Explain the step by step process of finding a function for a hyperbola given the center (1,4), vertices (-7,4) and (9,4), and a point on the hyperbola at (-11, -6). Make sure to include the location of the foci.

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Step-by-step explanation:

you drew already the right things, you have everything.

so, what is the problem ?

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.

so, for the 2 marked points you showed correctly the differences :

x changes by +8 (from -4 to 4).

y changes by -2 (from 3 to 1).

so the slope is -2/+8 = -1/4

the y-intercept we also see directly in the chart : +2.

Don't get me wrong, I am not exactly sure but I believe it is supposed to be 75$.

The equation of a line in point slope form is expressed according to the formula;

y-y0 = m(x-x0)

Given the following parameters

m = -3

(x0, y0) = (-4, 1)

Substitute into the formula above will givee;

y - 1 = -4(x+4)

y -1 = -4x - 16

y = -4x - 15

Next is to plot the graph of the line y = -4x - 15 on the coordinate plane as shown:

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Answer:

Finally, Juno and her satellite were able to return home to her family.

Step-by-step explanation:

Answer:

Finally, Juno and her satellite were able to return home to her family

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

(4x-20+x-1)/8 = (3x-9+4x-16)/12

(5x-21)/8=(7x-25)/12

(5x-21)/8 x 12/1 = (5x-21)/2 x 3/1 = (15x -63)/2

15x - 63 = 14x - 50

x=13

Answer:

.37 resolutions

Step-by-step explanation:

2×22/7×35

44.5×=220

0.37 revolutions

Answer:

The answer is C

Step-by-step explanation:

(I'm not completely sure)

Answer:

the portion of the drama clubs budget needed for each type of expense

Step-by-step explanation:

the number of inches of snow received each year by a ski resort

- you should use line graph to see data changing in consistent time period

the portion of the drama clubs budget needed for each type of expense

- you can use box plot to see the box plot to show median and q1 q3 of the expenses.

the number of heads and tails that came up in 100 coin flips

- you should use pie chart to see the percentages in entire population  

the number of votes received by each of four candidates

- you should use bar graph to compare 4 comparable object.

The portion of the drama clubs budget needed for each type of expense

A data set is a set of information. A data set corresponds to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row represents a specific record of the data set in question.

a) The number of inches of snow received each year by a ski resort

you should use a line graph to see data changing in the consistent time period

b) The portion of the drama club budget needed for each type of expense

you can use the box plot to see the box plot to show the median and q1 q3 of the expenses.

c) The number of heads and tails that came up in 100 coin flips

you should use a pie chart to see the percentages in the entire population  

d) The number of votes received by each of the four candidates

you should use a bar graph to compare 4 comparable objects.

Therefore a portion of the drama club's budget is needed for each type of expense.

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Answer:

hmm it's like ut I do know and my answer

Answer: That would be distributive

Step-by-step explanation:

Answer:

 5.93 years

Step-by-step explanation:

The continuous compounding formula tells you the amount after t years will be ...

  A = Pe^(rt) . . . . principal P compounded continuously at annual rate r for t years

  7400 = 5500e^(0.05t)

  ln(7400/5500) = 0.05t . . . . divide by 5500, take natural logs

  t = 20×ln(74/55) ≈ 5.93

It will take about 5.93 years for $5500 to grow to $7400.

The best selection for the quadrilateral with the given vertices is: parallelogram.

Recall:

Parallel lines are lines do not intersect and they are equal distant apart.

The opposite side of a parallelogram are of equal length.

Thus, the points of the vertices of the quadrilateral has been graphed in the diagram shown below:

Point A (-2,0)

Point B (0,4)

Point C (6,4)

Point D (4,0)

Find the distance between each vertices using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Distance between Point A (-2,0) and Point B (0,4):

[tex]AB = \sqrt{(0 -(-2))^2 + (4 - 0)^2} \\\\\mathbf{AB = \sqrt{20} }[/tex]

Distance between Point B (0,4) and Point C (6,4):

[tex]BC = \sqrt{(6 - 0)^2 + (4 - 4)^2} \\\\\mathbf{BC = 6 }[/tex]

Using the same distance formula, CD = √20 while AD = 6

This means that the opposite sides of the quadrilateral with the given vertices are equal in length. Parallelogram has two pairs of equal sides.

