4. Which statement is true for a preimage and its rotated image in the coordinate plane?

A.They are congruent.

B. They are exactly 4 units apart in the coordinate plane.

C. They were rotated around the origin since that is the only point in the plane you can use as the center of rotation.

D. They are two different sizes.

From calculations, the given integral ∫c x sin(y)ds is equal to [tex]20\left(-\frac{1}{3}\cos \left(4\right)+\frac{1}{9}\sin \left(4\right)-\frac{1}{9}\sin \left(1\right)\right)=0.806[/tex].

The integrals are the opposite of derivatives. They are used in several applications, like: calculations of areas, volumes and others.

For solving an integration, you should know its rules. For this question will be necessary to apply the following integration rules:

First, you should calculate the segment from the points (0, 1) and (4, 4).

segment=(4-0,4-1)=(4,3).

After that you should parametrize the segment:

r(t)=(0,1)+(4t,3t)= (4t,3t+1), where 0≤t≤1

Now, you can find dr/dt.

r'(t)=(4,3)

Consequently, the magnitude of |r'(t)| will be:

|r'(t)|  =[tex]\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25} =5[/tex]

Finally you can evaluate the integral: ∫c x sin(y)ds. From r(t), you know that x=4t and y=3t+1.

[tex]\int _0^1\:xsin\left(y\right)\:ds=\int _0^1\:4t\cdot sin\left(3t+1\right)\:\cdot 5ds=\int _0^1\:20t\cdot sin\left(3t+1\right)\:\cdot ds[/tex]

Applying the Rule Integration for a Constant.

[tex]\int _0^1\:20t\cdot sin\left(3t+1\right)\:\cdot dt\\ \\ 20\cdot \int _0^1t\sin \left(3t+1\right)dt\\ \\[/tex]

Applying the Rule Integration by Parts.

∫u v dx = uv -∫v du

u=t

dv= sin(3t +1 )dt, then v=

[tex]=20\left[-\frac{1}{3}t\cos \left(3t+1\right)-\int \:-\frac{1}{3}\cos \left(3t+1\right)dt\right]^1_0\\ \\=20\left[-\frac{1}{3}t\cos \left(3t+1\right)+\frac{1}{9}\sin \left(3t+1\right)\right]^1_0\\ \\ =20\left(-\frac{1}{3}\cos \left(4\right)+\frac{1}{9}\sin \left(4\right)-\frac{1}{9}\sin \left(1\right)\right)\\ \\ =0.806[/tex]

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The value of the integral  ∫c x sin(y)ds where c is the curve is 0.806 if the line segment is from (0,1) to (4,4).

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

First, we have to calculate line segment (0,1 ) to (4, 4)

= (4-0, 4-1) = (4, 3)

Parametric form of the segment:

P(t) = (0+4t, 3t)   where 0 ≤ t ≤ 1

Now differentiate the segment:

P'(t) = (4, 3)

The magnitude of the P'(t)

[tex]\rm P'(t) = \sqrt{4^2+3^2}[/tex]

P'(t)  = 5

Now the integration can be evaluated from the P(t)

[tex]\rm \int\limits^1_0 {xsin(y)} \, ds = \int\limits^1_0 {4tsin(3t+1)} \, 5ds[/tex]    ( x= 4t, y = 3t+1)

[tex]\rm \int\limits^1_0 {xsin(y)} \, ds = 20\int\limits^1_0 {tsin(3t+1)} \, ds[/tex]

The value of the integration:

[tex]\rm \int \limits^1_0 {tsin(3t+1)} \, ds = 0.040[/tex]

[tex]\rm \int\limits^1_0 {xsin(y)} \, ds = 20(0.04)[/tex]

[tex]\rm \int\limits^1_0 {xsin(y)} \, ds =0.806[/tex]

Thus, the value of the integral  ∫c x sin(y)ds where c is the curve is 0.806 if the line segment is from (0,1) to (4,4).

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Answer:

x = 54

Step-by-step explanation:

x/3 = x-36

x= 3x-36.3

2x= 36.3

x = 18.3

x = 54

Answer:

Step-by-step explanation:

The given age ratio is valid 12 years after the age at which Arnold was x years old. When Arnold was x, Ken was x-34.

  (x +12) = 3((x -34) +12) . . . . . the age relation in 2013

__

Solving for x, we have ...

  x +12 = 3x -102 +36

  78 = 2x . . . . . . . add 66-x

  39 = x

In 2001, Arnold was 39 years old.

_____

Additional comment

In 2001, Arnold was 39 and Ken was 5. Ken is 34 years younger.

