a^2 + b^2 + 2bc - 2ca - 2ab

The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.

The time dilation using the Lorentz transformation formula is presented as follows;

[tex]t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } [/tex]

From the question, we have;

The spaceship's speed, v = 0.6•c

∆t = Rest frame, Courtney's time, change = 10 years

Therefore;

[tex]\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8[/tex]

The time that elapses as measured by Andrea = 8 years

Andrea's age, A, at the end of the trip is therefore;

A = 10 years + 8 years = 18 years

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Answer:

The music group

Step-by-step explanation:

The experiment group is the group where something is being modified, so the music group is the one having their environment modified.

The principal is 1000

SI = PRT/100

Simple interest = 100

Rate = 5%

Time = 2 years.

SI = PRT/100

100 = (P × 5 × 2)/100

10000 = 10P

P = 10000/10

P = 1000

The lowest number in the data set is -5.

Let the data sets be consecutive numbers that has a highest number of 2.

Consecutive numbers mean that the.numvers follow each other. This will be:

-5, -6, -7, -8, -9, 0, 1, 2

Based on the numbers illustrated above, the lowest number is -5.

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Answer:

the answer might be 13.5

The system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

From the question, we are to determine the system that could have led to 9x = 27

1.

9x + 2y = 21

-9x - 2y = 21

Subtracting, we get

9x + 2y = 21

-9x - 2y = 21

-------------------

18x + 4y = 0

2.

10x - y = 15

x + y = - 12

Subtracting, we get

10x - y = 15

x + y = - 12

---------------------

9x -2y = 27

3.

7x - 2y = 15

x + y = 6

Here, multiply the second equation by 2

2 × [x + y = 6]

2x + 2y = 12

Now, add to the first equation

7x - 2y = 15

2x + 2y = 12

------------------

9x = 27

4.

4x + 3y = 24

-5x - 3y = 3

Subtracting, we get

4x + 3y = 24

-5x - 3y = 3

---------------------

9x + 6y = 21

Hence, the system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

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The graph of the line is shown in the attached image.

Given that the equation of the line y=-2/3x+1.

The line equation is an algebraic representation of the set of points, which together form a line in an exceedingly frame of reference.

First, we'll take the intercepts of equation y=-2/3x+1 . find

Find the y-intercept

The y-intercept is that the value of y when the worth of x is adequate zero

For x=0

y=-2/3(0)+1

y=1

The y-intercept is that the point (0.1)

Find the x-intercept

The x-intercept is that the value of x when the worth of y is adequate to zero

For y=0

y=-(2/3)x+1

0=(-2/3)x+1

-1=(-2/3)x

x=3/2 or 1.5

The y-intercept is that the point (1.5,0).

To plot the line on a graph, draw the intercepts and connect the dots as shown within the figure.

Therefore, the graph for the line y=-(2/3)x+1 is attached below.

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The equation of line with the given slope and y-intercept is y = (3/4)x + 4.

Given that;

We use the formula for equation of line to determine the equation.

y = mx + b

Where m is the slope and b is the y-intercept.

We plug in our values

y = mx + b

y = (3/4)x + 4

Therefore, the equation of line with the given slope and y-intercept is y = (3/4)x + 4.

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The mean distance is increased by a factor of [tex]2^{3/2}[/tex] if the orbital period  of planet y is twice that of the planet x.

Description of the Kepler's law.

The orbital period T and the mean distance from the sun, A, expressed in astronomical units (AU), are related in accordance with Kepler's third law.

The mathematical formula is,

T² = A³

Here, T denotes the orbital period and A represents the average separation or mean distance from the sun.

Now, if T(y) = 2T(x)

⇒ A'³(y) = 2A³(x)

A'(y) = [tex]2^{3/2}[/tex]A(y)

Thus, if orbital period of planet y is twice the orbital period of planet x, the mean distance is lengthened by a factor of [tex]2^{3/2}[/tex].

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Answer:

2 Superscript three-halves

Step-by-step explanation:

Edge

Answer:

They are parallel.

