15. Every year in Delaware there is a contest where people create cannons and catapults designed
to launch pumpkins as far in the air as possible. The equation y = 12 + 105x-16x² can be
used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the
pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How
many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the
ground, its height is 0 feet.)
(1 point)

The equation of the hyperbola with and vertices (1, 6) and (1, -12) and

asymptotes y = 3x - 6 and y=-3x is [tex]$\frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1$[/tex]

The answer provided below has been developed in a clear step by step manner.

Given asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex] and

vertices (1,6) and (1,-12)

What is hyperbola ?

Standard hyperbola through origin when values of x for the vertices are equal. [tex]$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$[/tex]

Now solve the asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex]

After solving we get [tex]$\mathrm{x}=1 \quad$[/tex]and [tex]$\quad \mathrm{y}=-3$[/tex]centre =(1,-3)

translation in form of [tex]$\mathrm{x}_1$[/tex] and [tex]$\mathrm{y}_1$[/tex]

[tex]$\mathrm{x}_1=\mathrm{x}-1 \quad$[/tex] and [tex]$\quad \mathrm{y}_1=\mathrm{y}+3$[/tex]

Distance from vertices (1,6) and (1,-12) to centre (1,-3) is [tex]$9=\mathrm{a}$[/tex]vertical symmetry the asymptotes have a slope [tex]$=\pm 3=a / b$[/tex] so [tex]$\mathrm{b}=\frac{9}{3} \Rightarrow \mathrm{b}^2=9$[/tex]

Put all the values of a and b into original equation

[tex]$$\begin{aligned}& x_1=x-1 \quad \text { and } \quad y_1=y+3 \\& \Rightarrow \frac{(y+3)^2}{3^2}-\frac{(x-1)^2}{9^2}=1 \\& \Rightarrow \frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1\end{aligned}$$[/tex]

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Answer: =268.19047cm^3 or 268.08 rounded

Step-by-step explanation: using [tex]\frac{4}{3} *\pi *r^{3}[/tex] to get my answer.

Hope this helps :)

The scientific notation of the wavelength of green light in a spectrum

is 3×10⁻⁶ feet.

In scientific notations numbers are written in the form of a base that is

0  ≤ b < 10 and multiplied by 10ⁿ where n represents integers.

We write large standard numbers in scientific form in a compact manner.

Given, The wavelength of green light in a spectrum is about 0.000003 feet.

Now, the decimal is 6 places before so we have to move the decimal 6 places to the right, and to maintain the actual value we'll raise it to 10⁻⁶.

Therefore, 0.000003 feet,

= 3×10⁻⁶ feet.

So, the wavelength of green light is 3×10⁻⁶ feet.

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The number of minutes will it take him to mow the entire yard will be 50 minutes.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Dad mowed 60% of the yard in 30 minutes.

Let 'A' be the entire area of the lawn and 'x' be the total time to mow the entire lawn. Then 60% of the lawn is given as,

⇒ 60% of A

⇒ 0.60A

The ratio of the area of the lawn to time remains constant. Then the equation is given as,

0.60A / 30 = A / x

x = 30 / 0.60

x = 50 minutes

The number of minutes will it take him to mow the entire yard will be 50 minutes.

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The value not predicted for the given information is "how many gallons the gas tank holds".

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions. You can think of expressions as being similar to phrases.

Here,

How many gallons the gas tank holds is the value that could not be predicted based on the information provided.

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Answer: Our answer set is( -1,-2 )

Step-by-step explanation:

y = x - 1

y = 3x + 1

We can use the combine method here.

==> - 1y + 1x = 1  (y = x - 1)

==>  -1y +3x = -1 (y = 3x + 1)

- 1y + 1x = 1  

 -1y +3x = -1

To single out any of the two variables, we need them to cancel out. Let us choose to cancel out y. We therefore multiply by negative 1 in the first re-arranged equation.

==> -1* (- 1y + 1x )= (1 ) * -1

Now we add the equations

==> 1y -1x = -1

==>-1y +3x = -1

______________

2x = -2

Divide.

==> x = -1

Now we insert x into any of the two original equations;

y = (-1) - 1

==> y = -2

Our answer set is( -1,-2 )

On solving the provide question, we got that - he equation of a line with a y-intercept of −5 and a slope of 8 is8x - y +5 = 0

The change in the y coordinate of a line with respect to the change in x coordinate is called the slope of the line. There was no net change in the x coordinate, but no net change in the y coordinate.

By using the Slope formula

(y - y1) = m (x - x1)

where m is slope

so,

(y - 5) = 8 X (x-0)

8x - y +5 = 0

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Answer:

Step-by-step explanation:

........................................................

Hello,

I hope you and your family are doing well!

