What is the circumference of a circle if the radius is 33 inches and pi is 3.14

A Dilation factor of 3 means that all dimensions of the figure are three times larger than those of the original figure. This applies to every dimension of the figure including height, width, and depth (if applicable). An example is a rectangle with original measurements 2 cm by 4 cm becoming 6 cm by 12 cm after dilation.

When a figure undergoes a dilation, all its dimensions are altered by the dilation factor.

In this case, the dilation factor is 3, which means that each dimension of the figure is three times larger than before.

It is important to note that this applies to all dimensions: height, width, and depth (if applicable).

For instance, suppose you have a rectangle with a height of 2 cm and width of 4 cm.

If the rectangle is dilated by a factor of 3, the new dimensions would be 6 cm (2 cm * 3) for height and 12 cm (4 cm * 3) for width.

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The question probable may be:

Explain the concept of dilation and provide an example illustrating how the dimensions of a figure change when subjected to a dilation factor. In particular, discuss the scenario where a rectangle with a height of 2 cm and width of 4 cm undergoes a dilation by a factor of 3. What are the new dimensions, and how does this align with the general principle of dilation?

Answer:

31.94 miles

Step-by-step explanation:

we know that

The circumference of a tire represents the distance traveled by the vehicle in one revolution

so

by proportion

Find out the distance traveled by the vehicle in 23,000 revolutions

[tex]\frac{88}{1}\ \frac{in}{rev}=\frac{x}{23,000}\ \frac{in}{rev}\\\\x=88(23,000)\\\\x=2,024,000\ in[/tex]

Convert inches to miles

Remember that

[tex]1\ mile=63,360\ inches[/tex]

To convert inches to miles divided by 63,360

therefore

[tex]2,024,000\ in=2,024,000/63,360=31.94\ miles[/tex]

Answer:Her Aunt paid her 4.50 and hour and her neighbor 6 an hour. The difference is 1.5

Step-by-step explanation:

Answer:66

Step-by-step explanation:

27.5x4.8/2

Answer:

66 meters squared

Step-by-step explanation:

You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.

Answer:

-2x-3y

Step-by-step explanation:

-1/4(8x+12y)

-8/4x-12/4y

-2x-3y

Final answer:

The expression -1/4(8x+12y) is expanded by distributing -1/4 to both 8x and 12y, resulting in the equivalent expression -2x - 3y.

Explanation:

To expand the expression -1/4(8x+12y), you need to distribute the term outside the parenthesis (-1/4) to each term inside the parenthesis. This process is known as the distributive property of multiplication over addition. Here's the step-by-step process:

In conclusion, the equivalent expression after expanding -1/4(8x+12y) is -2x - 3y.

Answer:

16 fluid ounces=2 cups

Hope this helps!

Step-by-step explanation:

Answer:

16 fluid ounces

Step-by-step explanation:

1 cup is equal to 8 fluid ounces, so 2 cups is 16 fluid ounces.

Answer:

30×3=90 10×9=90 45×2=90 . .

Answer: 5, 10, 18

Step-by-step explanation:

Answer:

15.7cm

Step-by-step explanation:

2 + 1.4 + 1.3 + 1.2 + 4.1 + 1.3 + 1.4 + 3

Answer:

Step 1: D for Divide. How many times will 5 go into 65? ...

Step 2: M for Multiply. You multiply your answer from step 1 and your divisor: 1 x 5 = 5. ...

Step 3: S for Subtract. Next you subtract. ...

Step 4: B for Bring down. ...

Step 1: D for Divide. ...

Step 2: M for Multiply. ...

Step 3: S for Subtract.

Step-by-step explanation:

Answer

wherever the decimal is, put it directly on top of the dividing line thing. Now that the decimal looks like a regular whole number you can divide like you usually would. Whenever you do regular long division, your answer is always going to be on the top of the line. Your answer should have a decimal in it ... and that should be your answer.