Step-by-step explanation:

They have the same slope, 7, and different y-intercepts, 4, -1/4, so they are parallel.

The recursive formula for the geometric sequence is given as follows:

D.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

With a recursive formula, it is given by:

[tex]a_n = a_{n-1} \times q[/tex]

For this problem, the first term and the common ratio are:

[tex]a_1 = 9, q = -\frac{1}{3}[/tex]

Then the recursive formula is:

D.

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The probability of drawing two yellow balls if they're not replaced exists 1/45.

The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.

Number of yellow marbles be 2

Number of pink marbles be 3

Number of blue marbles be 5

Total number of marbles = 2+3+5 = 10

The probability of removing the first yellow ball = 2/10

Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.

Probability of drawing the second yellow ball = 1/9.

Probability of drawing two yellow balls if they're not replaced

= 2/10 × 1/9

= 2/90

= 1/45

The probability of drawing two yellow balls if they're not replaced exists 1/45.

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The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.

According to the statement

Number of employees who sold three hurricane policies is 2

Number of employees who sold two hurricane policies is 6

Number of employees who sold 1 hurricane policies is 9

SO,

The total number of employees is 2+6+9=17.

The number that sold two hurricane policies or sold one hurricane policy is 6+9=15,

so the Probability = Total number of policies sold / total number of employees

Probability = 15/17

So, The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.

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 The range of the function f(x) = 2x² -7 with domain: x = {-4, -2, 0, 3} is y = (25, 1, -7, 11). Option D is the correct answer.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we substitute an x value, this set of values is what the function outputs. The y values are those.

In light of the query

x VS F(x) = 2x² -7

-4     F(4) = [tex]2(-4)^2 -7[/tex] = 25

-2     F(-2) = [tex]2(-2)^2 -7[/tex] = 1

0      F(0) = [tex]2(0)^2 -7[/tex] = -7

3      F(3) = [tex]2(3)^2 - 7[/tex] = 11

∴ Option D, y = (25, 1, -7, 11)

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1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)

2) [tex]\angle ACB[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ABC[/tex] and [tex]\triangle BED[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\therefore \triangle ACB \cong \triangle DEB[/tex] (HL)

5) [tex]\therefore \angle ACB \cong \angle DEB[/tex] (CPCTC)

The number of apples in the basket are; 24 apples

Let there be X number of apples and Y number of oranges.

Thus by the given ratio we can say that;

x/y = 3/8   -----(1)

(x — 1)/y = 1/3

3x — 3 = y   ----(2)

Substitute 3x - 3 for y in eq 1 to get;

x/(3x - 3) = 3/8

8x = 9x - 9

9x - 8x = 9

x = 9

Thus;

y = 3(9) - 3

y = 24 apples

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The rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)

Note that rotation about in clockwise 90 degrees direction when M(h , k) rotated about the origin, the new rotation coordinates would be in the form M' (k , -h)

Coordinates of the preimage were given as;

H ( -3, -2)

I ( 1, 1 )

J ( 0, -4)

The coordinates after a 90 degrees rotation about the origin, would be

For H ( -3, -2)

h = - (-3) = 3

k = -2

H' = ( -2, 3)

For I ( 1, 1)

h = - (1) = -1

k = 1

I' = ( 1, -1)

For J ( 0, -4)

h = - (0) = 0

k = -4

J' = ( -4, 0 )

Thus, the rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)

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Answer:

hi play truth and dare to with me in g met

Answer: y=3

Step-by-step explanation:

The x-axis is on the horizontal line, and the y-axis is on the vertical line. On the horizontal line at -1, just go up until you find where y is located.

By doing this, you can find that y=3.

Answer:

Step-by-step explanation:

All we have to do is find the point on the line where x = -1. If we know this, we can see how high the point is (i.e., find it's y-value). Then, we would know the value of y.

If we draw a vertical line from where x equals -1, we see that it crosses the line at point (-1, 3). This means that we can draw a line from the point to the number -1 on the x-axis and another line from the point to the number 3 on the y-axis.

Hence, the y-value when x=-1 would be 3.