Therefore, the best selection for the quadrilateral with the given vertices is: parallelogram.

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Answer:

Part A: The two types of types of transformation are

1) Rotation of 11.3° about (1, 2)

2) By algebraic transformation

Part B:

Rotation by 11.3° and T(2 - y)×1/2 + x, 0)

Part C: The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)

Step-by-step explanation:

The coordinates through which the linear function f(x) passes = (1. 3) and (3, 13)

The coordinates through which the linear function g(x) passes = (1, 3) and (1, 13)

The equation for f(x) in slope and intercept form. y = m·x + c is given as follows;

The slope, m = (13 - 3)/(3 - 1) = 5

The equation in point and slope form is y - 3 = 5×(x -1)

y = 5·x - 5 + 3 = 5·x - 3

y = 5·x - 3

The equation for g(x) in slope and intercept form. y = m·x + c is given as follows;

The slope, m = (13 - 3)/(1 - 1) = ∞

∴ The equation in point and slope form is x = 1

Therefore, the two equations meet at the point (1, 2)

The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)

2) Another transformation that can be used is to rotate f(x) by the vertex angle as follows

Vertex angle is 90° - tan⁻¹(m) = 90° - tan⁻¹(5) ≈ 11.3°

Rotation of f(x) by 11.3° about (1, 2) gives g(x)

Hope this helped!

Answer:

b(-1)= -6

b(0)= -4

b(4)=  4

Step-by-step explanation:

2(-1) - 4

-2-4=-6

2(0) - 4

0 - 4 = -4

2(4) - 4

8 - 4 = 4

Answer:

-6, -4, 4

Step-by-step explanation:

The total values in the dataset is 24 values

From the given histogram, to get the number of values in the dataset, we will have to trace each bar to the y-axis and then take the sum.

The total values of the dataset = 13 + 3 + 3 + 5

The total values of the dataset = 24 values

Hence the total values in the dataset is 24 values

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Answer:

answer is 22, is you add all the values

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\impliedby y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{5}}x-8[/tex]

so we're really looking for the line of a slope of 3/5 and passing through (0,-3)

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{0}) \\\\\\ y+3=\cfrac{3}{5}x\implies y=\cfrac{3}{5}x-3[/tex]

Answer:

10

Step-by-step explanation:

it is 10 cause 634+10=644

Answer:

10

Step-by-step explanation:

What is the missing addend?

We can fill in the blank with x

634+x=644

Now we need to get x to the other side

The rule to do this is what we do on one side we have to do the same thing to the other side

so if we subtract 634 on one side we also have to do that on the other side as well:

634-634+x=644-634

634-634 is 0

So it is

x=644-634

644-634 is 10

x=10

So the missing addend is 10

Hope this helps!

Step-by-step explanation:

formula y2-y1 / x2-x1

m = 5 / -10 = 1 / -2 = -0.5

Answer:

Nonlinear positive association

Step-by-step explanation:

It is nonlinear because it does not form a straight line.

It is positive because it is going up to the right.

I hope this helps!

Answer:

y=1/5x-31/5 (or y=0.2x-6.2 in decimals)

Step-by-step explanation:

x=5y-8     (original equation)

x+8=5y (Addition Property of Equality)

1/5x+8/5=y (Division Property of Equality, slope of original equation is 1/5)

y-y1=m(x-x1)    (point-slope formula)

y-(-5))=1/5(x-(6)) (plug in the slope that was found earlier and the point given in the question)

y+5=1/5(x-6)

y+5=1/5x-6/5   (Distributive Property of Multiplication)   Note:  5 = 25/5

y=1/5x-31/5 (Subtraction Property of Equality, and there's your answer)

y=0.2x-6.2 (This is the same answer, but written with decimals)

Answer:

boom bam ba boom bam ba

Answer:

hope you understand my answer:)

Answer:

x = 11/7

Step-by-step explanation:

[tex]7x+6-2x=12x-7+2\\\\5x+6=12x-5\\\\5x+6-5x=12x-5-5x\\\\6=7x-5\\\\6+5=7x-5+5\\\\11=7x\\\\\frac{11}{7}=\frac{7x}{7}\\\\\frac{11}{7}=x[/tex]

the slope is -14/6 or the simplified version is -7/3