The maximum height of the ball is found at 64 feet

Hello! remember to write complete and clear questions in order to get good and exact answers. I've found a similar question so I have written it in a comment above. We know that h(t) models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds. This equation follows a quadratic function so from math we know that the maximum or minimum of this type of functions is found at the vertex of its graph. So:

[tex]f(x)=ax^2+bx+c \\ \\ \\ Vertex \ (h,k): \\ \\ h=-\frac{b}{2a} \\ \\ k=f(-\frac{b}{2a}) \\ \\ \\ Our \ function \ is: \\ \\ h(t)=-16t^2+64t \\ \\ \\ Comparing: \\ \\ a=-16 \\ \\ b=64 \\ \\ c=0 \\ \\ \\ h=-(\frac{64}{2(-16)})=2 \\ \\ k=-16(2)^2+64(2) \\ \\ k=64[/tex]

Finally, the maximum height of the ball is found at 64 feet

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Answer:

Senior citizen tickets = 9

Student tickets = 10

Step-by-step explanation:

We begin by converting the question into simultaneous linear equations;

Senior citizen tickets = a

Student tickets = b

4a + 6b = 96

8a + 13b = 202

to find a,

if 4a +6b = 96

a = 96/4 - 6b/4

a = 24 - 1.5b

We now substitute this into the second equation

8(24 - 1.5b) + 13b = 202

192 - 12b + 13b = 202

b = 202 - 192

b = 10

We now put the value of b in either equation

4a + 6b = 96

4a + 6(10) = 96

4a + 60 = 96

4a = 96 - 60

4a = 36

a = 9

Answer:

The bowling ball has only potential energy as it sits on top of a building.

The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.

The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.

Therefore the bowling ball will have more potential energy as it sits on top of the building.

Step-by-step explanation:

The bowling ball has only potential energy as it sits on top of a building.

The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.

The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.

Therefore the bowling ball will have more potential energy as it sits on top of the building.

Answer:

Before the ball hits the ground it has more potential energy but when is going down it looses potential energy and creates kinetic energy so when the ball hits the floor it would have more kinetic energy.

Step-by-step explanation:

Answer:

the degree for the polynomial is 2

Answer:

480 tons

Step-by-step explanation: You have to figure out how many minutes are in 24 hours. (1440 min) Then, you multiply 1440 x 1/3.

Answer:

the answer is 480

Step-by-step explanation:

it is common sense but in your case it is uncommon sense

Answer:

The system has infinitely many solutions

Step-by-step explanation:

we have

[tex]5x+3y=9[/tex] ----> equation A

[tex]-10x-6y=-18[/tex] ----> equation B

Multiply by -2 both sides equation A

[tex]-2(5x+3y)=-2(9)[/tex]

[tex]-10x-6y=-18[/tex] ----> equation C

Compare equation B and equation C

The equations are identical (is the same line)

therefore

The system has infinitely many solutions

Is a consistent dependent system

Step-by-step explanation:

The complete question:

What is the value of y in the formula shown when x = [tex]\dfrac{4}{5}[/tex] ?

[tex]y=\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]

We have,

[tex]\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]       ...... (1)

To find, the value of y = ?

Put x = [tex]\dfrac{4}{5}[/tex] in equation (1), we get

[tex]y=\dfrac{4}{\dfrac{4}{5}}+\sqrt{\dfrac{4}{5}+0.2}-5(\dfrac{4}{5})[/tex]

[tex]=5+\sqrt{0.8+0.2}-4[/tex]

[tex]=1+\sqrt{1}[/tex]

= 1 + 1

= 2

Thus, the value of y is equal to 2.

Answer:

45 metres

Step-by-step explanation:

You have to get the base to answer the question.

Do this by dividing 315 by 15 then timesing by 2

You get 42.

Do 42^2 = 1764

Do 15 ^2 = 225

Because you want the hypotenuse you add them

1764 + 225 =1989

Do the square root of 1989 which is 45 to the nearest metre

Answer:

25.80

Step-by-step explanation:

Area = 315 [tex]m^{2}[/tex]

Area = l*b

315 = 15 *b

b= 315/15

b = 21

From Right angled Triangle ,

Hypotenuse square = side square + side square

[tex]x^{2}[/tex] = [tex]21^{2}[/tex] + [tex]15^{2}[/tex]

[tex]x^{2}[/tex] = 441 + 225

[tex]x^{2}[/tex] = 666

apply sq root on both sides, the we get

[tex]\sqrt{x^{2}} = \sqrt{666}[/tex]

x= 25.80

Answer:

74°

Step-by-step explanation:

all angles of a triangle will always end up equal to 180°

68 + 38 = 106

180 - 106 = 74

Answer:

s = 32

Step-by-step explanation:

-5(s - 30) = -10

-5s + 150 = -10

-5s = -10 - 150

-5s = -160

s = -160/-5

s = 32

Answer:

27 can go into 224 8 times by dividing 224 by 27 .

We can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.

Given that, two pairs of corresponding sides and the corresponding included angles are congruent.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

If two pairs of corresponding sides are equal and corresponding included angles are equal.

By SAS congruence theorem, two triangles are congruent.

Therefore, we can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.