In 2013, Arnold was 51 and Ken was 17. Arnold was 3 times Ken's age.

Answer: A

Step-by-step explanation:

You can multiply the coordinates by 4, giving (0,0)

Answer:

it'sssssss 2.51

Step-by-step explanation:

========≈==================

Answer:

4/8 or 1/2

Step-by-step explanation:

Convert all size to x/8

1/4=2/8 and 1/2=4/8

Multiply size of beaker by how many there are filled

1/8 * 2= 2/8

2/8*7= 14/8

4/8*3 =12/8

then add all of them together = 28/8

convert 4 liters to 32/8

Subtract 32/8 - 28/8 = 4/8

Answer:

4.696% (B)

Step-by-step explanation:

13/17 = 0.76470588

12/15 = 0.8

0.8 - 0.76470588 = 0.03529412

0.03529412 /  0.76470588 = 0.04615285

0.04615285 · 100 = 4.61538494

(I rounded 13/17, the closest answer is 4.696)

percentage increase:

final value - starting value / starting value · 100

Answer:

what does the -514 relate with 11/12?

Step-by-step explanation:

11/12 written as a decimal is .91

Answer:

It would be -514.916 with a _ over the six.

Step-by-step explanation:

11/12 is equal to 0.916666, where the six goes on forever. This is called a repeating decimal. In a repeating decimal, you would put this symbol _ over the number that repeats, in this case, 6. Or you would round, but that"s not given in this question.

Hey there!

Combine Like Terms and see if the expressions are equivalent or not.

6x-4-x

6x-x-4

5x-4

Is 5x-4 equivalent to 7x-4? No.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

Answer:

Given;  7x – 4 and 6x – 4 – x

To Find; how you can tell if the expressions 7x – 4 and 6x – 4 – x are equivalent

Solution; This question can be easily solved by letting some value of x and putting in both the equation to check whether both are equal or not

Let x=1

7x-4=3 and 5x-4=1

Since both are not equal Hence the given equations are not equalnation:

Answer:

option C

Step-by-step explanation:

y = -x + 7

Hope this helps you

Answer:

4

Step-by-step explanation:

Elissa uses 8.5 inches of thread per bracelet.

She has 40 inches of thread.

To find the maximum number of bracelets she can make, we need to divide.

40 / 8.5 = 4.70588...

We cannot have an unfinished bracelet, so we have to round down.

She can make 4 bracelets with 40 inches of thread.

Answer:

4 bracelets

Step-by-step explanation:

if 8.5 inches makes 1 friendship bracelet

what about 40inches

8.5inches=1 bracelet

40 inches=?

cross mulltiply

40x1

-------

8.5

=4 12/17 bracelets

12/17 of a bracelet is not a complete one

=4 complete friendship bracelets

aaaaaand 4 happy friends

Extraneous solutions are the values that we get when solving equations which aren't really solutions to the equation.

Your information is incomplete. Therefore, an overview will be given.  An extraneous solution is the root of a transformed equation which is not a root of the original equation since it was excluded from the domain of the original equation.

The reason extraneous solutions exist is simply that some operations produce extra answers, and these operations are a part of the path to solving the problem.

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Answer:

$13.50

Step-by-step explanation:

if the total is $31.50, it is both the blouse and the skirt together, so uf you take away the blouse from the total ($31.50 - $18) then yiu are keft with the price of the skirt

Answer:

-4, 10.

Step-by-step explanation:

(x – 3)^2 = 49

x - 3 = ±√49

x = 3 ± 7

= -4, 10.

Answer:

C. b= a+4

Step-by-step explanation:

Answer:

13x + 14

Step-by-step explanation:

5x + 6 + 3x = 8x + 6.

8x + 6 + x + 1 + x + 1 + 2= 10x + 10

10x + 10 + (2²)(i think) = 10x + 14

10x + 14 + 3x = 13x + 14

final answer

Answer:

[tex]13x+14[/tex]

Step-by-step explanation:

First take all the sides and add:

[tex]5x+6+3x+3x+2+2+2+x+1+x+1[/tex]

Then Combine Like terms:

[tex]5x+3x+3x+x+x+6+2+2+2+1+1[/tex]

There is your answer:

[tex]13x+14[/tex]

(If I misunderstood the handwriting, please tell me, and I will fix my mistakes)

Answer:

No

Limit given:

point:

This value of u = 1  does not fall under the condition, "u is greater than 8".

Number line:

Answer:

No

Step-by-step explanation:

The given inequality is :

Therefore, the only solutions to this inequality must be greater than 8.

