Identify the image of a triangle with vertices L(−3,4), M(−2,1), and N(0,2) under a dilation with a scale factor of −3 centered at the origin. HELP ASAP!!

width = w

length = 2w - 5

Perimeter = 26

The formula for perimeter is:

P = l + l + w + w

Plug in corresponding values into this equation...

26 = (2w - 5) + (2w - 5) + w + w

Now you must solve for w

26 = 2w - 5 + 2w - 5 + w + w

Combine like terms

26 = 2w - 5 + 2w - 5 + w + w

26 = 6w - 5 - 5

26 = 6w - 10

Bring -10 to the other side by adding it to both sides

26 + 10 = 6w + (-10 + 10)

36 = 6w + 0

36 = 6w

Isolate w by dividing 6 to both sides

36/6 = 6w/6

6 = w

Width is 6 cm

To find length plug 6 in for w in the equation 2w - 5

2(6) - 5

12 - 5

7

Length is 7 cm

Hope this helped!

~Just a girl in love with Shawn Mendes

[tex]\bf \textit{volume of a cube}\\ V=s^3~~ \begin{cases} s=&side's\\ &length\\ \cline{1-2} V=&64 \end{cases}\implies 64=s^3\implies \sqrt[3]{64}=s\implies \boxed{4=s} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{scaling all sides by a factor of 5}}{V=s^3\implies V=(4\cdot 5)^3}\implies V=20^3\implies V=8000[/tex]

Answer:

8,000

Step-by-step explanation:

When the sides of the cube are scaled by a factor of k, the volume increases by a factor of k3. Here, the new volume is 64 cubic meters × 53 = 8,000 cubic meters.

Answer:

[tex]\large\boxed{LCM(121x^2-9y^2,\ 11x^2+3xy)=121x^3-9xy^2}[/tex]

Step-by-step explanation:

[tex]121x^2-9y^2=11^2x^2-3^2y^2=(11x)^2-(3y)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(11x-3y)\underline{(11x+3y)}\\\\11x^2+3yx=x\underline{(11x+3y)}\\\\LCM(121x^2-8y^2,\ 11x^2+3yx)=\underline{(11x+3y)}(11x-3y)(x)\\\\=(121x^2-9y^2)(x)=121x^3-9xy^2[/tex]

Answer:

  $24,153

Step-by-step explanation:

Jan's monthly income from commissions is ...

  4.15% × $48,500 = $2012.75

Multiplied by 12 months in the year, that is ...

  $2012.75 × 12 = $24,153 . . . . gross annual income from commissions

Answer:

A. bar graphs

C. pie charts or circle graphs

Step-by-step explanation:

The most suitable graphs for displaying categorical data are bar graphs and pie charts, as bar graphs are used to compare categories or show changes over time, while pie charts are ideal for displaying parts of a whole.

The most appropriate types of graphs for displaying categorical data are bar graphs and pie charts or circle graphs. In a bar graph, the length of each bar represents the number or percent of individuals in each category. Bars in a bar graph can be vertical or horizontal and are used to compare categories or show changes over time. Pie charts show categories of data as wedges in a circle, with each wedge representing a percentage of the whole, making it ideal for showing parts of a whole.

A stem-and-leaf plot, on the other hand, is useful for showing all data values within a class and mainly represents quantitative data rather than categorical data. Histograms, while similar to bar graphs, are used for displaying the distribution of quantitative, not categorical, data. Therefore, for categorical data, bar graphs and pie charts are most suitable.

Answer:

  A. 8

Step-by-step explanation:

The length of the remaining side will be between the sum and difference of the given sides:

  5 + 13 = 18 . . . . upper limit of 3rd side length

  13 - 5 = 8 . . . . . lower limit of 3rd side length

The only answer choice in this range is 8.