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Answer:

46

Step-by-step explanation:

47.84 / 1.04, which is 46

The opening price of Company A's stock before the 4% increase to the closing price of $47.84 was $46.00.

To calculate the opening price of Company A's stock at the beginning of the day, before the 4% gain, we need to work backwards from the closing price. Since the stock closed at $47.84 after gaining 4%, we can represent the closing price as 104% of the opening price. Thus, the equation to find the opening price (OP) is:

OP x1.04 = $47.84

Now we solve for OP:

OP = $47.84 / 1.04

OP = $46.00

The opening price of Company A's stock at the beginning of the day was $46.00.

Answer:

Therefore 6th year his income was $19,700.

Step-by-step explanation:

Given, Joe's annual income has been increasing in some dollar amount . The first year his income was $15,200 and 4th  year his income was $17,900.

A=$17900, P= $15,200 and n = 3 year

[tex]A= P(1+\frac{r}{100} )^n[/tex]

[tex]\Leftrightarrow 17900=15200(1+\frac{r}{100})^3[/tex]

[tex]\Leftrightarrow (1+\frac{r}{100})^3=\frac{17900}{15200}[/tex]

[tex]\Leftrightarrow (1+\frac{r}{100})=(\frac{17900}{15200})^{\frac{1}{3} }[/tex]

[tex]\Leftrightarrow \frac{r}{100}=(\frac{17900}{15200})^{\frac{1}{3} }-1[/tex]

[tex]\Leftrightarrow r=5.60[/tex]

Let  [tex]t^{th}[/tex] year Joe's income was $19,700.

[tex]\therefore 19700=15,200(1+\frac{5.60}{100} )^{t-1}[/tex]

[tex]\Leftrightarrow 1.296= (1+0.056)^{t-1}[/tex]

[tex]\Leftrightarrow 1.296= (1.056)^{t-1}[/tex]

[tex]\Leftrightarrow log(1.296)= (t-1)log(1.056)[/tex]

[tex]\Leftrightarrow \frac{log(1.296)}{log(1.056)}= (t-1)[/tex]

[tex]\Leftrightarrow t-1= 4.75[/tex]

[tex]\Leftrightarrow t= 4.75+1[/tex]

[tex]\Leftrightarrow t = 5.75[/tex] ≈6

Therefore 6th year his income was $19,700.

y=3x+38 is the expression for Sidney's weekly salary.

Step-by-step explanation:

Given,

Casey's weekly salary = x

Let,

y be the weekly salary of Sidney's.

According to given statement;

Sidney makes $38 more than 3 times Casey's weekly salary.

Sidney's weekly salary = 3 times Casey's weekly salary + $38

[tex]y=3x+38[/tex]

y=3x+38 is the expression for Sidney's weekly salary.

Keywords: variable, addition

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Answer:

[tex]S =19P\\S-19P = 0[/tex]                              

Step-by-step explanation:

We are given the following in the question:

Let P be the number of professor and S be the student in a college.

According to the question:

There are 19 times as many students as professors.

We have to write an equation to show the given relationship between professors and students.

[tex]S =19P\\S-19P = 0[/tex]

The above situation is the situation that represents the given relationship.

Answer:

1)  ∠DCE = (180  - x)°

2)   x  = 60°

Step-by-step explanation:

Here, given :  Lines AD and BE intersect at point C

(a)  Now, as we know, c BE is a straight line.

⇒∠BCD + ∠DCE = 180 °  (LINEAR PAIR)

⇒x °  + ∠DCE = 180 °

or, ∠DCE = (180  - x)° ....... (1)

(b) ∠DCE  = 120°

Putting the value in the equation (1), we get:

120°  = (180  - x)°

or, x =  180 - 120° = 60°

or, x  = 60°

Answer:

Explanation:

[tex]391\:\mathrm{divides\:by}\:17\quad \:391=23\cdot \:17[/tex]

[tex]=17\cdot \:23[/tex]

17, 23 are all prime number. So no further factorization possible

[tex]=17\cdot \:23[/tex]

So,

Answer:

Explanation:

[tex]291\:\mathrm{divides\:by}\:3\quad \:291=97\cdot \:3[/tex]

[tex]=3\cdot \:97[/tex]

3, 97 are all prime number. So no further factorization possible

[tex]=3\cdot \:97[/tex]

So,

Answer:

Explanation:

37 is a prime number. So no further factorization possible

[tex]=37[/tex]

So,

Answer:

Explanation:

[tex]411\:\mathrm{divides\:by}\:3\quad \:411=137\cdot \:3[/tex]

