The product of four consecutive positive integers is 1 less than $461^2$. What is the least of these four numbers?.

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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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: 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 )

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:

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

The width of Mary's rectangular room is 5 feet.

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle

So, we consider Mary's room a rectangular room:

With an area of 40ft² and a length is 8ft.

Area of rectangle: l*w

Where l stands for length and w stands for width.

Now, calculate the width using the formula as follows:

Area = l*w

40 = 8*w

w = 40/8

w = 5ft

Therefore, the width of Mary's rectangular room is 5 feet.

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Answer:

99

Step-by-step explanation:

Since the triangles are similar, we know the ratio of the sides is a constant. We know that SQ is 55, and the corresponding side on the other triangle is 10. This lets us find the ratio for the whole triangle! The ratio is 55/10, or 5.5.

To solve for RS, consider the corresponding side on the other triangle(LS) which is 18. We multiply that by the ratio to get 18 * 5.5 = 99, which is the length of RS.

I don't know if you need to solve for x, but if you do, here it is! We have [tex]99 = 12x+3[/tex] (the equation for side RS). subtracting 3 from both sides results in [tex]96 = 12x[/tex], and dividing by x gives us that x = 8.

Thank you! Feel free to ask me any questions about my answer. I hope this helps!

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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Answer: 95 percent confidence interval

Step-by-step explanation: "you have a 5 percent chance of being wrong. with a 90 percent confidence interval, you have a 10 percent chance of being wrong a 99 percent confidence interval would be wider than a 95 percent confidence interval for example plus or minus 4.5 percent instead of 3.5 percent"

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 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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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!

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Answer:

Step-by-step explanation:

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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.

Answer:

b). were 18 when their parents were naturalized

Step-by-step explanation

I know I am right because I believe this is Civics or U.S History. I did Civics in 7th, and U.S History I am currently doing. hope this helps!

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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The number of weeks it will take them to have saved thesame amount is 8 weeks

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.

if x represents the the number of weeks for saving and y represents the equal saved amount, then

42+16x = y equation 1

-70+ 30x = y equation 2

subtract equation 1 from 2

-70-42+16x- 30x= 0

-112+14x= 0

collect like terms

-112=-14x

divide both sides by 14

x= -112/-14

x= 8weeks

therefore it will take them 8 weeks to have equal savings

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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

Answer:-1/2

Step-by-step explanation:

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.)

[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, 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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The each day of the trip will cost the family $212   .

In the question ,

it is given that ,

a family is going on 3 day trip ,

the cost for hotel for 3 days is = $336 ,

So , the cost for the hotel for 1 day is = $336/3 = $112 ,

the amount budgeted for the food is one hundred dollar

the cost for the food for 1 day is = $100 .

So , the cost for each day is = cost of food + cost of hotel

Substituting the values of food and hotel ,

we get ,

= 100 + 112

Adding both the terms ,

we get ,

= 212

Therefore , the cost for each day is = $212 .

The given question is incomplete , the complete question is

A family is going to on a trip for 3 days the total cost for the hotel is $336. One hundred dollar for the day was budgeted for food. How much will each day of the the trip will cost ?

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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.

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 :)