_____

Comment on question and answers

Please note that this would not be an allowed answer for some triangle inequality questions. Some authors insist that the sum of the two shortest sides be greater than the longest side, so the triangle has non-zero area. Other authors allow the sum to be greater than or equal to the longest side. The only viable answer choice here is one that makes use of the "or equal to" condition. The 5-8-13 triangle will look like a line segment of length 13. It will have no area.

Answer:

THE CORRECT ANSWER IS 10, PLEASE DO NOT CHOOSE 8, IT WAS WRONG FOR ME SO THE CORRECT ANSWER IS 10

Step-by-step explanation:

To solve this you must plug in 9 for x and -4 for y in the equation

X + 3y like so...

9 + 3(-4)

In accordance to the rules of PEMDAS you must multiply first, which will get you...

9 + (-12)

Add these two together and you get:

-3

Hope this helped

~Just a girl in love with Shawn Mendes

Answer:

-2

Step-by-step explanation:

Answer:

All are discrete sets

Step-by-step explanation:

Any set for which you can list the elements is a discrete set, even if that list has "..." (continues in like fashion). Sets that are not discrete are those that are continuous, such as "all real numbers" or "the numbers between 0 and 1".

The discrete sets from the options given are A. {1,3,5,7,...}, C. {5,8}, and E. {-3,6,9,17,24}.

A discrete set is one where the elements are separate and distinct, often meaning each member can be counted and there is no continuous spectrum of values between any two elements.

A. {1,3,5,7,...} - This set represents odd numbers which is discrete because we can identify each individual element.

B. (-10,20) - This is not a set but an interval representing a continuous range of real numbers; therefore, it is not discrete.

C. {5,8} - This set has only two elements, each distinct and countable, making it discrete.

D. (1,99) - Similar to B, this is an interval showing a continuous range of real numbers, and thus not discrete.

E. {-3,6,9,17,24} - This set includes separate, identifiable numbers and is therefore discrete.

Answer:

  B. It is a one-to-one function.

Step-by-step explanation:

Each value of the domain maps to a unique value of the range. It is a one-to-one function.

Answer:

B. It is a one to one function.

Step-by-step explanation:

It is a function, if we trace the vertical line [tex]x=a[/tex] it intersects exactly one point of the graph (in the case that [tex]a\neq0[/tex].Moreover, the line [tex]x=0[/tex] doesn't intersects the graph, hence the given graph is the graph of a function with domain [tex]\mathbb{R}-\{0\}[/tex]. On the other hand, a function f(x) is one to one, if whenever f(x)=f(y) it holds that x=y, in terms of the graph of a function this mean that whenever we trace a vertical line [tex]y=b[/tex] it intersects exactly one point, which is exactly the case fo our given graph. Threfore, it is the graph of a one to one function

Answer:

The answer is C.

Step-By-Step Explanation:

Once you combine the like terms of 5x^2-8x-7 and 2x^2-3x-7 you get 7^2-11x-5. Then you need to subtract x^2-9x-4 from 7^2-11-5x. Then you will get the answer which is C.

Answer:

  C.  6x² -2x -1

Step-by-step explanation:

You want the sum of ...

  (5x² -8x +2) + (2x² -3x -7) - (x² -9x -4)

Eliminating parentheses gives ...

  5x² -8x +2 +2x² -3x -7 -x² +9x +4

Grouping like terms, we have ...

  (5x² +2x² -x²) + (-8x -3x +9x) + (2 -7 +4)

Then combining like terms gives ...

  6x² -2x -1 . . . . matches choice C

Answer:

  1. the range of f^-1(x) is {10, 20, 30}.

  2. the graph of f^-1(x) will include the point (0, 3)

  3. n = 8

Step-by-step explanation:

1. The domain of a function is the range of its inverse, and vice versa. The range of f^-1(x) is {10, 20, 30}.

__

2. See above. The domain and range are swapped between a function and its inverse. That means function point (3, 0) will correspond to inverse function point (0, 3).

__

3. The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

You are given a1 = 2, a12 = 211, so ...

