Arrange the hyperbolas in increasing order of the horizontal widths of their asymptote rectangles.

Answer:

  f(x) = 4·sin(2/7x) +1

Step-by-step explanation:

The sinusoidal function y = a·sin(kx) +b will have cross its midline at (0, b), and a peak value of (x, y) = (π/(2k), a+b). We can use these facts to find the values of a, k, and b for the sinusoidal function.

__

  (0, b) = (0, 1)   ⇒   b = 1

  (7π/4, 5) = (π/(2k), a+1)

This gives rise to two equations:

  7π/4 = π/(2k)

  k = π/(2(7π/4)) = 2/7

and

  a+1 = 5

  a = 4

Using the found values for the parameters of the function, we have ...

  f(x) = 4·sin(2/7x) +1

Answer:

7,13,31,85,247......

Step-by-step explanation:

[tex]a_n =3^n + 4[/tex]

        [tex]\sf a_1=3^1 + 4 = 3 + 4 = 7\\\\a_2 = 3^2 + 4 = 9 + 4 = 13\\\\a_3 = 3^3 + 4 = 27 + 4 = 31\\\\a_4 = 3^4 + 4 = 81 + 4 = 85\\\\a_5 = 3^5 + 4 = 243 + 4 = 247[/tex]

The length of EC shown in the diagram is 66.2.

"To understand the calculation, check below."

ΔBE - ΔAE = ΔAB

ΔAB = 180°- 117°

ΔAB = 63°

Δ[tex]BE-[/tex] Δ[tex]AB-[/tex] Δ[tex]BC[/tex] = Δ[tex]CD[/tex] (Congruent angles)

Δ[tex]CD= 180 - 63 - 15[/tex]

Δ[tex]CD=102[/tex]

[tex]EC = 102 + 63[/tex]

[tex]EC=165[/tex]

[tex]L = 165[/tex] • [tex]2\pi23/360[/tex]

[tex]L = 66.2[/tex]

Therefore, EC = 66.2

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Answer:

Vertical Reflection Apply a reflection over the line y=-1 The procedure to determine the coordinate points of the image is the same as that of the previous example with minor differences in that the change will be applied to the y-value and the x-value stays the same.

Step-by-step explanation:

Answer:

Domain: [tex]-3\leq x\leq 3[/tex]

Range: [tex]0\leq y\leq 1.5[/tex]

Increasing: [tex]0\leq x\leq 3[/tex]

Decreasing: [tex]-3\leq x\leq 0[/tex]

No constant intervals

Step-by-step explanation:

Hope this helped

Answer:

It does not matter.

Step-by-step explanation:

How to find a slope with just two points,

Step One: Identify two points on the line.

Step Two: Select one to be (x1, y1) and the other to be (x2, y2).

Step Three: Use the slope equation to calculate the slope.

Example

Let's say that points (15, 8) and (10, 7) are on a straight line. What is the slope of this line?

Step One: Identify two points on the line.

In this example, we are given two points, (15, 8) and (10, 7), on a straight line.

Step Two: Select one to be (x1, y1) and the other to be (x2, y2).

It doesn't matter which we choose, so let's take (15, 8) to be (x2, y2). Let's take the point (10, 7) to be the point (x1, y1).

Step Three: Use the equation to calculate the slope.

Once we've completed step 2, we are ready to calculate the slope using the equation for a slope:

[tex]slope=\frac{y2-y1}{x2-x1} =\frac{8-7}{15-10} =\frac{1}{5}[/tex]

We said that it really doesn't matter which point we choose as (x1, y1) and the which to be (x2, y2). Let's show that this is true. Take the same two points (15, 8) and (10, 7), but this time we will calculate the slope using (15, 8) as (x1, y1) and (10, 7) as the point (x2, y2). Then substitute these into the equation for slope:

[tex]slope=\frac{y2-y1}{x2-x1} =\frac{7-8}{10-15} =\frac{-1}{-5}=\frac{1}{5}[/tex]

We get the same answer as before!

Often you will not be given the two points but will need to identify two points from a graph. In this case, the process is the same, the first step being to identify the points from the graph. Below is an example that begins with a graph.

So therefore it does not matter.

No, it does not matter which point you choose as (x₁, y₁) and which point you choose as (x₂, y₂) when using slope formula. Slope between two points on line remains same regardless of order in which you choose points.

The slope formula is given by slope = (y₂ - y₁) / (x₂ - x₁)

This is because the slope represents the rate at which the y-coordinate changes with respect to the x-coordinate.

If you swap the points (x₁, y₁) and (x₂, y₂), the change in y and the change in x will simply swap as well, but their ratio, which is the slope, will remain unchanged. For example, if the slope between (x₁, y₁) and (x₂, y₂) is m, then the slope between (x₂, y₂) and (x₁, y₁) will also be m.

This property of the slope formula makes it convenient and efficient to calculate the slope between two points, regardless of their order, as it will yield the same result.

