7.1.1 use the results of section 3.7 to show that each member of isom (r2) is either a translation or a rotation. 7.1.2 why does an isometry map any circle to a circle? we took care to write the inverse of the isometry r1r2r3 as r3r2r1 because only this ordering of terms will always give the correct result. 7.1.3 give an example of two reflections r1 and r2 such that r1r2

The coordinates of the point 3/10 of the way from a to b is (-0.3, -6.3)

The given parameters are:

The position of the point is given as:

Location = 3/10

Express as ratio

m ; n = 3 : 10 - 3

This gives

m ; n = 3 : 7

The coordinates of the point are then calculated as:

Point = Location * (mx2 + nx1, my2 + ny1)

This gives

Point = 3/10 * (3 * 9 + 7 * -4, 3 * 7 + 7 *  -6)

Evaluate

Point = 3/10 * (-1, -21)

This gives

Point =  (-0.3, -6.3)

Hence, the coordinates of the point 3/10 of the way from a to b is (-0.3, -6.3)

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Complete question

find the coordinates of the point 3/10 of the way from a to b

the coordinates of b is (9,7)

the coordinates of a is (-4,-6)

Answer:

Step-by-step explanation:

Hello there. To solve this question, we'll have to remember some properties about inverse trigonometric functions.

Given the expression:

We want to express it as an algebraic function of x.

For this, imagine the following triangle:

Now, we find the missing leg of the triangle applying Pythagoras theorem:

Now, finding the sine and cosine of the angles alpha and beta, we get:

First, remember the sine of an angle is equal to the ratio between the opposite side to the angle and the hypotenuse of the triangle. The cosine of the same angle is equal to the ratio between the adjacent side to the angle and the hypotenuse of the triangle.

Therefore, we have:

This means that:

Now, the expression we had earlier turns into:

For this, we'll use the angle sum formula:

Which gives us:

Plugging the results we got earlier, this is simply:

As x > 0, because we're using it as a triangle side (but it could be negative considering inverse sine and cosine as functions), we get:

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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Answer:

Step-by-step explanation:

From the first sentence x (the number) is 2 more than another number (y). So, x+2=y. The sum of the squares of the two numbers is 42, meaning that \(\\ (x+2)^{2}\)+\(y^{2}\)=42. First, we square root the ENTIRE equation to get rid of the square. If you do one thing to one side, you have to do it to the other. After this, we have x+2+y=\(\sqrt{42}\). Now, we subtract 2 from the other side to isolate the variable. You can isolate either one but normally I go for x. Now we have x+y=\(\sqrt{42}\)+2. Now, we want to get y to the other side so we subtract it from the left side and the right side which gives us x=-y+\(\sqrt{42}\)+2. now we know what X is equal to. Now we plug in x for \(\\ (x+2)^{2}\)+\(y^{2}\)=42, which gives us          \((-y+\sqrt42}+2+2)^{2}\)+\(y^{2}\)=42. Now we only have one variable which is what we want. Next, we square root the entire thing to get rid of the squares, which gives us -y+\(\sqrt{42}\)+4+y=\(\sqrt{42}\). I got lost in my work. I must have done something wrong I cant find out. If anyone wants to pick up where I left off go ahead but there's a timer and I have one minute left. I cant finish the problem in a minute. I'm sorry and hopefully I lead you somewhere.

Answer:

9a² - 36

Step-by-step explanation:

Area of a parallelogram is A= b*h

Given in the picture

b= 3a +6

h = 3a -6

A = (3a+6) (3a-6)

- we can use that  (a+b)(a-b) = a²-b²

A = (3a)² - 6²

  = 3²a² - 6²

  = 9a² - 36

This question is of a topic called subset that is a part of set theory.

statement 1 is true. statement 2 is true. statement 3 is false, statement 4 is true.

I assume the questioner has the basic understanding of set theory and what subsets are.

Statement 1st "{1,2,3,4,5} ⊄ {1,2,4}" is true because here not every element of set {1,2,3,4,5} is an element of set {1,2,4}.

Statement 2nd "{11, 13, 15} ⊂ { 11, 12, 13, 14, 15, 16, ... }"  that is set {11, 13, 15} is a proper subset of set { 11, 12, 13, 14, 15, 16, ... } is true since every element of set {11, 13, 15} belongs to set { 11, 12, 13, 14, 15, 16, ... } also set

{11, 13, 15} is not equal to set  { 11, 12, 13, 14, 15, 16, ... }.

statement 3rd "∅ ⊈ {d, f, g, n}" is false since ∅ = null set is the subset of every set.

statement 4th "{21, 22, 23, 26, 29} ⊆ {21, 22, 23, 26, 29}" is true both sets have same elements therefore are subsets of each other and hence both are also equal to each other.