  211 = 2 + d(12 -1)

  209/11 = d = 19 . . . . . solve the above equation for the common difference

Now, we can use the same equation to find n for an = 135.

  135 = 2 + 19(n -1)

  133/19 = n -1 . . . . . . . subtract 2, divide by 19

  7 +1 = n = 8 . . . . . . . . add 1

135 is the 8th term of the sequence.

1. Filling in the table is just a matter of plugging in the given [tex]x,y[/tex] values into the ODE [tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{xy}3[/tex]:

[tex]\begin{array}{c|ccccccccc}x&-1&-1&-1&0&0&0&1&1&1\\ y&1&2&3&1&2&3&1&2&3\\\frac{\mathrm dy}{\mathrm dx}&-\frac13&-\frac23&-1&0&0&0&\frac13&\frac23&1\end{array}[/tex]

2. I've attached what the slope field should look like. Basically, sketch a line of slope equal to the value of [tex]\dfrac{\mathrm dy}{\mathrm dx}[/tex] at the labeled point (these values are listed in the table).

3. This ODE is separable. We have

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{xy}3\implies\dfrac{\mathrm dy}y=\dfrac x3\,\mathrm dx[/tex]

Integrating both sides gives

[tex]\ln|y|=\dfrac{x^2}6+C\implies y=e^{x^2/6+C}=Ce^{x^2/6}[/tex]

With the initial condition [tex]f(0)=4[/tex], we take [tex]x=0[/tex] and [tex]y=4[/tex] to solve for [tex]C[/tex]:

[tex]4=Ce^0\implies C=4[/tex]

Then the particular solution is

[tex]\boxed{y=4e^{x^2/6}}[/tex]

4. First, solve the ODE (also separable):

[tex]\dfrac{\mathrm dT}{\mathrm dt}=k(T-38)\implies\dfrac{\mathrm dT}{T-38}=k\,\mathrm dt[/tex]

Integrating both sides gives

[tex]\ln|T-38|=kt+C\implies T=38+Ce^{kt}[/tex]

Given that [tex]T(0)=75[/tex], we can solve for [tex]C[/tex]:

[tex]75=38+C\implies C=37[/tex]

Then use the other condition, [tex]T(30)=60[/tex], to solve for [tex]k[/tex]:

[tex]60=38+37e^{30k}\implies k=\dfrac1{30}\ln\dfrac{22}{37}[/tex]

Then the particular solution is

[tex]T(t)=38+37e^{\left(\frac1{30}\ln\frac{22}{37}\right)t}[/tex]

Now, you want to know the temperature after an additional 30 minutes, i.e. 60 minutes after having placed the lemonade in the fridge. According to the particular solution, We have

[tex]T(60)=38+37e^{2\ln\frac{22}{37}}\approx\boxed{51^\circ}[/tex]

5. You want to find [tex]t[/tex] such that [tex]T(t)=55[/tex]:

[tex]55=38+37e^{\left(\frac1{30}\ln\frac{22}{37}\right)t}\implies\dfrac{17}{37}=e^{\left(\frac1{30}\ln\frac{22}{37}\right)t}[/tex]

[tex]\implies t=\dfrac{30\ln\frac{17}{37}}{\ln\frac{22}{37}}\approx\boxed{45\,\mathrm{min}}[/tex]

Answer: Y = 4x - 14

Step-by-step explanation:

See paper attached. (:

Answer:

[tex]\large\boxed{a.\ y=24}[/tex]

Step-by-step explanation:

[tex]\dfrac{y-9}{5}=3\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{y-9}{5\!\!\!\!\diagup_1}=5\cdot3\\\\y-9=15\qquad\text{add 9 to both sides}\\\\y-9+9=15+9\\\\y=24[/tex]

Answer:

Explanation:

1) The two parallel sides of different legths [tex]1\frac{3}{4}[/tex] and [tex]1\frac{1}{4}[/tex] constitute the bases of a trapezoid.

