A figure is contained completely in Quadrant III of the coordinate plane. After applying the composition Ro.-90° ry to the figure, in which quadrant does the image lie?​

Answer:

  23.20°, 71.57°, 85.24°

Step-by-step explanation:

The angle between two vectors can be found by making use of the definition of the dot product. The computed angle is the angle between the  vectors when they are placed tail-to-tail.

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vector definition

The second attachment shows the given points plotted as A, B, C in the order given. In the diagram, the vectors a, b, c are defined as BA, CB, AC, respectively. That is, the vector a is ...

  a = A -B = (-6, -9) -(2, 7) = (-6-2, -9-7) = (-8, -16)

The vectors are defined in counterclockwise order around the triangle, though that makes no difference to the calculation.

dot product definition

The definition of the dot product of vectors A and B is ...

  A·B = |A|×|B|×cos(θ) . . . . . where θ is the angle between the vectors

Solving for the angle, we find it to be ...

  [tex]\theta=\arccos\left(\dfrac{\vec{A}\cdot\vec{B}}{|\vec{A}|\,|\vec{B}|}\right)[/tex]

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Because of the way the vectors in this solution are defined, the angle between any given pair of vectors will be an exterior angle of the triangle. In order to find the measure of the interior angle, we must reverse one of the vectors. That is, the dot product used in our computation will be the opposite of the dot product of the vectors we have found.

The spreadsheet shown in the first attachment does the necessary computations.

As a check, the spreadsheet shows the sum of the angle values. (The rounded values add up to 180.01°.)

The interior angles of the triangle are 23.20°, 71.57°, 85.24°.

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Additional comment

Another way to find the interior angles from coordinates is to consider the slope of each side of the triangle as being the tangent of the angle it makes with the x-axis. The difference of these angles can be used to find the interior angles of the triangle. Less work is involved because there is no dot-product or magnitude computation.

Answer:

The Sierpinski triangle is also called the Sierpinski gasket.

Step-by-step explanation:

The Sierpinski triangle is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915.

Answer:

6.36 years (the .36 repeats), so rounded is 6.4.

Step-by-step explanation:

First, I'm going to convert all measurements to meters.

Since 1000 mm = 1 m, divide 44 by 1000.

44/1000 = 0.044 m

Since 100 cm = 1 m, divide 72 by 100.

72/100 = 0.72 m

Next, I'm going to setup an equation using y = mx + b.

b is the beginning amount which is 0.72.

m in the equation represents the rate which is 0.044.

y represents the total which is 1.

Plugin the numbers and solve for x.

1 = 0.044x + 0.72

1 - 0.72 = 0.044x + 0.72 - 0.72

0.28 = 0.044x

0.28/0.044 = 0.044x/0.044

6.36 = x

Answer: x=12

Step-by-step explanation:

Answer:

  x=1

Step-by-step explanation:

The equation can be simplified and solved using the rules of exponents and the usual inverse operations.

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Interpreted according to the Order of Operations, your equation is ...

  ((2^2)x)^3 = 64

  (4x)^3 = 64x^3 = 64 . . . . . . use (ab)^c = (a^c)(b^c)

  x^3 = 1 . . . . . . . . . . . . . . divide by 64

  x = ∛1 = 1

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Perhaps you want x in the exponent:

  (2^(2x))^3 = 64

  2^(6x) = 2^6 . . . . . . . . . use (a^b)^c = a^(bc)

  6x = 6 . . . . . . . . match exponents

  x = 1 . . . . . . divide by 6

_____

Additional comment

Folks are often not careful about identifying exponents. It is helpful if you write the exponent in a way that leaves no ambiguity.

That statistic is based on a pinterest quote, the actual statistic is closer to 8-10%

Answer:

is that the ixl

website ????????????????????????????????

Answer: x=-5, y=20

Step-by-step explanation:

Opposite sides of a parallelogram are congruent, so AB=CD.

[tex]x^{2}-15=-2x\\x^{2}+2x-15=0\\(x+5)(x-3)=0\\x=-5, 3[/tex]

But as distance must be positive, as CD=-2x, x must be negative, so x=-5.

Opposite angles of a parallelogram are congruent, so [tex]m\angle D=m\angle B[/tex].