To calculate the amount of interest earned on a savings account, you can use the following formula:

interest = principal * rate * time

In this case, the principal is $9,500, the rate is 3.75%, and the time is 1 year. Plugging these values into the formula, we get:

interest = $9,500 * 3.75% * 1 year = $356.25

So, in a year, Alice would earn $356.25 in interest on her savings account.

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Happy Holidays!

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$30200\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=30200\left(1+\frac{0.06}{1}\right)^{1\cdot 5} \implies A=30200(1.06)^5\implies A \approx 40414.41[/tex]

The value of x from the equation (221x3 + 154x2 + 228x + 41) / (17x + 4)-4 is 992

(221x3 + 154x2 + 228x + 41) / (17x + 4)-4

Multiplying 221*3 and 154*2 =663,308

( 663+308 + 228x + 41) / (17x + 4)-4

( 971+ 228x + 41) / (17x + 4)-4

=( 971+ 228x +41)

       (17x + 4)

=1012+228x

    (17x + 4)

-x=-992

x=992

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Answer:

14+9(x-1)=y

Step-by-step explanation:

If x is the number of pizza's being delivered and the first pizza costs $14 then that pizza is already accounted for by the 14 in the equation, so you subtract x by 1 before multiplying it by 9, then add the 14 to the product you then get the total cost: y

Answer: y = [tex]-\frac{2}{3} x[/tex] -5

Step-by-step explanation:

Distribute:

-3y-5=-2x(x+11)+2

Rewrite:

-3y-5=-2x-22+2

Combind alike terms:

-2x-20

Rewrite again:

-3y-5=-2x-20

Add 5 to both sides and rewrite:

-3y=-2x-15

Divide by -3:

y=[tex]-\frac{2}{3} x[/tex] - 5

(Sorry if it's incorrect im barely paying attention lol)

Answer:

the number of terms N in the series is approximately 8.57, which is approximately equal to 9.

Step-by-step explanation:

The mean of a series is calculated by taking the sum of all the terms in the series and dividing it by the number of terms. In this case, the mean of the continuous series Efm=300+20m is given as x=15+m.

To find the number of terms N in the series, we can use the formula for the mean to solve for N. The formula for the mean is:

mean = sum of terms / number of terms

Substituting the given values, we get:

15+m = (300+20m) / N

We can then multiply both sides of the equation by N to isolate the sum of terms:

(15+m) * N = 300+20m

This simplifies to:

15N + mN = 300 + 20m

We can then combine like terms to get:

(15+20)N = 300

35N = 300

Dividing both sides by 35, we get:

N = 300/35

N = 8.57

Since the number of terms must be a whole number, the number of terms N in the series is approximately 8.57, which is approximately equal to 9.

y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

In the perpendicular lines the product of slopes will be -1

m1m2=-1

y=x+4 is the given line, it has slope of 1, so the perpendicular line will have slope -1.

The line is passing through (8,2)

2=-1(8)+b

2=-8+b

2+8=b

10=b

Hence, y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4

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Answer:

  x = 125

Step-by-step explanation:

Given a heptagon with 60° and 90° angles marked, one marked 2x°, and the remaining angles marked x°, you want o know the value of x.

The sum of the interior angles of a heptagon is ...

  180° × (7 -2) = 900°

Using the given values, this tells us ...

  90° +x° +x° +x° +x° +60° +2x° = 900°

  6x = 750 . . . . . . . divide by °, subtract 150

  x = 125 . . . . . . divide by 6

The value of x is 125.

__

Additional comment

The attached figure is drawn with correct angles.

The sum of interior angles of an n-gon is 180°×(n -2).

Answer:

x ≥ -7

Hope this helps : )

Step-by-step explanation:

The number line is showing a closed dot which means that the number the dot is on is a solution to the equation too. Since the arrow is pointing to the right (positive/greater numbers), then the sign is greater than and equal to.

The value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3⁢x+y+2⁢z=6 6⁢x−2⁢y=2 3⁢x+y−2⁢z=0

It is defined as the relation between three variables, if we plot the graph of the linear equation we will get a plane.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The linear equations are:

3⁢x+y+2⁢z=6

6⁢x−2⁢y=2

3⁢x+y−2⁢z=0

From equation (I) and (III)

6x + 2y = 6

From the above equation and equation (II)

12x = 8

x = 8/12 = 2/3

y = 1

z = 3/2

Thus, the value of x, y and z are 2/3, 1, and 3/2 if the system of equations 3⁢x+y+2⁢z=6 6⁢x−2⁢y=2 3⁢x+y−2⁢z=0

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A number line use to graph the inequality y ≥ 4.

Explanation :

y = − 4 is a horizontal line at -4, since

y ≥ − 4, the area above -4 will be shaded and the line will be solid since it is greater than AND equal to:

graph{y>=-4 [-10, 10, -5, 5]}

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Answer:

You draw the line of the graph and every point on the line is a solution

Step-by-step explanation:

y = mx + b  You graph the b which is the y intercept.  This is where the graph crosses the x axis.  In this case it is -12.  From that point (0,-12)  You follow a pattern which is the slope.  In this case the slope is -3.  That mans that you move three units down and then 1 unit right.