2) The two equal anglesare the base angles of the trapezoid, and mean that it is an isosceles trapezoid.

An isosceles trapezoid is truncated isosceles triangle.

The definition of trapezoid is a quadrilateral with at least two parallel sides.

The drawing is attached: only the green lines represent the figure, the dotted lines just show how this is derived from an isosceles triangle.

Answer:

trapezoid

Step-by-step explanation:

Answer:

The work shown in the simplification below is incorrect.

Step-by-step explanation:

To start; we have to know  what csc(t) and sec(t) is.

csc(t) = 1/sin(t)      and    sec(t)= 1/cos(t)

So in the above simplification it was all mixed up, csc(t) was substituted with 1/cos(t) instead of 1/sin(t) and sec(t) was substituted with 1/sin(t) instead of 1/cos(t).

So, we are going to solve it the right way;

csc(t) sec(t) = [tex]\frac{1}{sin(t)}[/tex]   ÷   [tex]\frac{1}{cos(t)}[/tex]

                   =  [tex]\frac{1}{sin(t)}[/tex]   ×   [tex]\frac{cos(t)}{1}[/tex]

                    =[tex]\frac{cos(t)}{sin(t)}[/tex]

                    = cot(t)

Therefore csc(t) sec(t) = cot(t)   and not tan(t).

The simplification shown is not correct because the steps used are incorrect and the resulting expression is not equivalent to the original. The correct simplification is csc(t) sec(t) = 1/(sin(t) * cos(t)).

The simplification shown is not correct. Let's break it down step by step:

To simplify the expression correctly, we can use the reciprocal identities: csc(t) = 1/sin(t) and sec(t) = 1/cos(t). When multiplying these together, we get:

csc(t) * sec(t) = (1/sin(t)) * (1/cos(t)) = 1/(sin(t) * cos(t)).

So, the correct simplification is csc(t) sec(t) = 1/(sin(t) * cos(t)).

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Answer:

it doesnt say the prices on here

Step-by-step explanation:

The answer is:

There will be necessary 13 ounces of salad dressing.

Why?

Since we already know that there will be needed 0.56 ounces of salad dressing per cup, and the recipe calls 2.1 cups of lettuce per person, we need to calculate the total ounces of salad dressing per each person, and then, calculate it for 11 persons.

So, calculating we have:

[tex]SaladDressingPerPerson=Cups*SaladDressing=2.1*0.56oz\\\\SaladDressingPerPerson=1.176oz[/tex]

Therefore, we know that there will be needed 1.176 ounces of salad dressing per person.

Then, calculating the ounces of dressing for 11 dinner guests, we have:

[tex]TotalOunces=SaladDressingPerPerson*NumberOfPersons\\\\TotalOunces=1.176ounces*11=12.94ounces=13ounces[/tex]

Hence, we have that there will be necessary 13 ounces of salad dressing.

Have a nice day!

Answer:

the answer is D

Step-by-step explanation:

Answer:

  [tex]-4r^3-3r^2+2rs-5[/tex]

Step-by-step explanation:

The terms have powers of r that are 2, 0, 1, and 3 (in the order shown here). You want to rearrange those terms so the powers have order 3, 2, 1, 0. The above answer shows that arrangement.

Ordering a polynomial in descending powers of r involves arranging the terms from the highest to the lowest exponent of r. When squaring exponentials, square the digit and double the exponent. For large r compared to d, d can be disregarded.

Ordering a polynomial in descending powers of r involves organizing the terms from highest to lowest exponent of the variable r. For example, for a polynomial of r as 6r^4 - 2r + 7r^2 - 3, we would arrange it as 6r^4 + 7r^2 - 2r - 3. Note that the polynomial starts with the term with the highest power of r (r^4), followed by the term with the next highest power (r^2). The process continues down to the term with the lowest power of r (r), and lastly, the constant term (-3). Remember to retain the corresponding coefficients while reordering terms.