[tex]4y+26=106\\4y=80\\y=20[/tex]

Answer:

y = - 5 or y = 9

Step-by-step explanation:

using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (- 1, y )

d = [tex]\sqrt{(-1-4)^2+(y-2)^2}[/tex]

   = [tex]\sqrt{(-5)^2+(y-2)^2}[/tex]

   = [tex]\sqrt{25+(y-2)^2}[/tex]

equating to [tex]\sqrt{74}[/tex] , that is

[tex]\sqrt{25+(y-2)^2}[/tex]  = [tex]\sqrt{74}[/tex] ( square both sides )

25 + (y - 2)² = 74 ( subtract 25 from both sides )

(y - 2)² = 49 ( take square root of both sides )

y - 2 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 2 to both sides )

y = 2 ± 7

Then

y = 2 + 7 = 9 or y = 2 - 7 = - 5

Solution:

[tex] - 18 \sqrt{10} [/tex]

[tex] = - 6 \sqrt{2} \: \: • \: \: 3 \sqrt{5} [/tex]

2. Apply radical rule : [tex] \sqrt{a} \sqrt{b} = \sqrt{ab} [/tex] , [tex]a \geqslant 0[/tex], [tex]b[/tex]

[tex] = 6 \sqrt{2 \: • \: 5} \: • \: 3[/tex]

=[tex]6 \sqrt{10} •3[/tex]

[tex] = - 18 \sqrt{10} [/tex]

Answer:

F(x) = (x+2)(-x+3)(x-2)^2. I think answer should be like this

Based on the interest rate and continuous compounding, the investment would double in value after 18.5 years.

We have given that,

investment to double at a 3 3/4% interest rate,

The future value using continuous compounding is:

= Amount x e ^ (rate x time)

Interest is

= 3.75%

2 = e ^ (0.0375 x time)

In2 = 0.0375 x time

t = In2 / 0.0375

t= 18.5 years

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Answer:

40

Step-by-step explanation:

32÷100= 0.32

0.32×125= 40

convert your percentage into a number first, so that you are working with normal numbers only, and then multiply that by your total.

The critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

The dataset is given as:

21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1

The sample mean is:

[tex]\bar x = 22.1[/tex]

The significance level is

α = 0.010

Start by calculating the degrees of freedom using:

df = n - 1

Where n represents the sample size (n = 7)

So, we have:

df = 7 - 1

df = 6

Using the table for t critical values for a two-tailed test, we have:

Critical value = ±3.7074

Hence, the critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

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Answer:

[tex]m\angle B = 28^{\circ}[/tex]

Step-by-step explanation:

All angles in a triangle must add up to [tex]180^{\circ}[/tex]

We can solve for [tex]\angle B[/tex] using this knowledge

[tex]\angle B + 40 + 112 = 180\\\angle B + 152 = 180\\\boxed{\angle B = 28}[/tex]

That is the answer

- Kan Academy Advance

The new dimension of the rectangle are as follows;

The new dimension of the rectangle can be found as follows;

The sides of a square are equal.

Therefore,

let the side of the square = x

Hence,

length = x + 3

width = x + 1

area of rectangle = lw

where

Therefore,

24 = (x + 3)(x + 1)

24 = x² + x + 3x + 3

24 = x² + 4x + 3

x² + 4x + 3 - 24

x² + 4x - 21 = 0

(x - 3)(x + 7)

Therefore,

x = 3 or -7

It can't be negative. Hence, x = 3 ft

Therefore, the new dimension of the rectangle are as follows;

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Answer:

(18,27) , because the rate of change of the function is 4/3

Step-by-step explanation:

Answer:

266[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

if a 45 minute workout is 1000 calories, at the same rate, a 12 minute workout would be 266 calories and 2 thirds. [tex]\frac{12}{45}[/tex] x 1000 = 266[tex]\frac{2}{3}[/tex]

The options that are true as a result of doubling the rectangle dimensions are;

p → q represents the original conditional statement.

p → ~q represents the contrapositive of the original conditional statement.

We are told that;

Doubling the dimensions of a rectangle increases the area by a factor of 4.

Now, p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.

Thus, using conditional statements notation, we can say that;

p → q represents the original conditional statement.

p → ~q represents the contrapositive of the original conditional statement.

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Due to length restrictions, we kindly invite to check the explanation of this question to understand the derivation of the polynomic expressions.

Cubic functions are polynomials of grade 3. In this case, we have pairs of cubic functions of the following form:

y = (x - h)³ + k       (1)

y = - (x - h)³ + k     (2)

a) Where (h, k) are the coordinates of the vertex of each cubic function. There is a translation of (x, y) = (3, 1) between each two consecutive pairs of cubic functions. Hence, we have the following fourteen cubic functions:

b) Another family of functions with a similar pattern is shown below:

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Answer:

-34+x/4

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

Since you did not specify, we will assume that your equation is equal to 0.
1. (-34+2x)/(-8) = 0     (multiply both sides by -8)
2. (-34+2x) = 0  (add 34 to both sides)
3. 2x = 34 (divide both sides by 2)
4. x = 17

Answer:

SORRY I DONOT KNOW THE ANSWER

Step-by-step explanation:

i am sorry i do not know the amswer

Answer:

  E.  18.6

Step-by-step explanation:

The diagonals of a rhombus bisect each other at right angles. The means all of the triangles shown are right triangles, and the two marked angles are complementary.

