A hyperbola centered at the origin has a vertex at (0,−40) and a focus at (0, 41). which are the equations of the asymptotes? y = ±x y = ±x y = ±x y = ±x

Answer:

Step-by-step explanation:

If you use the formula [tex]m = \frac{y2 - y1} {x2 - x1}[/tex] with x1 being 7, y1 being 0, -5 being x2 and 5 being y2, then you can subtract. 5(y2) minus 0(y1) is 5, and -5(x2) minus 7(x1) is -12. The formula would look like this: [tex]m = \frac{5 - 0}{-5 - 7} \frac{5}{-12}[/tex].

(tip: you need to do rise over run, aka y over x, shown as [tex]\frac{y}{x}[/tex] or [tex]\frac{rise}{run}[/tex])

I hope I helped you answer your question, and helped better understand it as well

Answer:

[tex]\sf y = -\dfrac{1}{2} x +4[/tex]

Find slope (m):

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m): \dfrac{0-4}{4-0} = -\dfrac{1}{2}[/tex]

Now, find equation:

[tex]\sf y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex]

[tex]\rightarrow \sf y - 4 = -\dfrac{1}{2} (x - 0)[/tex]

[tex]\rightarrow \sf y = -\dfrac{1}{2} x +4[/tex]

Division is one of the four fundamental arithmetic operations. The number of pints of water Scott drank yesterday is 4.2 pints.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. Therefore, the length of each piece of rope in inches will be,

Length of piece = 14.35 inches/7 = 2.05 inches

Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. Therefore, the number of pints of water Scott drank yesterday is,

Number of pints = 3.5 bottles × 1.2 pints = 4.2 pints

Hence, The number of pints of water Scott drank yesterday is 4.2 pints.

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Answer: 6.7 units for the diagonal from J to L

Step-by-step explanation:

you can use the Pythagorean theorem to find the diagonal (hypotenuse)

a^2 + b^2 = c^2

by counting units from M to J you have a length of 3 for the "a" value

by counting units from M to L you have a length of 6 for the "b" value

3^2 + 6^2 = c^2

9 + 36 = c^2

45 = c^2

take square root of both sides

6.7 = c

the diagonal is 6.7 units

The translation rule that maps point D' to D" is (x + 3, y) and  the coordinate of point A" is (9,3)

The coordinates are given as:

A(-6,3) B(-4,5) C(-1,6) and D(-3,2)

When reflected across the y-axis, the transformation rule is:

(x,y) -> (-x,y)

So, we have:

A' = (6,3)

D' = (3,2)

Point D" on the grid is (6,2).

This means that the translation rule that maps both point is (x + 3, y)

In (a), we have:

A' = (6,3)

Using the translation rule (x + 3, y), we have:

A" = (6 + 3,3)

A" = (9,3)

Hence, the coordinate of point A" is (9,3)

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Volume is a three-dimensional scalar quantity. The volume of the empty space is 20.602 units³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the volume of the prism, the box is 96 units³ and the diameter of the cylindrical container is 4 units(Radius=2 units), while the height of the cylinder is 6 units. Therefore, The volume of the empty space is,

The volume of the empty space

= Volume of prism - Volume of the cylindrical container

= 96 units³ - (π×2²×6) units³

= 96 units³ - 75.398 units³

= 20.602 units³

Hence, the volume of the empty space is 20.602 units³.

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Answer:

(x-1)^2

=x^2 - 2x + 1

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

Givens

Comment

This is a proportion. A proportion is 2 equal ratios. If you know 3 parts of a proportion, you can solve for the 4th.

Equation

wage/time = wage2/time2                   Substitute values.

Solution

367.40 /22 = 584,50 /x                        Cross multiply

367.40x = 22 *584.50                          Simplify the right

367.40x = 12859                                   Divide both sides by 367.40

x = 12859/367.40

x = 35

Answer

Genesis will have to work 35 hours.

The area of sector AOB  whose radius OA 5 units is 19.6 sq. units.

A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.

Here, Radius of Circle = 5 units

         length of arc AB / circumference = 1/4

        So, Area of Sector AOB = one fourth of area of circle

                                                  = 1/4 X π X r²

                                                 = 0.25 X 3.14 X 5²

                                                 = 0.25 X 3.14 X 25

                                                 = 19.625 sq. units

Thus, the area of sector AOB  whose radius OA 5 units is 19.6 sq. units.

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Answer:

19.6

Step-by-step explanation:

Answer:

K=-6/11

Step-by-step explanation:

3(k/3+4-2k)=3(-9k)

K+12-6k=-27k

12-5k=-27k

12=-22k

K=-6/11

Answer:

[tex]x=-2\\[/tex]

Step-by-step explanation:

[tex]8^x=\frac{1}{64}\\xlog8=log\frac{1}{64}\\x=\frac{log\frac{1}{64}}{\log8}\\x=-2[/tex]

First we write the equation given

Next we take the log of both sides. This turns [tex]x[/tex] into a normal term instead of an exponent, but turns [tex]8[/tex] and [tex]64[/tex] into the log version of themselves.

Next we can divide both sides by [tex]log8[/tex] to isolate [tex]x[/tex].

This gives us our answer of [tex]\boxed{-2}[/tex]

Reason:

The largest sin(x) can get is 1, and the same goes for sin(3x).

Consequently, the largest 2sin(3x) can get is 2.

You can visually verify these claims by graphing each function with a tool like Desmos. Take note of the y coordinate of the highest points. See below.

Therefore, the largest f(x) = 2sin(3x)+C can get is 2+C or C+2

The measure of <YXP and <YZQ are 35 and 65 degrees respectively

Equilateral triangles are triangles that has equal sides and angles.