[tex]=3\cdot \:137[/tex]

3, 137 are all prime number. So no further factorization possible

[tex]=3\cdot \:137[/tex]

So,

Answer:

Explanation:

[tex]387\:\mathrm{divides\:by}\:3\quad \:387=129\cdot \:3[/tex]

[tex]=3\cdot \:129[/tex]

[tex]129\:\mathrm{divides\:by}\:3\quad \:129=43\cdot \:3\\=3\cdot \:3\cdot \:43[/tex]

3, 43 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:43[/tex]

So,

Answer:

Explanation:

113 is a prime number. So no further factorization possible

[tex]=113[/tex]

So,

Answer:

Explanation:

293

[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]

[tex]=293[/tex]

[tex]293\mathrm{\:is\:a\:prime\:number,\:therefore\:no\:factorization\:is\:possible}[/tex]

[tex]=293[/tex]

So,

Answer:

Explanation:

[tex]451\:\mathrm{divides\:by}\:11\quad \:451=41\cdot \:11[/tex]

[tex]=11\cdot \:41[/tex]

11, 41 are all prime number. So no further factorization possible

[tex]=11\cdot \:41[/tex]

So,

Answer:

Explanation:

[tex]459\:\mathrm{divides\:by}\:3\quad \:459=153\cdot \:3[/tex]

[tex]=3\cdot \:153[/tex]

[tex]153\:\mathrm{divides\:by}\:3\quad \:153=51\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:51[/tex]

[tex]51\:\mathrm{divides\:by}\:3\quad \:51=17\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

3, 17 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

So,

Answer:

Explanation:

[tex]385\:\mathrm{divides\:by}\:5\quad \:385=77\cdot \:5[/tex]

[tex]=5\cdot \:77[/tex]

[tex]77\:\mathrm{divides\:by}\:7\quad \:77=11\cdot \:7[/tex]

[tex]=5\cdot \:7\cdot \:11[/tex]

5, 7, 11 are all prime number. So no further factorization possible

[tex]=5\cdot \:7\cdot \:11[/tex]

So,

Answer:

Explanation:

So,

Keywords: prime factor

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Answer:

Yes it is a function given by f(x) = 2x

Step-by-step explanation:

Any function can approximated as series or a polynomial. For example,

[tex]e^{x} = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} ...[/tex]    (exponential function)

(n! or n factorial is equal to n(n-1)(n-2)...3.2.1 ;  3! = 3.2.1 = 6)

and for the series to converge(the sum does not go to infinity), higher order terms must tend to zero.

General form of a polynomial/series: [tex]f(x) = a + bx +cx^{2} + ...[/tex]

For the given set of points, we can start with the straight line equation:

[tex]f(x) = y = a + bx[/tex]    ........(1)

Let us take two points from the given relation: (-5, -10), (-1, -2)

and put the respective x and y values in equation (1), we get two equations, which we can then solve simultaneously to get values of [tex]a[/tex] and [tex]b[/tex]:

[tex]-10=a-5b[/tex]    ........(2)

[tex]-2=a-b[/tex]    ..........(3)

Now (3) - (2) gives us: [tex]b=2[/tex] and putting the value of [tex]b[/tex] in any of the above equation gives us [tex]a=0[/tex]

Hence, we get the equation, [tex]f(x)=y=2x[/tex]

It can be seen that all the given points satisfies this relation and since we get a unique [tex]y[/tex] for every [tex]x[/tex], we can call this a function.

Final answer:

The provided relation is a function because each x-value is unique and maps to exactly one y-value, fulfilling the criterion that every element of the domain is associated with exactly one element of the range.

Explanation:

The question asks if a relation containing the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10) is a function. To determine if this relation is a function, we need to examine if any x-value (the first number in each pair) repeats with a different y-value (the second number in each pair). Upon inspection, we see that each x-value is unique to a single y-value, which means that each element of the domain maps to a unique value in the range. Therefore, we can conclude that this relation is indeed a function.

In general, a function is defined as a relation in which every element of the domain (set of all first elements) is associated with exactly one element of the range (set of all second elements). This criterion is met in the relation provided as each x-value is unique and paired with only one y-value.

Answer:

x-y=-2

Step-by-step explanation:

Divide both sides if the equations by 3.

(3y-3x)÷3=6÷3

y-3x÷3=2

calculate the quotient

y-x=2

multiply both sides of the equation bub -1

-1x(-x)-1y=-1x2

any expression multiplied by -1

x-1y=-1x2

any expression multiplied by 1 remains the same.

x--y=-1x2

x-y=-2