I highlighted a few points on the line.  Every point on the line is a solution.

Knowing that the teacher indicates the chapter of the book to use and the delivery date, the resources that were provided for the research on sustainable energy are:

They are elements that must be taken into account and that are usable to develop the investigation.

Some examples of these resources are:

¡Hope this helped!

Answer:-1/2

Step-by-step explanation:

Answer:

182

Step-by-step explanation:

152

+31

---------

182

Answer: 7

Step-by-step explanation:

The initial value of the function is the value of [tex]y[/tex] when [tex]x=0[/tex].

Answer:

which class question is this

Using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The four basic mathematical operations, according to the majority of people, are addition, subtraction, multiplication, and division.

So, the strawberries both Landon and Colin will get are:

We know that Landon and Colin brought 1/2 strawberries.

They share is equally that is:

1/2 ÷ 2

Now, solve as follows:

1/2 ÷ 2

1/2 ÷ 2/1

1/2 * 1/2

1/4

Therefore, using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.

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The flux of  out of S is [tex]14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)[/tex].

What is Flux of the Vector Field?

Solving the flux of the vector field using the divergence theorem which has the following formula [tex]$\iint_S F \cdot d S=\iiint_E div} F(x, y, z) d V$[/tex] where F is the vector field [tex]$F=P i+Q j+R k$[/tex] and div F means the divergence of F which has the formula  [tex]$F=\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial z}$[/tex]

Here, we let the vector field to be [tex]$\vec{F}=x i+y j+z k$[/tex]

[tex]$\vec{F}=x i+y j+z k$[/tex]

Now solving for [tex]${div} F$[/tex]

[tex]$$\begin{aligned}& {div} F=\frac{\partial x}{\partial x}+\frac{\partial y}{\partial y}+\frac{\partial z}{\partial z} \\& {div} F=1+1+1=3\end{aligned}$$[/tex]

Thus,

[tex]\iint_S F \cdot d S=\iiint 3 d V[/tex]

From the given region the limits of integrations in spherical coordinates are,

[tex]0 \leq \theta \leq 2 \pi, 0 \leq \phi \leq \frac{\pi}{4}, 1 \leq \rho \leq 2[/tex]

Thus,

[tex]\iint_S F \cdot d S=\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} \int_1^2 3 \rho^2 \sin \phi d \rho d \phi d \theta[/tex]

Integrate with respect to [tex]$\rho$[/tex]

[tex]\begin{aligned}& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 3\left[\frac{1}{3} \rho^3\right]_1^2 \sin \phi d \phi d \theta \\& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 7 \sin \phi d \phi d \theta\end{aligned}[/tex]

Integrate with respect to [tex]$\phi$[/tex]

[tex]\begin{aligned}& =\int_0^{2 \pi} 7[-\cos \phi]_0^{\frac{\pi}{4}} d \theta \\& =\int_0^{2 \pi} 7\left(-\frac{\sqrt{2}}{2}+1\right) d \theta\end{aligned}[/tex]

Integrate with respect to [tex]$\theta$[/tex]

[tex]\begin{aligned}& =7\left(-\frac{\sqrt{2}}{2}+1\right)[\theta]_0^{2 \pi} \\& =14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)\end{aligned}[/tex]

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Answer:

  (c)  12(2v-7)

Step-by-step explanation:

You want the expression resulting from factoring out the greatest common factor from the sum 24v -84.

The greatest common factor here is the GCF of 24 and 84. We note that ...

  24 = 12·2

  84 = 12·7

and 2 and 7 have no common factors. Then the GCF of 24 and 84 is 12.

The factored expression is ...

  24v -84 = 12(2v -7)

__

Additional comment

The GCF can also be found by considering the remainder from dividing 84 by 24. That remainder is 12, which divides both numbers with a remainder of 0. Hence 12 is the GCF.

If the remainder did not divide both numbers with a remainder of 0, then the process is repeated to find the GCF of the smaller number (24) and the remainder. (This is a description of Euclid's algorithm for finding the GCF.)

The line r has slope 6 and coordinates in the specified coordinate plane, based on the given dilation (0, 12)

Dilation:

Dilation is the scaling factor multiplied by the supplied line to line ratio.

Given

Line p in the coordinate plane has a y-intercept and a slope of 6. (0, 8). Line p is dilated by a factor of 4 with center to produce line r. (0, 4).

Here, we need to determine line r's slope and y-intercept.

Here, the scaling factor is known to be 4.

Consider the line r's slope, which won't change, and its intercept, which will be their ordinate added.

So, it can be written as,

=> Intercept = 8 + 4

=> Intercept = 12

Therefore, the line r has slope 6 and coordinate (0, 12).

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