Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3

Answer: right

Step-by-step explanation:

[tex]-499 > -500[/tex], and larger numbers are to the right of numbers smaller than them on the number line.

The function that is the solution of the differential y" + y = sin(x) is: y(x) = -1/2(x cos x)

A function is an expression, rule, or law in mathematics that describes a connection between one factor (the independent variable) and another variable (the dependent variable).

Take a look at the the following differential equation:

y" + y = sin (x)

The auxiiliary equation is

m² + 1 = 0

m² + 1-1 = -1

m² + 0 = -1

m² = -1

m = ±√-1

m = ±i

So, the complimentary function is yₐ (x) = c₁ cos x + c₂ sin x

Let the particular integral be:

yₙ (x) = A cos x + B sin x

yₙ '(x) = - A sin x + B cos x

yₙ ''(x) = - A cos x + B cos x

yₙ ''(x) = - (A cos x + B cos x)

After we have substituted yₙ (x); and yₙ''(x) in the given differential equation

y'' + y = sin (x)

= - (A cos x + B cos x) + (A cos x + B cos x)  = sin(x)

0 = sin (x)

If we take the particular integral to be:
yₙ (x) =  x(A cos x + B cos x)

yₙ '(x) = x(-A sin x + B cos x) + A cos x + B cos x

yₙ ''(x) = x(-A cos x - B sin x) - A sin x + B cos x + -A sin x + B cos x

Substitute yₙ (x), yₙ''(x) into the stated differential equation

y'' + y = sin (x)

x (-Acosx - Bsin x) - Asinx + Bcosx + (-Asinx + Bcosx) - x (Acosx + Bsin x) = sin (x)

-Axcosx - Bxsin x - Asinx + Bcosx -Asinx + Bcosx - Axcosx + Bxsin x = sin (x)

-2Asinx + 2Bcosx = sin(x)

Compare the coefficients of like terms on both sides of the equation

-2A = 1, B = 0

A = -1/2, B = 0

Substitute A = -1/2, B =0 into the assumed solution.

yₙ(x) = x((-1/2)cosx + (0) sinx)

= -1/2xcosx +0

= -(1/2)xcosx

Now, the general solution for the given differential equation is:

y(x) = yₓ(x) +yₙ (x)

y (x) - c₁cosx + c₂sin x -1/2x cosx

Hence, the solution is:

y(x) = -1/2xcosx

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Full Question:

Which of the following functions are solutions of the differential equation y'' + y = sin x? (Select all that apply.)

A) y = 1 2 x sin x

B) y = cos x

C) y = x sin x − 5x cos x

D) y = − 1 /2 x cos x

E) y = sin x

Answer:

y =- [tex]\frac{1}{4}[/tex]x - 1

Step-by-step explanation:

You are asked to give the equation of the line in slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Y-intercept is the point where the graph intersects the y-axis at point (b, 0). The graph seems to cross the y-axis at (-1, 0), so the b value is -1.

Slope is rise over run. Looking at the graph, it goes down 1 unit every 4 units to the right, so the slope is -1/4.

Answer:

Below in bold.

Step-by-step explanation:

The slope is -1/4 and y-intercept is -1

y = -1/4x - 1

The equation of the graphed parabola is y=a[tex](x+3)^{2}[/tex]-4.

Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).

We are required to find the equation of the graphed parabola.

The equation of a quadratic function of vertex (h,k) is given by:

y=a[tex](x-h)^{2}[/tex]+k

In the above equation a is the leading coefficient.

We have been given point (-3,-4).

We have to just put the value of h=-3 and k=-4 and the required equation will be as under:

y=a[tex](x+3)^{2}[/tex]-4

Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a[tex](x+3)^{2}[/tex]-4.