When dealing with terms involving the squaring of exponentials, remember to square the digit as usual and double the exponent. For instance, (r^3)^2 would be r^6.

Also, comparisons of terms such as r » d (meaning r is much larger than d), we disregard d as its contribution to the final polynomial will be negligible.

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Answer:

  4√41 ≈ 25.61 feet

Step-by-step explanation:

The shortest route is the one that crosses the longest edge between room surfaces. In this case, that is the 16-foot edge between the floor and wall opposite the amplifier, or the 16-foot edge between the ceiling and the wall adjacent to the amplifier.

The length of the required wire is ...

  √((8+12)² +16²) = √656 = 4√41 ≈ 25.61 . . . feet

Answer:

√((8+12)² +16²) = √656 = 4√41 ≈ 25.61 feet

Step-by-step explanation:

Answer:

A  

But it needs explanation.

Step-by-step explanation:

The first one hides the fact, but it is indeed the answer.

6x + 12x = 90 degrees is the way the equation should actually be set up.

A does that by adding 90 to both sides to start with.

6x + 12x + 90 = 90 + 90

The reason it does this is to show that the three angles (6x   12x and 90 make up the entire straight angle shown in the diagram.

The answer is going to be the same.

18x = 90                      Combine like terms on the left

18x /18 = 90 / 18          Divide by 18

x = 5

Answer:

A

Step-by-step explanation:

The 3 given angles form a straight angle and sum to 180°, hence

6x + 12x + 90 = 180 ← is the required equation

Answer:

The perimeter of triangle is [tex]P=(\sqrt{10}+3\sqrt{2})\ units[/tex]

Step-by-step explanation:

Let

[tex]A(1.4),B(2,7),C(0,5)[/tex]

we know that

The perimeter of the triangle is equal to

[tex]P=AB+BC+AC[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance AB

[tex]A(1.4),B(2,7)[/tex]

substitute the values

[tex]AB=\sqrt{(7-4)^{2}+(2-1)^{2}}[/tex]

[tex]AB=\sqrt{(3)^{2}+(1)^{2}}[/tex]

[tex]AB=\sqrt{10}\ units[/tex]

step 2

Find the distance BC

[tex]B(2,7),C(0,5)[/tex]

substitute the values

[tex]BC=\sqrt{(5-7)^{2}+(0-2)^{2}}[/tex]

[tex]BC=\sqrt{(-2)^{2}+(-2)^{2}}[/tex]

[tex]BC=\sqrt{8}\ units[/tex]

[tex]BC=2\sqrt{2}\ units[/tex]

step 3

Find the distance AC

[tex]A(1.4),C(0,5)[/tex]

substitute the values

[tex]AC=\sqrt{(5-4)^{2}+(0-1)^{2}}[/tex]

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

[tex]AC=\sqrt{2}\ units[/tex]

step 4

Find the perimeter

[tex]P=AB+BC+AC[/tex]

[tex]P=\sqrt{10}+2\sqrt{2}+\sqrt{2}[/tex]

[tex]P=(\sqrt{10}+3\sqrt{2})\ units[/tex]

Answer:

  D.  $248.08

Step-by-step explanation:

Your question does not involve any taxes, so we'll compute the lease payment based on car value. We presume the Down Payment, Security Deposit, and Acquisition Fee are paid at the time the lease is signed, so are not part of the financing.

Then we have ...

  lease payment = depreciation fee + financing fee

where these fees are calculated from ...

  depreciation fee = ((net capitalized cost) - (residual value))/(months in lease)

and ...

  financing fee = ((net capitalized cost) + (residual value))×(lease factor)

___

Using the given numbers, we have ...

  net capitalized cost = MSRP - Down Payment = $28,500 -1,900 = $26,600

  depreciation fee = ($26,600 -12,900)/60 = $13,700/60 = $228.33

  financing fee = ($26,600 +12,000)×0.0005 = $39,500×0.0005 = $19.75

  lease payment = $228.33 + 19.75 = $248.08

_____

In the attached, the "new car lending rate" is 2400 times the lease factor, so is 1.2. This is an equivalent APR.

