Need help finding the one complete period of a non transformed contangent function

The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

The given coordinate are (8, -1) and (2, -5).

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

The standard form of an equation is Ax + By = C.

The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].

Multiply each term by 3 of the equation.

[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]

⇒3y + 3 = 2x - 16

Subtract 2x from both sides of a equation.

That is, -2x + 3y + 3 = - 16

Subtract 3 from both sides of a equation.

That is, -2x + 3y = - 19

Multiply each term by - 1 from both sides of an equation.

That is, 2x - 3y = 19

Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

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Answer:

11 and 22

Step-by-step explanation:

let one positive integer be n then the other is 2n , so

n × 2n = 242

2n² = 242 ( divide both sides by 2 )

n² = 121 ( take square root of both sides )

n = [tex]\sqrt{121}[/tex] = 11

2n = 2 × 11 = 22

the 2 integers are 11 and 22

Answer:

Show the process

Answer:

Option B is correct

Answer:

B there is enough raspberries to make 4 pie they can 6 pies if they 2 more of raspberries

The value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2

(1) y/3 + 6 = -3/2

Multiply through by 3

y + 18 = -9/2

Subtract 18 from both sides

y = -18 - 9/2

Take LCM

y = (-18 * 2 - 9)/2

Evaluate

y = -45/2

(2) -2r/3 - 3 = 3

Multiply through by 3

-2r - 9 = 9

Add 9 to both sides

-2r = 18

Divide by 2

r = -9

(3) 2/3 - 2x = x

Multiply through by 3

2 - 6x = 3x

Add 6x to both sides

2 = 9x

Divide by 9

x = 2/9

(4) 7x/2 + -5/2 = 9/2

Multiply through by 2

7x - 5 = 9

Add 5 to both sides

7x = 14

Divide by 7

x = 2

Hence, the value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2

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53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]

54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]

55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]

56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32

Sin3A=Cos3A

Cos(90-3A)=Cos3A

90-3A=3A

90=3A+3A

90=6A

90/6=A

^•^

The answer is A=15

[tex]4(a + 3) = - 32 \\ 4a + 12 = - 32 \\ 4a = - 32 - 12 \\ 4a = - 44 \\ a = - 11[/tex]

Hope it helps

Please give brainliest

Step-by-step explanation:

4(a+3)=-32

4(a+3)/4=-32/4

(a+3)=-8

a+3-3=-8-3

a=-11

Answer:

y = x/2 -3

Step-by-step explanation:

x - 2y = 6

Slope intercept form is y = mx+b  where m is the slope and b is the y intercept

We need to solve for y

Subtract x from each side

x-2y-x = -x+6

-2y = -x+6

Divide each side by -2

-2y/-2 = -x/-2 +6/-2

y = x/2 -3

The slope intercept form is

y = x/2 -3

Answer: slope intercept form is

y = x/2 -3

Step-by-step explanation:

hope this helps ; )

Triangle ABC is similar to triangle DEC, ∠B ≅ ∠E and 3DE = 2BC

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Right triangle ABC is reflected over AC, then dilated by a scale factor of 2/3 to form triangle DEC, hence:

Triangle ABC is similar to triangle DEC, corresponding angles are congruent (∠B ≅ ∠E) and DE = (2/3)BC i.e. 3DE = 2BC

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Step-by-step explanation:

tan x = sin x / cos x

[tex]tan \: x \: = \frac{ \frac{7}{15} }{ \frac{4 \sqrt{11} }{15} } = \frac{7}{4 \sqrt{11} } [/tex]

Answer: C

Step-by-step explanation:

The inverse of a function maps the domain onto the range.

Step-by-step explanation:

Line L → 2x - 3y = 6

Where a = 2 and b = -3

• So, we can use this formula to find the gradient of Line L.

m = -a/b

m = -2/-3

m = 2/3 IS THE ANSWER

Answer:

gradient = 2/3

Step-by-step explanation:

Here is another way....manipulate the equation to y = mx+ b form

  where m = slope ( gradient)

2x - 3y = 6          add 3 y to both sides

6 + 3y = 2x         subtract 6 from both sides

3y = 2x - 6          divide by 3

y = 2/3 x - 2        gradient = 2/3

The box plot that represents the data is the first option.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Minimum value = 30

Maximum value = 57

1st quartile = 1/4 (n + 1)

1/4 x 10 = 2.5th term = 35

Third quartile = 3/4 x (n + 1 )

3/4 x 10 = 7.5 term = 53

Median = 46

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Answer:

center = (-5, -7)

radius = 21

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]

Comparing the given equation with the standard equation of a circle:

Hence, the coordinates of centre is (-5,-2).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The given equation  of circle,

(x+5)² + (y+7)² = 21²

We know that,

Equation of a circle is:

(x-a)² + (y-b)² = r²

where:

(a, b) is the center

And r is the radius

Comparing with the given equation we have,

center = (-5,-7)

And radius = 21 units

Thus,

Coordinates =  (-5,-7).