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Answer:

the value of m will be 20

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

(-3, -13)

(-1, -7)

(1, -1)

(3, 5)

(5, 11)

Step-by-step explanation:

Plug x into the equation y = 3x - 4 for each value of x to obtain the y value.

For example:

y = 3(3) - 4

y = 9 - 4

y = 5

Answer:

\((fog)(x) = f(g(x)) \\ = 7(4 - 2x) - 7 \\ = 28 - 14x - 7 \\ = 21 - 14x \\ = - 14x + 21\)

\((gof)(x) = g(f(x)) \\ = 4 - 2(7x - 7) \\ = 4 - 14x + 14 \\ = 18 - 14x \\ = - 14x + 18\)

I hope I helped you^_^

Answer:

The first equation of this system is y =2 x + 3.

The second equation of this system is y = 3x −1 .

The solution of the system is (4,11).

Step-by-step explanation:

PLATO correct

The first equation of this system is y = 2x + 3 while the second equation of this system is y = 3x - 1.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

For the first line, using the points (0, 3) and (2, 7):

\(y-3=\frac{7-3}{2-0}(x-0)\\ \\y=2x+3\)

For the second line, using the points (0, -1) and (2, 5):

\(y-(-1)=\frac{11-(-1)}{4-0}(x-0)\\ \\y=3x-1\)

The first equation of this system is y = 2x + 3 while the second equation of this system is y = 3x - 1.

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Answer:

Yes. The vertical line never touches the graph at more than one point at the same time.

Step-by-step explanation:

this is the plato and edmentum answer

(make sure this is the right question)

As the vertical line touches the graph of the equation y = 2x - 3 it is a function.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, An equation y = 2x - 3.

Now, If we draw a vertical line and it touches the graph at only one point

the equation is a function but if the vertical line touches the graph at more than two points the equation is not a function.

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The graph matches the description of Andre's distance as a function of time. Hence, the graph is accurate.

The graph given is a distance time graph which shows how a body moves through a certain distance during a particular interval of time. The peak distance reached is 20 yards. Turning back 5 yards is also depicted with a regression in the peak distance.

Also, the period where there was no change in the distance for 3 seconds was also showcased before walking back to a starting position denoted by the point along the origin.

Hence, the graph is correct.

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Answer:

Line ZL and line LZ.

Step-by-step explanation:

Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.

Brainliest please.

Answer:

Step-by-step explanation

Oh

The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.

The geometric shape of a square has 4 equal ends and four equal, right-angled angles (90 degrees). It is an unusual instance of a rectangle with equal sides. The symbol "" is frequently used to denote a square, which is a two-dimensional figure. A square's area is equal to the sum of its sides doubled, or s2, where s denotes the width of a side. The circumference of a square, or 4s, where s is the height of a side, is the total of the lengths among all four sides. Many real-world uses for squares can be found in the fields of mathematics, architecture, construction, and design.

given

The square office's area is:

\(C = 9 \times $87.41 = $786.69\)

A = s2 = 3 2 = 9 metres square

To completely replace the carpet, it would cost:

Cost per square meter equals C = A.

where a square meter costs $87.41. When we change the values, we obtain:

As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.

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Answer:

500 times

Step-by-step explanation:

Divide the thickness of a cat hair by the thickness of a human hair.

4.0 × 10^-1 / 8.0 × 10^-4 =

= 0.5 × 10^3

= 500

500 times

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Answer:

FRIEND?

Step-by-step explanation:

Answer:

Смотрите в объяснении.

Step-by-step explanation:

x=4

x=-2

x=-3

x=20

x=-400

Надеюсь, это помогло! :)

Answer:

16 ×6=6 7+6 5 y = 2 + 4 y( 4. 8)y =14

Answer:

Step-by-step explanation:

Regular price  = $ 83

Discount  = 95% of 83

               = 0.95 * 83

              = $ 78.85

Price after discount = 83 - 78.85

                                = $ 4.15

Answer:

$4.15

Step-by-step explanation:

Multiply 83 by .05 to get the new price of $4.15. Additionally, multiply 83 by .95 to get the amount taken off ($78.85).