Effectively, the monthly lease fee is the average of the depreciating car value over the life of the lease multiplied by this APR. The depreciation for this purpose is assumed to be linear.

It’s D because you add all of them up

Answer:

P= 3

Q= -14

R= -5

Step-by-step explanation:

Just solve the equation on the right side, you'll get:

=3x^2 -15x +x -5

=3x^2 -14x -5

Now compare it to the equation on the left side,

The coefficient of x^2 on the left is "p", on the right that we just solved is 3.

Same for "q" which is the coefficient on the left, on the right it's -14.

And for "r" it's -5 from the equation on the right.

Expanding the right side of the equation (3x + 1)(x - 5), we get 3x^2 - 14x - 5. Matching coefficients, we find that p = 3, q = -14, and r = -5.

To solve for the values of p, q, and r that will make the equation px2 + qx + r = (3x + 1)(x - 5) true, we need to expand the right side and then compare coefficients. Expanding the right side, we have:

3x2 - 15x + x - 5

This simplifies to:

3x2 - 14x - 5

Now, we match the coefficients from the expanded form to the left side of the equation:

p must match the coefficient of x2, which is 3.

q must match the coefficient of x, which is -14.

r must match the constant term, which is -5.

Therefore, the correct values are:

A. p = 3

D. q = -14

E. r = -5

Answer:

  A.  $3.63

Step-by-step explanation:

You can choose the correct answer simply by estimating.

The almonds are about $5.50 for each of the 2 kg, so will total about $11. Since the total amount paid is just over $25, the amount paid for cashews is about $25 -11 = $14.

That amount pays for 4 kg of cashews, so 1 kg will be half of half that amount, or about $3.50 -- certainly, less than $7.26.

_____

If you want to write an equation, you can write ...

  2(5.49) +4(c) = 25.50

  4c = 14.52 . . . . . . . . . . . . subtract 10.98

  14.52/4 = c = 3.63 . . . . . divide by the coefficient of c

1 kg of cashews has a price of $3.63.

Answer:

2 root 21

Step-by-step explanation:

14 + 6 equals 20

Add x is 21

2 root21

Answer:

B. 2sqrt(30)

Step-by-step explanation:

The three right triangles are similar.

In the left right triangle, the short leg measures 6, and the hypotenuse measures x.

In the large triangle, the short leg measures x, and the hypotenuse measures 6 + 14 = 20.

Since all three triangles are similar, the ratios of the lengths of corresponding sides are equal.

6/x = x/20

x^2 = 6 * 20

x^2 = 120

x = sqrt(120)

x = sqrt(4 * 30)

x = 2sqrt(30)

Answer: B. 2sqrt(30)

Answer:

1. 24%

2.38%

Step-by-step explanation:

Answer:

The first one is 24% and the second one is 38%

Step-by-step explanation:

i did it on egdenuity

 The clouds wlll interfere for 21 ⁹/₁₀ days in a year

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here one 50-day period, cloud cover obstructed nighttime views just 6% or for the 50  day period the cloud obstructed t = 6% of 50

                                                                                      = 3 days

the number of 50 days period in a year = 365/50

                                                                   = 350/50 + 15/50

                                                                   = 7 + 15/50

 Therefore the number of days the cloud will obstruct is = (7 + 15/50)×3

                                                                                              = 21⁹/₁₀

Hence the clouds will obstruct 21⁹/₁₀ days in a year.

Learn more about percentages here:

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Final answer:

Based on a 50-day sample with 6% cloud coverage, one would predict that at Anza-Borrego Desert State Park, clouds will interfere with stargazing for approximately 22 days out of the year.