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The solution to the system of equations is given as follows:

x = 1 and x = 3.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the two equations are:

[tex]\frac{1}{x - 2} = x - 2[/tex]

Applying cross multiplication:

(x - 2)(x - 2) = 1

x² - 4x + 4 = 1

x² - 4x + 3 = 0

(x - 1)(x - 3) = 0

Hence the solutions are:

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Question 4

1) [tex]\overline{AC} \cong \overline{AE}, \overline{AB} \cong \overline{AD}[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle ABC \cong \triangle ADC[/tex] (SAS)

Question 5

3) [tex]\angle ABC \cong \angle DCB[/tex] (all right angles are congruent)

4) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

5) [tex]\triangle ABC \cong \triangle DCB[/tex] (AAS)

Surface area of the rectangular solid = 416 in.².

Volume = 480 in.³.

Surface area = 2(wl+hl+hw)

Volume = (length)(width)(height).

Given the following:

Length (l) = 12 in.

Width (w) = 10 in.

Height (h) = 4 in.

Surface area = 2(wl+hl+hw) = =2·(10·12+4·12+4·10) = 416 in.².

Volume = (12)(10)(4) = 480 in.³.

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Answer:

V≈3053.63

A≈1017.88

Step-by-step explanation:

V=[tex]\frac{4}{3}[/tex]π [tex]r^{3}[/tex]=[tex]\frac{4}{3}[/tex]·π·[tex]9^{3}[/tex] ≈3053.62806

A=4π[tex]r^{2}[/tex]=4·π·[tex]9^{2}[/tex] ≈1017.87602

Bob is 2 years older than Carol and the reverse of Carol's age is 3 times Bob's age, which makes Bob's to be 17 years.

Let 1B represent Bob's age and let 1C represent Carol's age, we can write the following equations;

Reversing Carol's age gives;

The multiples of 3 that have the form X1 have 7 as the rightmost number.

Given that 1B is a teenager, we have;

When;

The reverse of Carol's age is therefore;

Therefore, from the given description, Bob's age 1B = 17 years

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So lets try to prove it,

So let's consider the function f(x) = x^2.

Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity).

Using the Intermediate Value Theorem,

it would be enough to show that at some point a f(x) is less than 2 and at some point b f(x) is greater than 2. For example, let a = 0 and b = 3.

Therefore, f(0) = 0, which is less than 2, and f(3) = 9, which is greater than 2. Applying IVT to f(x) = x^2 on the interval [0,3}.

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The number of blue balls that are needed to balance four green, two yellow and two white balls is 16 blue balls.

Green(g)

Blue (b)

Yellow (y)

White (w)

First step is to formula an equation

3g=6b

g=2b

2y=5b

y=5/2b

4w=6b

w=3/2b

Second step is to substitute

4g+2y+2w

=4(2b)+2(5/2b)+2(3/2b)

=8b+5b+3b

=16b

Therefore 16 blue balls are needed.

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Answer:

f(1) = 81

Step-by-step explanation:

f(n + 1) = 1/3 f(n)

⇔ f(n) = 3 × f(n + 1)

……………………………

if f(3) = 9  ⇒  f(2) = 3 × f(3) = 3 × 9 = 27

Then

f(1) = 3 × f(2) = 3 × 27 = 81

Considering the surface area of the spherical ballon, it will take 7 seconds for the the balloon to fully inflate.

The surface area of a sphere of radius r is given by:

[tex]S = 4\pi r^2[/tex]

In this problem, the surface area is of [tex]784\pi[/tex] cm², hence the radius in cm is found as follows:

[tex]784\pi = 4\pi r^2[/tex]

[tex]4r^2 = 784[/tex]

[tex]r^2 = \frac{784}{4}[/tex]

[tex]r^2 = 196[/tex]

[tex]r = \sqrt{196}[/tex]

r = 14 cm.

The radius start at 0 cm, inflating at a rate of 2 cm/s, hence it will take 7 seconds for the the balloon to fully inflate, as 14 cm/(2 cm/s) = 7 s.

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The correct option is (c) h = 10sin(π15t)+35.

The equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds is  h = 10sin(π15t)+35.

The blades of a turbine, which resemble propellers and function much like an airplane wing, capture the wind's energy.

A pocket of low-pressure air develops on one side of the blade when the wind blows. The blade is subsequently drawn toward the low-pressure air pocket, which turns the rotor.

Calculation for the equation of the model height-

Let's now review each choice individually and select the best one.