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Answer:

[tex](-4, -\frac{1}{2} )[/tex]

Step-by-step explanation:

A (-5, -4)

B (-3, 3)

We can apply the midpoint formula: [tex](\frac{-5 + -3}{2} , \frac{-4 + 3}{2} )[/tex]

[tex]= (-4, -\frac{1}{2} )[/tex]

hope this helped! :)

Answer:

5  5/9

Step-by-step explanation:

9 goes into 50 4 times and the subtract that from 50

Answer :

5 [tex]\frac{5}{9}[/tex]

Explanation:

50/9= 5.5555555555556 = 5

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (5) and multiply it by the original denominator (9). The result of that multiplication is then subtracted from the original numerator:

50 - (9 x 5) = 5

Step 3: Our mixed fraction

We've now simplified 50/9 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

5 [tex]\frac{5}{9}[/tex]

Perimeter of larger sail

Now

Let shorter sail's Perimeter be x

#2

Let they be 2x and 7x

Smaller angle

Answer:

352

Step-by-step explanation:

sssplit the shapes and then do regular formula

a = lh

Answer:

f(4) = 25

Step-by-step explanation:

substitute x = 4 into f(x)

f(4) = 2(4)² - 7 = 2(16) - 7 = 32 - 7 = 25

The correct value of z in this figure is 190⁰

The image given in this question is of a circle. To solve it, let's calculate it as an equation of the first degree.

– First, let's: add the data that are on the circle and equate the equality as 360⁰, which is the value of the degree of a circle.

145 + 24 + z = 360⁰

– Now, let's: add the natural terms to each other. And finally, we'll isolate z and subtract 360⁰ by the number that's left.

145 + 24 + z = 360⁰

170 + z = 360⁰

z = 360⁰ - 170

z = 190⁰

So, the value of z, will be 190⁰

Answer:

sale price

Step-by-step explanation:

price of an item that is being offered at a lower price than usual

Answer:

172.8 m^2

Step-by-step explanation:

7.2/2 = 3.6

3.6*4.8 = 17.28

17.28*10 = 172.8

Answer:

The angle is acute. This type of angle must be between 0° and 90°, and Orla's estimate is not.

If the trigonometric expression is sin θ = -√2/2. Then the value of angle θ will be 5π/4, 7π/4, and 13π/4.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The trigonometric expression is given below.

sin θ = -√2/2

The expression can be written as

sin θ = -1/√2

Then the value of angle θ will be

θ = sin⁻¹ (-1/√2)

θ = 5π/4, 7π/4, and 13π/4.

Thus, the correct options are B, C, and E.

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Answer:

B,C,E

Step-by-step explanation:

Answer:

S₂₀₀ = 121800

Step-by-step explanation:

the sum to n term of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 12 and d = a₂ - a₁ = 18 - 12 = 6 , then

S₂₀₀ = [tex]\frac{200}{2}[/tex] [ (2 × 12) + (199 × 6) ]

       = 100(24 + 1194)

      = 100 ×1218

     = 121800

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

   Find the gradient of the line joining (-1,9) and (3,5)

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Use the slope formula:-

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Replace the letters with the numbers:-

[tex]\boxed{\frac{5-9}{3-(-1)}}[/tex]

[tex]\circ[/tex] On simplification,

[tex]\boxed{\frac{-4}{3+1}}[/tex]

[tex]\circ[/tex] On further simplification,

[tex]\boxed{\frac{-4}{4}}[/tex]

[tex]\circ\sf{SLOPE=-1}[/tex]

[tex]\rule{300}{1}[/tex]

Using the distance formula, each side of the park is 13 units long

The vertices of the park are given as:

(26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).

The length of each side is calculated using the following distance formula:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

Using any consecutive points, we have:

[tex]d = \sqrt{(13.5 - 1.5)^2 + (12 -7)^2} = 13[/tex]

Hence, each side of the park is 13 units long

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[tex]~~~~~~(2x+34)+(x+71) = 180\\\\\implies 3x + 105=180\\\\\implies 3x = 180-105\\\\\implies 3x = 75\\\\\implies x = \dfrac{75}3\\\\\implies x = 25[/tex]

Answer:

10

Step-by-step explanation:

48-20=28

28-18=10

that is how I see it at least

Answer:

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

from the survey:

32/80 - 0.4 love math

0.4*900

= 360

Answer:

The common difference is the difference between any two consecutive terms in an arithmetic sequence.

The formula which is used to find the common difference in AP is

d = an - an-1

Here the common difference is

d = a2 - a1 = 8 - 2 = 6

d = a3 - a2 = 14 - 8 = 6

d = a4 - a3 = 20 - 14 = 6

d = a5 - a4 = 26 - 20 = 6

2, 8, 14, 20, 26 … = 2, (2 + 6), (8 + 6), (14 + 6), (20+ 6) …

Therefore, the common difference is 6.

Step-by-step explanation:

Using it's concept, it is found that the inequality represents the domain of the exponential piece is:

d) [tex]x \leq -2[/tex].

The domain of a function is the set that contains all possible input values.

Researching this problem on the internet, we have that the function is divided as follows:

Hence, for the domain of the exponential piece, option d is correct.

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Answer:

c=__ and a=__

Step-by-step explanation:

767.50=1.25(c)+2.25(a).

366=c+a

normally from here, I would just guess the number of adults and children. It does take a while doing it that way, but maybe you know a quicker way. Hope this helps :)