From the given diagram;

<YZQ + 90 + 25 = 180

<YZQ =180 -115

<YZQ = 65degrees

Determine the measure of <YXP

<YXP = 60 - 25 (XYZ is a 60degrees triangle)

<YXP = 35 degrees

Hence the measure of <YXP and <YZQ are 35 and 65 degrees respectively

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Answer:

P = 20 cm

Step-by-step explanation:

the perimeter (P) is the sum of the 4 sides (s)  of the square

the sides of a square are congruent , then

P = 4s = 4 × 5 = 20 cm

Answer:

They are all non triangles, but I'm not in your math class, so I don't know.

Step-by-step explanation:

The equation of the function is y = sec(2(x + π/6)) + 2

From the graph, we have the following parameters:

A secant function is represented as:

y = A sec(b(x + c)) + d

Where:

A = 0.5 * (max - min) = 0.5 * (3 - 1) = 1

b = Period = 2

c = Phase shift = π/6

d = 0.5 * (max + min) = 0.5 * (3 + 1) = 2

So, we have:

y = 1 * sec(2(x + π/6)) + 2

Evaluate

y = sec(2(x + π/6)) + 2

Hence, the equation of the function is y = sec(2(x + π/6)) + 2

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Answer

The answer is B on Edgenuit

Step-by-step explanation:

Desmos

Answer:

p = 5

Step-by-step explanation:

Given equation:

2p - 3 = p+2

To Find:

Soln:

2p - 3 = p + 2

Subtract p from both sides:

=>2p-3−p = p+2-p

=>p-3 = 2

Add 3 to both sides:

=>p−3+3 = 2+3

=>p = 5

Hence,the value of p would be 5.

We can plug the value we got to the original equation to verify:

=> 2p - 3 = p + 2

=> 2(5) -3 = 5 + 2

=> 10 - 3 = 7

=> 7 = 7 [Proved]

Hence,this equation is true.

[tex]\rule{225pt}{2pt}[/tex]

Acronym PEMDAS rule means:

Answer:

p = 5

Step-by-step explanation:

First we add 3 to both sides to make :

2p = p + 5

Now we subtract p from both sides :

p = 5

Hope this helped and brainliest please

Answer:

To find the value of x, use the formula

(n-2) x 180,  where n is the number of sides.

In this case, we have a TRIangle, which has THREE sides.

So, n=3

(3-2) x 180

1 x 180

180

If the total sum of the angles  is 180, then  the  measure of one angle would be 180 divided by 3, which is 60.

Let me know if this helps, or if you got any more questions

Answer:

x=2.7

Step-by-step explanation:

tan34 = x/4

x = 4tan34 = 2.7

Answer:

  6 square units

Step-by-step explanation:

The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.

__

Any right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.

Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.

The fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.

The tangent ratio is ...

  Tan = Opposite/Adjacent

Applying that to angle β, we have

  tan(β) = OD/AD   [eqn 1]

  tan(β) = BC/AC   [eqn 2]

These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.

Equation [eqn 1] tells us ...

  AD = OD/tan(β)

Equation [eqn 2] tells us ...

  BC = AC·tan(β)

The area of ΔADB is ...

  Area = 1/2bh

  Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))

  Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel

The length of AC is given as 6, and we know OD = 2, so the area is ...

  Area = 1/2(2)(6) = 6

The area of triangle ADB is 6 square units.

Answer:

6x+6

Step-by-step explanation:

a linear expression has no power attached to the x (the unknown)

The equation to represent the proportional relationship is c = 0.25d

Let c = the number of cans

Let d = the number of days

So, we have:

c = kd

Where k represents the constant of proportionality.

From the given parameters, we have:

3 = 12k

Divide both sides by 12

k = 0.25

Substitute k = 0.25 in c = kd

c = 0.25d

Hence, the equation to represent the proportional relationship is c = 0.25d

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If your bottom time is 25 minutes, general rules recommend that you ascend immediately to 15 feet then remain there for 8 minutes. You should then go to the surface and not dive for 6 hours.

The recommended bottom time is 24 minutes which means that staying there for 25 minutes will have exceeded this recommendation.

You should immediately ascend to 15 feet or 5 meters, and then wait there for 8 minutes. Then return to the surface and avoid diving for the next 6 hours.

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Answer:

Answer:

The answer is c, hope this helps

Step-by-step explanation:

Answer:

490,000 grams

Step-by-step explanation:

To convert from kilograms to grams - multiply the number of kilograms by 1000. (there are 1000 grams in a kilogram)

[tex]490 * 1000 = 490,000[/tex]

Answer:

490000

Step-by-step explanation:

1 kg : 1000 gram

So,

490 kilograms : 490 ×1000 grams

: 490000 grams

Step-by-step explanation:

the perimeter is simply the distance you would have to walk when going around the whole object once.

so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.

so, the perimeter of a rectangle is

2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m

If Larry is measuring the object's mass, the object he is most likely measuring is; D: A horse.

There are different units of measurement for different parameters such as meters for length, seconds for time, Amperes for current e.t.c.

Now, we are talking about measurement of an object mass in grams. This means it has to be a living thing and as such from the options, the only living thing is a horse.

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The income tax for the married couples under filing a joint return receives a standard deduction of $25,100.

An income tax is a type of tax that governments impose on income generated by businesses and individuals within their jurisdiction.

In this case, the income tax for the married couples filing a joint return receives a standard deduction of $25,100

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Answer:

43.4%

Step-by-step explanation:

229.99 - 129.99

= 100

The percent reduction is:

100/229.99 * 100

=43.4%