The blade is horizontal at time t = 0. As a result, h = 35 at t = 0 is valid for all of the possibilities in this situation.

They accomplish two spins in a minute. The blades will so complete one rotation in 30 seconds. and they will complete a quarter rotation in 15/2 seconds. Because of this, the blade will be vertically up from time t = 0 to t = 15/2. Its height in this instance should be 35 + 10 = 45 ft. Let's now examine the available possibilities.

If we put t=15/2 in the options

Option (a) gives h = 25

Option (b) gives h = -10sin(15/2) + 35

Option (c) gives h = 45

Option (d) gives h = 10sin(15/2) + 35

Therefore, the correct equation is given in option c.

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The complete question is -

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

a) h = −10sin(π15t)+35  

b) h = −10sin(πt)+35

c) h = 10sin(π15t)+35

d) h = 10sin(πt)+35

The solution to the system of equations is the point ( -1, 9 ).

What is the solution to a system of linear equations?

If you have a system of equations that contains two equations with the same two unknown variables, then the solution to that system is the ordered pair that makes both equations true at the same time.

The system of equations

y = -3x + 6 ...................(1)

y = 9 .................(2)

Substitute equation (2)  in equation

9 = -3x + 6

subtract  both sides

9 - 6 = -3x + 6 - 6

3 = -3x

Divide by  -3 both sides

  x = -1

the solution is the point ( -1, 9 )

Therefore,the solution to the system of equations is the point ( -1, 9 ).

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The complete question is -

Y = –3x + 6  y = 9 what is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)

Answer:

c

Step-by-step explanation:

What is the solution to the system of equations?

(–21, 9)

(9, –21)

(–1, 9)

(9, –1)

El precio resultante con descuento de 12 % es igual a 342.32 pesos.

En este problema tenemos que determinar el precio resultante, el cual es igual al precio inicial menos el descuento. A continuación, se presenta la siguiente expresión:

x = 389 · (1 - 12/100)

x = 389 - 46.68

x = 342.32

El precio resultante con descuento de 12 % es igual a 342.32 pesos.

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Maximum value = 880/3.

Maximizing the objective function in the LP model means that the value occurs in an acceptable set of decisions. Linear programming refers to selecting the best alternative from the available alternatives that can represent the objective and constraint functions as linear mathematical functions.

As mentioned above, the equation is an example of a constraint. You can use this to think about what it means to solve equations and inequalities. For example, solving 3x + 4 = 10 yields x = 2. This is an easy way to express the same constraints.

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By applying the Theorem of Intersecting Secant to circle Q, an equation which is correct about the measure of ∠MNP is: A. m∠MNP = One-half(x – y).

The Theorem of Intersecting Secant states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

For this exercise, the following points should be noted:

By applying the Theorem of Intersecting Secant to circle Q shown in the image attached below, we can infer and logically deduce that angle MNP will be given by this formula:

m∠MNP = One-half(x – y).

m∠MNP = ½(x – y)

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The synthetic division's representation of the dividend is 2x3 + 10x2 + x + 5.

Given that

An L shape is created when two lines intersect vertically and horizontally.

The shape has entries in two rows.

Entries in row 1 are 2, 10, 1, and 5.

Blank, -10, and 0 are the entries in row 2.

A simplified method of dividing a polynomial with another polynomial equation of degree one is known as synthetic division.

On the exterior, to the left of the form, is entry number 5.

The entry stands for the divisor's zero.

If the variable is x, then this entry to the variable is;

2x³+10x²+x+5

The dividend is thus represented by synthetic division as

2x³+10x²+x+5

The Question is incomplete And complete question is given below!!

What dividend is represented by the synthetic division below? A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0. Negative 10 x squared minus 5 2 x cubed 10 x squared x 5 2 x squared 1 2 x cubed x.

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Answer:

The answer on Edge is A= 1

Step-by-step explanation:

Answer: No

Step-by-step explanation:

There is only one pair of congruent angles that can be determined, but to prove triangles similar, there needs to be two pairs of congruent angles.

Answer:

23

Step-by-step explanation:

small brain

The answer choice which best fits the function described in the task content is; Choice A; time(length).