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Answer:

the answer is $62

Step-by-step explanation:

if you subtract 110 by 98 you get 12 and the same for the rest so if you subtract 74 by 12 you get 62

Hope that help :)

Answer:

62

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = x² + 7x - 5 ............ (1)

2x - y = - 9 ................ (2)

(1) ------> (2)

2x - ( x² + 7x - 5 ) = - 9

- x² - 5x + 14 = 0 ........ (3)

- 1 × (3)

x² + 5x - 14 = 0

( x + 7 )( x - 2 ) = 0

[tex]x_{1}[/tex] = - 7 and [tex]x_{2}[/tex] = 2

2( - 7) - [tex]y_{1}[/tex] = - 9 ⇒ [tex]y_{1}[/tex] = - 5

2(2) - [tex]y_{2}[/tex] = - 9 ⇒ [tex]y_{2}[/tex] = 13

The solutions of system are

( - 7, - 5 ) and ( 2, 13 )

The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid GHJK that was rotated 180° about the origin.

The rule for 180-degree rotation about the origin:

(x, y) → (-x , -y)

From the graph:

Coordinate of H' is (-3, -2)

(-3, -2) → (3, 2)

Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

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Factor the rational function,

.

.

.

.

Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.

.

.

So our domain can be all reals except 1.

Range: First factor out the x-1. We will be left with

.

Since 1 isn't in the domain, plug in 1 to find the what won't be in the range

.

So 7 isn't in the range,

End Behavior:

Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.

Answer:

8

Step-by-step explanation:

To one decimal place:

[tex]2 \sqrt{10} = 6.3[/tex]

[tex]10 \sqrt{2} = 14.1[/tex]

So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.

Cooper left his dinner server a 19% tip.

To find the percent tip, we need to first subtract the cost of the meal from the total amount paid, which will give us the tip amount:

Tip amount = Total amount paid - Cost of the meal

Tip amount = $33.32 - $28

Tip amount = $5.32

Now we can calculate the percentage of the tip by dividing the tip amount by the cost of the meal and multiplying by 100:

Percent tip = (Tip amount / Cost of the meal) x 100

Percent tip = ($5.32 / $28) x 100

Percent tip = 0.19 x 100

Percent tip = 19%

Therefore, Cooper gave a 19% tip on his dinner.

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Answer:

-6

Step-by-step explanation:

Well you just plug in the value 3 for x. This will give you the following equation: [tex]\frac{4(3+3)(3+1)}{(3+5)(3-5)}[/tex] which simplifies to [tex]\frac{4(6)(4)}{(8)(-2)}[/tex] which further simplifies to [tex]-\frac{96}{16}[/tex] which can further be simplified by dividing the two numbers and that results in -6

Answer:

A

Step-by-step explanation:

it really only means to replace every x by 3 and then simply calculate.

4(3+3)(3+1) / ((3+5)(3-5)) =

= 4×6×4 / (8×-2) = 96/-16 = -6

The common ratio of the given Geometric progression is one-half.

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is the form a,ar,ar^2, ...

Given that the sequence begins with 12, i.e a = 12

and also given that the sequence are in Geometric Progression.

By dividing the preceeding number by 2, we get the successive number

Then the Geometric sequence is 12, 12×1/2, 12×1/4, 12×1/8, 12×1/16 ...

= 12, 6, 3, 3/2, 3/4, ...

Common ratio = Second term / First term

= 6/12

=1/2

Therefore, the common ratio of the given geometric progression is one-half.

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Answer:

its a

Step-by-step explanation:

Answer:

Step-by-step explanation:

m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.

m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.

m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.

The three right options are:

m∠5 ₊ m∠6 = 180° which represents a linear pair.

∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.

m∠2  m∠3  m∠5 = 180° as the sum-triangle

sum-triangleproperty.

Given,

the interior angles of the triangle are 2,3,5

the exterior angle at ∠2 is ∠1.

the exterior angle at ∠3 is ∠4.

the exterior angle at ∠5 is ∠6.

Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.

Apply the exterior angle property of a triangle.

The sum of the opposing internal angles determines the outer angle of a triangle.

For exterior ∠1 we get

∠1 = ∠5 ₊ ∠3

Similarly, for exterior ∠4 we get

∠4 = ∠5 ₊ ∠2

Then for exterior ∠6 we get

∠6 = ∠2 ₊ ∠3

∴ through the exterior angle property we get the correct option as

m∠6 = m∠2 ₊ m∠3

Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°

∴ m∠2 ₊ m∠3 ₊ m∠5 = 180°

We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,

∴ m∠5 ₊ m∠6 = 180°

Hence we get the statements which match the diagram are:

m∠5 ₊ m∠6 = 180°

m∠2 ₊ m∠3 ₊ m∠5 = 180°

m∠6 = m∠2 ₊ m∠3

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Median: 6

Range: 9

Mode: 7, appeared 3 times