockets have the same initial velocity and acceleration.

1.I agree with Serena that we can draw the graphs for the other two rockets by shifting the functions. We can use the same equation and just adjust the values of the horizontal and vertical shifts.

2. The equation f(t) = -6t² represents a quadratic function, which has a parabolic shape when graphed. If we apply a transformation to this function, such as a vertical or horizontal shift, the shape of the graph will change accordingly.

3. The term 82.14 likely represents the maximum height achieved by the rocket, since the equation f(t) = -6t² gives the height of the rocket as a function of time. The value of h(t) = 82.14 corresponds to a specific time when the rocket reaches its maximum height.

4. If the second rocket is launched 3 seconds after the first one, the graph of the second rocket will be shifted horizontally by 3 units to the right compared to the graph of the first rocket. This represents a time delay of 3 seconds between the two launches.

5. The equation of the second rocket would be f(t) = -6(t-3)², assuming that the second rocket has the same initial velocity and acceleration as the first rocket but is launched 3 seconds later.

6. Since the third rocket is launched 3 seconds after the second rocket and from a tall platform, its graph will be shifted horizontally to the right by 6 units compared to the graph of the first rocket.

9. A: Based on the graph, the third rocket was launched at approximately 5:20 PM.

B: Based on the graph, the first rocket lands at approximately 5:15 PM.

C: Based on the graph, all three rockets are in the air between approximately 5:10 PM and 5:25 PM, so the approximate interval during which all three rockets are in the air is 15 minutes.

Therefore,  spends an additional 6 seconds in the air before landing. The vertical shape of the graph will depend on the specifics of the rocket's launch and trajectory.

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Answer:

4.875 (round to 5) quarts of stain

Step-by-step explanation:

13 feet × 15 feet = 195 square feet

195 / 40 = 4.875

Buy 4.875 quarts of stain.

The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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Answer:

64 tea bags for 9.28

Step-by-step explanation:

The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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Answer:

\(sinx=-\dfrac{12}{13}\)

\(cosx=-\dfrac{5}{13}\)

\(cotx=\dfrac{5}{12}\)

Step-by-step explanation:

Given that:

\(\dfrac{12}{5} = tan(x)\)

\(\pi <x < 3\pi/2\)

i.e. x is in 3rd quadrant. So tan is positive.

To find:

sin(x), cos(x), and cot(x).

Solution:

Given that:

\(\dfrac{12}{5} = tan(x)\)

We know by trigonometric identities that:

\(tan\theta =\dfrac{Perpendicular}{Base}\)

Comparing with the given values:

\(\theta=x\)

Perpendicular = 12 units

Base = 5 units

Using pythagorean theorem, we can find out hypotenuse:

According to pythagorean theorem:

\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\)

\(\Rightarrow Hypotenuse=\sqrt{12^2+5^2}\\\Rightarrow Hypotenuse=\sqrt{169} = 13 units\)

We can easily find out the values of:

\(sinx, cos x\ and\ cot x\)

\(sin\theta =\dfrac{Perpendicular}{Hypotenuse}\)

\(sinx =\dfrac{12}{13}\)

Given that x is in 3rd quadrant, sinx will be negative.

\(\therefore sinx =-\dfrac{12}{13}\)

\(sin\theta =\dfrac{Base}{Hypotenuse}\)

\(cosx =\dfrac{5}{13}\)

Given that x is in 3rd quadrant, cosx will be negative.

\(\therefore cosx =-\dfrac{5}{13}\)

\(cot\theta = \dfrac{1}{tan\theta}\)

Given that x is in 3rd quadrant, cotx will be positive.

\(cotx = \dfrac{1}{\dfrac{12}{5}} = \dfrac{5}{12}\)

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Trout increased its predicted average population.

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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On solving the provided question, we can say that the equation of inequality will be as follows 150x + 100y \(\leq\) 300

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

A patient is not allowed to have more than 300 milligrams of cholesterol per day from a diet of eggs and meat.

Each egg provides 150 milligrams of cholesterol.

Each once of meat contains 100 milligrams of cholesterol

so, the equation of inequality will be as follows

150x + 100y \(\leq\) 300

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Answer:

4(2y+1)(5y+3)

Step-by-step explanation:

........

The solutions to the equation sin(θ) = √2/2 over the interval [0, 2π) are θ = π/4 and θ = 3π/4.

What is the trigonometric ratio?

the trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

We know that sin(θ) = √2/2 is one of the standard angles in trigonometry, and it corresponds to an angle of 45 degrees or π/4 radians.

To solve the equation sin(θ) = √2/2 over the interval [0, 2π), we need to find all values of θ that satisfy the equation within this interval.