It follows from the task content that the function takes the length of a race and returns the time needed to complete it.

On this note, it follows that the time taken is a function of the length of the race.

Hence, the appropriate name of the function is; Choice A.

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Using the given table:

a) the average rate of change is 32.5 jobs/year.

b) the average rate of change is 12.5 jobs/year.

For a function f(x), the average rate of change on an interval [a, b] is:

[tex]\frac{f(b) - f(a)}{b - a}[/tex]

a) The average rate of change between 1997 and 1999 is:

[tex]A = \frac{695 - 630}{1999 - 1997} = 32.5[/tex]

So the average rate of change is 32.5 jobs/year.

b) Now the interval is 1999 to 2001.

The rate this time is:

[tex]A ' = \frac{720 - 695}{2001 - 1999} = 12.5[/tex]

So the average rate of change is 12.5 jobs/year.

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Answer: C

Step-by-step explanation:

[tex]\frac{5\pi}{4}[/tex] is in the third quadrant, so both x and y are negative.

Therefore, the only possible answer is C.

The root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3

The graph that completes the question is added as an attachment

The polynomial function is given as:

x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12

From the attached graph, we have the following highlight:

The curves of both equations intersect at

x = -3, x = -2 and x = 3

This means that the root of the polynomial function is -3, -2 and 3

Hence, the root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3

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Complete question

Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12

What are the roots of the polynomial equation?

A) –3, –2, 3

B) –3, 2

C) 18, 32

D) 18, 32, 66

Answer:

Step-by-step explanation:

A Geometric sequence can be used:

To Model this sequence you need to use this formula

A (subscript n) = Ar(n-1)

a = value of the first term

n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)

r = the common ratio, this is obtained by dividing the second term in the sequence by the first.

So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term

n = 4 since you want to find the 4th term in the sequence

Plug it in and the results are

4th term = 27(2/3)^(4-1)  = 8

The answer is 8

The value of y from the given expression is 5

Given:

BD = 16

BC = 2y - 2

CD = y + 3

Since AC is a perpendicular bisector of BD:

BC  =  CD

2y - 2 = y + 3

2y - y = 3 + 2

y  =  5

Hence, the value of y from the given expression is 5

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Answer:

42.1

Step-by-step explanation:

The formula to calculate distance is √[(x₂ - x₁)² + (y₂ - y₁)²]. Using (22,27) as our x1 and y1, and (2,-10) as our x2 and y2.

Therefore our formula is √[(2 - 22)² + (-10 - 27)²].

(2 - 22)² = 400

(-10 - 27)² = 1369

(Make sure for both of these you put the negative number in parenthesis and the exponent outside them, if you are using a calculator of some sort)

Then we add and square root

√[400 + 1369] = 42.0594816896

The distance between the points (22,27) and (2,-10) is 42.1 units

The coordinates of the points are (22,27) and (2,-10)

The distance is calculated as:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]d = \sqrt{(22 -2)^2 + (27 +10)^2[/tex]

Evaluate

[tex]d = \sqrt{1769[/tex]

Take the square root

d = 42.1

Hence, the distance between the points (22,27) and (2,-10) is 42.1 units

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Answer:

26

Explanation:

[tex]\int\limits^{25}_{-1} {e^{x-[x]}} \, dx[/tex]

simplify

[tex]\int\limits^{25}_{-1} {e^{0} \, dx[/tex]

any variable to the power 0 is 1

[tex]\int\limits^{25}_{-1} 1 \, dx[/tex]

integrating 1 gives x

[tex]\left[ \:x \: \right]^{25}_{-1}[/tex]

apply limits

[tex]25 - (-1)[/tex]

add terms

[tex]26[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-[x]}dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-x}dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^0dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}dx[/tex]

[tex]\\ \rm\hookrightarrow \left[x\right]_{-1}^{25}[/tex]

[tex]\\ \rm\hookrightarrow 25-(-1)[/tex]

[tex]\\ \rm\hookrightarrow 25+1[/tex]

[tex]\\ \rm\hookrightarrow 26[/tex]