On substituting u = 1 in the inequality,

since the shape made by the angles is a quadrilateral, or namely a polygon of 4 sides, hmmm the sum of all interior angles in a polygon is

180(n - 2)

n = number of sides

so that polygon has a total of interior angles of 180(4 - 2) = 360.

Check the picture below.

Answer:What is the probability of spinning a 2 on the spinner?

Image result for You roll a number cube and then spin a spinner with two equal-sized sections. What is the probability of rolling a number greater than 3 and spinning red? A. 1/4 B. 1/6 C. 1/3 D. 1/2

There are 2 sections on the spinner that contain a '2'. The probability of spinning a 2 is 2 / 8 . The probability of spinning a 3 is also 2 / 8

Step-by-step explanation:

The probability of rolling a number greater than 3 and spinning red is 1/4.

We need to determine the favorable outcomes (the outcomes that satisfy both conditions) and the total possible outcomes.

The numbers greater than 3 and corresponding to the red section are: 4R, 5R, and 6R. So, there are 3 favorable outcomes.

Since we have a number cube with 6 sides and a spinner with 2 sections, the total possible outcomes are the product of the number of sides on the cube and the number of sections on the spinner, which is 6 × 2 = 12.

The probability is calculated by dividing the number of favorable outcomes by the total possible outcomes.

Probability = Favorable outcomes / Total possible outcomes

= 3 / 12

= 1 / 4

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Answer: No

Step-by-step explanation:

This is not an isosceles triangle because there are different angle measurements. The rule of an isosceles triangle is that it must always have two equal sides and angles.

The area of the triangle def round to the nearest tenth of a square unit is 10.3 square units.

When the two sides and an angle of a  triangle is known, then the area of the triangle can be found out with the following formula.

[tex]A=ab\sin\left(\dfrac{C}{2}\right)[/tex]

Here, a,b are the adjacent sides and C is the angle made between them.

The image of the triangle DEF is attached below. In this the two adjacent sides are given with the length 5 units ans 8 units long.

The angle made between them has the measure of 31 degrees. Put the values in the above formula as,

[tex]A=(5)(8)\sin\left(\dfrac{31}{2}\right)\\A=10.3\rm\; unit^2[/tex]

Hence, the area of the triangle def round to the nearest tenth of a square unit is 10.3 square units.

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Answer: A, 10.3

Step-by-step explanation: edge 2022

The value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20

They are those expressions which are found by squaring binomial expressions.

Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.

Let the binomial term was ax + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:

[tex](ax + b)^2 = a^2x^2 + b^2 + 2abx[/tex]

Comparing this expression with the expression we're provided with:

[tex]x^2 + 10x + c[/tex]

we see that:

[tex]a^2 = 1 \implies a = \pm 1\\b^2 = 10\\b = \pm 10\\2ab = c\\\pm2(10)1 = c\\c = \pm 20\\[/tex]

Thus, the value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20

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Answer:

-3

Step-by-step explanation:

a= -4

So the first and second should be multiply together

first=-4

second=12

12/-4=-3

Answer:

BDC  and ADB

Step-by-step explanation:

Answer:

7 pairs of shoes

Step-by-step explanation:

So your equation is P(x) = -6x² + 60x - 126. This is a parabolic function, and it looks like we can factor it.

First, let's factor out -6 from the equation to simplify it. If we divide each part of the equation by -6, that leaves us with -6(x² - 10x + 21).

Now, we can factor the equation further by finding two numbers that add up to -10 and multiply to get 21. We know that both have to be negative numbers since they add up to a negative number and multiply to a positive one. The numbers you get are -3 and -7, making the equation P(x) = -6(x-3)(x-7).

x = 3 or 7. To maximize profit, you should sell 7 pairs of shoes.

Hope this helps! :)

Answer:

16.80 ft long

Step-by-step explanation:

Answer:

20.25

Step-by-step explanation:

The area of a rectangle is calculated by multiplying its width and length:

The area of the smaller rectangle is given as 9 ft^2 so to find its width we divide the given area with length which is 4.5

9/(4.5) = 2

The given rectangles are similar so their side lengths must be proportional

(4.5)/x = 2/9 cross multiply expressions

2x = 40.5 divide both sides by 2

x = 20.25

Collinear points: Three points A, B and C are said to be collinear if they lie on the same straight line.

There points A, B and C will be collinear if AB + BC = AC as is clear from the adjoining figure.

In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is, either AB + BC = AC or AC +CB = AB or BA + AC = BC.

In other words,

There points A, B and C are collinear if:

(i) AB + BC = AC i.e.,

Or, (ii) AB + AC = BC i.e. ,

Or, AC + BC = AB i.e.,