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Complementary angles total 90°.

  (x°) +(4x -3)° = 90° . . . . . the marked angles are complementary

  5x = 93 . . . . . . . . . . . .  divide by °, add 3

  x = 93/5 = 18.6 . . . . . divide by the coefficient of x

The value of x is 18.6.

u₁₂ represents the amount of loan remaining after 12 years

The function is given as:

u₀ = 8000

[tex]u_n = u_{n-1}(1 + 0.054) - 500[/tex]

Given that the subscript n in [tex]u_n[/tex] represents number of years and [tex]u_n[/tex] represents the amount left to be paid after n years.

We can conclude that:

u₁₂ represents the amount of loan remaining after 12 years

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The given equation is equivalent to Option D .

The mission option is

A. x+10= x+10

B. x+9 =x² + 20x + 100

C. x² +81 = x² + 100

D. x² + 81 = x² +20x + 100

An equation is a mathematical statement formed when two algebraic expression is equated by an equal sign .

An equation is given in the question

[tex]\rm \sqrt{x^2 + 81} = x +10[/tex]

[tex]\rm {x^2 + 9^2} = (x +10)^2[/tex]

[tex]\rm {x^2 + 81} = x^2 +20x + 100[/tex]

Therefore the given equation is equivalent to Option D .

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Both the first and second statements are true and therefore Option D is the correct answer .

A function can be defined as the equation that identifies relation between a dependent variable and an independent variable.

A function always has a defined range and domain.

In the following statements

I. If f '(c) = 0, then f has a local maximum or minimum at x = c.

f'(c) = 0

It means that the slope of f(x) = 0 at x = c

If f has a local maximum or minimum at x = c  It is a True statement

II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].

If f'(x) = 0 on (a, b),

then f is neither increasing nor decreasing

and therefore is constant on [a, b]

So it is a True statement.

III. The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [−1, 1].

No the theorem cannot be applied as, f is neither continuous nor differentiable at x = 0

It is a False Statement.

Therefore Option D is the correct answer.

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A. The number of hours of training that you can purchase with a $3,000 training budget at $40 per employee per hour and a one-time $200 fee is 70-employee-training-hours.

B. Each employee will get 7 hours of training, assuming your organization has 10 employees.

The training cost of employees varies from one organization to another.

The training cost also depends on the training provider and the number of hours of training being offered.

Training budget = $3,000

One-time fee = $200

Remainder after the one-time fee = $2,800 ($3,000 - $200)

Training costs per employer per hour = $40

Hours of training to purchase = 70 ($2,800/$40)

Thus, an organization with 10 employees can obtain 70 hours of training with the training budget.

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Answer:

not equivalent

Step-by-step explanation:

solve for x

4-5x=24

-5x=20

x = - 4

5x=20

x = 4

no they are not equivalent

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2812\\ P=\textit{original amount deposited}\dotfill & \$1900\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2812=1900[1+(0.08)(t)]\implies \cfrac{2812}{1900}=1+0.08t\implies \cfrac{37}{25}=1+0.08t \\\\\\ \cfrac{37}{25}-1=0.08t\implies \cfrac{12}{25}=0.08t\implies \cfrac{ ~~ \frac{12}{25} ~~ }{0.08}=t\implies 6=t[/tex]

Answer:  Check out the screenshot below for the answers

==========================================================

Explanation:

For each column, we divide the values by the sum of each column.

The sum of the first column is 6+8 = 14, and the sum of the second column is 7+3 = 10.

Column 1:

Those values are approximate to two decimal places.

Column 2:

Those values are exact.

The values in bold are then filled in the table as you see below.

A result like 0.43 means that 43% of those who play a sport also play an instrument. The other values are interpreted in a similar fashion.

200 is the median (50%) of the data represented in the box plot. The fraction of the books has 200 or fewer pages is: 1/2.

In a box plot, the median is indicated as the value marked by the vertical line that divides the rectangular box of the box plot.

The median is the middle of the data and represents the 50th percentile. That is 1/2 the data.

In the box plot given, 200 pages is the median. Therefore, the fraction of the books that have 200 or fewer pages is: 1/2.

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