Explanation:

The Anza-Borrego Desert State Park had cloud coverage that obstructed nighttime views 6% of the time during a 50-day period. To predict how many days a year clouds would interfere with stargazing, you would use this percentage. The calculation is as follows:

Find the total number of days in a year, which is 365.

Calculate 6% of 365 days to find the number of days with cloud coverage. This is done by multiplying 365 by 0.06.

The result gives you the predicted number of days with cloud coverage obstructing stargazing. In numbers: 365 days/year × 0.06 (6%) = 21.9 days/year.

Therefore, based on the given sample, you would predict that clouds will interfere with stargazing at Anza-Borrego Desert State Park for approximately 22 days each year (rounding 21.9 up to the nearest whole number).

Answer:

  P' = (4, 4)

Step-by-step explanation:

T(x, y) is a function of x and y. Put the x- and y-values of point P into the translation formula and do the arithmetic.

  P' = T(8, -3) = (8 -4, -3 +7) = (4, 4)

_____

Comment on notation

The notation can be a little confusing, as the same form is used to mean different things. Here, P(8, -3) means point P has coordinates x=8, y=-3. The same form is used to define the translation function:

  T(x, y) = (x -4, y+7)

In this case, T(x, y) is not point T, but is a function named T (for "translation function") that takes arguments x and y and gives a coordinate pair as a result.

Translation is the process of transferring text from one language into another, aiming to maintain the original message's style, tone, and nuances. This practice requires a solid understanding of both the source and target languages.

Translation refers to the process of converting text from one language into another. The goal of translation is to accurately convey the meaning of the source language into the target language, while preserving the style, tone, and nuances. For example, if you want to translate the English phrase 'Hello, how are you?' into French, the translation would be 'Bonjour, comment ça va?'.

Handling translations can be tricky due to cultural differences, idiomatic expressions, and grammatical rules of the different languages. Practice and immersion in both languages can help improve translation skills.

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The tire has a circumference [tex]24\pi[/tex] inches, or [tex]2\pi[/tex] feet. It has a linear speed of 60 mph, or 88 feet/second. This means that any point on the rim of the tire will have traveled 88 feet in 1 second. We have

[tex]\dfrac{88}{2\pi}=\dfrac{44}\pi\approx14.006[/tex]

which means the tire completes a little over 14 revolutions in 1 second. One complete revolution corresponds to a rotation of 360º. Then its angular speed in degrees per second is

[tex]\left(\dfrac{44}\pi\dfrac{\rm rev}{\rm s}\right)\dfrac{360\,\rm deg}{1\,\rm rev}}=5042\dfrac{\rm deg}{\rm s}[/tex]

Given the car's speed of 60 mph and the tires' diameter of 24 inches, we can convert them to more standard units of meters and seconds. Using the physical concept that the angular speed equals the rate of change of angular displacement, we calculate the angular speed of the tires in radians per second. The result is then converted back to the desired unit of degrees per second, yielding an approximate angular speed of 5041 deg/sec.

To determine the angular speed of the tires, we need to understand some basic physics. First, we should calculate the linear velocity in more standard units. As we know 1 mile is approximately 1609.34 meters, and 1 hour is 3600 seconds, thus we can convert 60 mph into approximately 26.82 meter per second.

Next, the diameter of the tire is given as 24 inches, which is approximately 0.61 meters (as 1 inch = 0.0254 meters), so the radius r of the tire will be half of that, which is about 0.305 meters. The linear speed v of the edge of the tire is equal to the speed of the car, v = 26.82 meter per second.

The angular velocity w is defined as the rate of change of angular displacement with respect to time, which can also be expressed in terms of linear velocity and radius of the circular path as w = v/r. Plugging in our values, we can calculate w to be approximately 87.9 rad/sec.

Now, to convert to degrees per second, we should know that 1 radian is equal to approximately 57.2958 degrees. Therefore, the angular speed of the tire in degree per second is approximately 5041 degrees per second, or rounded to the nearest degree per second, it's approximately 5041 deg/sec.

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