Since sin(θ) is positive in the first and second quadrants of the unit circle, we know that the solutions lie in those quadrants.

The first solution is θ = π/4, which corresponds to the angle of 45 degrees or π/4 radians in the first quadrant.

The second solution is θ = 3π/4, which corresponds to the angle of 135 degrees or 3π/4 radians in the second quadrant.

Therefore, the solutions to the equation sin(θ) = √2/2 over the interval [0, 2π) are θ = π/4 and θ = 3π/4.

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Answer: No. She should have multiplied 12 and 1/2 to alive.

Step-by-step explanation:

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Answer:

5

Step-by-step explanation:

By using proportionality, it can be calculated that-

The value of constant of proportionality k is 9

What is proportionality?

Suppose there are two quantities. Proportionality indicates that if there is a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Proportionality can be direct or inverse

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of a commodity and quantity of a commodity are in direct proportion

Inverse proportion

Two quantities are said to be in inverse proportion if on increasing the value of one quantity, the value of other quantity decreases and vice versa.

For example Number of men and number of days taken by those men to complete a job.

Here, the equation is y = kx

When x = 2, y = 18

18 = k \(\times\) 2

k = \(\frac{18}{2}\)

k = 9

The value of constant of proportionality k is 9

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In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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Answer:

8, 9, 10, 11, 12 etc.

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

9 x {[14÷2+(4‐1)] - 8

9 x {[7 + (3)] - 8

9 x [7 + 3] - 8

9 x [10] - 8

90 - 8

82

I hope this helps!

Answer:

√8

Step-by-step explanation:

√2x√2x√2 is 2x2x2 which is 8 then the square root √8.

Answer:

27 1/2

Step-by-step explanation:

The equations that could be used to solve for the number of male runners (m) in the race are (m+75)/m = 3 / 2 and 150 + 2m = 3m. The correct options are A and B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that at a running race, the ratio of female runners to male runners is 3 to 2. There are 75 more female runners than male runners.

The ratio is written as,

f/ m = 3 / 2

There are 75 more female runners than male runners.

f = m + 75

The equation can be written as,

f / m = 3 / 2

( m + 75 ) / m = 3 / 2

Or

150 + 2m = 3m

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Answer:

The price per pound of apples is greater than $1.

Step-by-step explanation:

Please consider the complete question:

Three coworkers decided to buy fruit to share at lunch time. Antonii spent $1.47 on bananas.Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges. If Laura bought 2.1 pounds of apples, is the price per pound of apples greater than or less than $1 ? how can you tell?

To find the price of apples per pound, we need to divide total amount paid by Laura ($2.88) with total pounds of apples (2.1 pounds) bought.

Price of apple per pound = \(\frac{2.88}{2.1}\)

Price of apple per pound = $1.37142857

Since the price of apples per pound is $1.37, therefore, the price per pound of apples is greater than $1.

We can simply tell that the price per pound of apples is greater than $1 because 2.88 is greater than 2.1. So when we will divide 2.88 by 2.1, then we will get a number greater than 1.

Using unitary method, the price per pound of apples is greater than $1.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that three coworkers decided to buy fruit to share at lunch time. Antonii spent $1.47 on bananas.Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges. If Laura bought 2.1 pounds of apples, then

To determine the price of apples per pound, we need to divide total amount paid by Laura with total pounds of apples bought.

Price of apple per pound = 2.88/ 2.1

Price of apple per pound = $1.37142857

Since the price of apples per pound is $1.37, thus, the price per pound is greater than $1.

We can simply tell that the price per pound of apples is greater than $1 because 2.88 is greater than 2.1.

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Answer:

f(X)=2x is the correct answer

x = 10% solution

y = 15% solution

let's start at the beginning, without the equation just yet, so let's start off by making a table for the substances and let's use the decimal format for the percentages to get the actual amounts.

\(\begin{array}{lcccl} &\stackrel{mL}{quantity}&\stackrel{\textit{\% of mL that is}}{\textit{alcohol only}}&\stackrel{\textit{mL of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{10\% sol'n}&x&0.10&0.10x\\ \textit{15\% sol'n}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&50&12&6 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.10x+0.15y=6 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{x+y=50\implies y=50-x}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.10x+0.15(\underset{y}{50-x})=6} \\\\\\ 0.10x+7.5-0.15x=6\implies -0.05x+7.5=6\implies -0.05x=-1.5 \\\\\\ x=\cfrac{-1.5}{-0.05}\implies \boxed{x=30}\hspace{15em}\stackrel{50~~ - ~~30}{\boxed{y=20}}\)

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer: This is an iscosceles trapezoid. I put a pencil straight across teh edges and they are equal.

Step-by-step explanation:) Hope this helps