The number of minutes it take to complete the same job if sandy and randy work together than if sandy works alone is 18mins.

According to this question, Sandy rakes and bags the leaves on her front lawn in 30 mins while Randy does the same job in 20 mins.

To calculate the time it will take both of them to work together, we use the following expression;

1/30 + 1/20 = 1/x

x = 12mins

Therefore, it will take 30 - 12 = 18 mins, to complete the same job if sandy and randy work together than if sandy works alone.

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Answer: II only: (-1, 4)

Step-by-step explanation:

x^2 - 3x - 4 is a parabolic function. When you factor the equation, it comes out to f(x) = (x-4)(x+1). Thus, the function as zeros at -1 and 4. Since the a value is positive, the parabola points up. Therefore, if you graph the function, it is negative between -1 and 4, so the answer is II only

Answer:

The answer that you have highlighted is correct.

Step-by-step explanation:

When you are dividing, you divide the exponents

-10 - (-4)

-10 + 4

-6

Let's see

seven eighths means 7/8

So

Forty two eighths

There is a total of 90 handshakes.

There are 5 sets of triplets.

If we select one of the sets, each of the triplets will have one handshake with the other 12 people. So we have 36 handshakes at this point.

Now we only care for the other 4 sets.

We select one set again, each triple on that set will have one handshake with the other 9 people, so for the 3 triplets, we have a total of 27 new handshakes.

For the remaining 3 sets we do the same, this time we add 18 handshakes.

Finally, there are 2 sets of triplets, this time we add 9 new handshakes.

To get the total number of handshakes we need to add them all:

36 + 27 + 18 + 9 = 90

There is a total of 90 handshakes.

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The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.

Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.

When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.

From the given information:

4x + 5y = -12  --- (1)

-2x + 3y = -16 ----- (2)

From equation (1)

4x+5y+(−5y) = −12 + (−5y)       (Add -5y to both sides)

4x = −5y − 12

Divide both sides by 4

[tex]\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}[/tex]

[tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]

Replacing the value of x in [tex]\mathbf{ \dfrac{-5}{4}y-3}[/tex] into equation (2); we have:

[tex]=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}[/tex]

[tex]\mathbf{\dfrac{11}{2}y+6 =-16}[/tex]

Simplifying both sides of the equation, we have:

[tex]\mathbf{\dfrac{11}{2}y+6-6 =-16-6}[/tex]

[tex]\mathbf{\dfrac{11}{2}y=-22}[/tex]

Cross multiply

11y = -44

y = -4

Replace the value of y = -4 into [tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]

[tex]\mathbf{x= \dfrac{-5}{4}(-4)-3}[/tex]

x = 2

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Answer: (8 * x) -3

Step-by-step explanation:

The term product refers to multiplication, so let the unknown number be x and multiply it by 8. Then you can subtract 3 afterwards.

*= multiplication

Multiply by 6

And

Multiply by 3

eq(1)-eq(2)

Then

From Equation 1

[tex] \dfrac{x}{2} + \dfrac{2y}{3} = - 1 [/tex]

[tex] \dfrac{3x + 4y}{6} = - 1[/tex]

[tex]3x + 4y = - 6 [/tex]

From Equation 2

[tex]x - \dfrac{y}{3} = 3 [/tex]

[tex] \dfrac{3x - y}{3} = 3[/tex]

[tex]3x - y = 9[/tex]

By eliminating ;;

For that multiply equation 2 by 4

12x - 4y = 36 _(3)

By taking equation (1) and (3)

3x + 4y = -6

12x - 4y = 36

__________

15x = 30

x = 30/15

x = 2

Putting the value of x in 2

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

[tex]6 - y = 9[/tex]

[tex]6 - 9 = y[/tex]

[tex]-3 = y[/tex]

So The value of x = 2 and y = -3

Answer: 120 hr

Step-by-step explanation: 15$ every hr so for 120 hrs it would be 1,800$ plus the signing bonus of 200$ would total 2,000$ but with out the bonus she would have to work 134 hrs for 2,010$

Answer:

circle

Step-by-step explanation:

any point on the circumference of a circle is equidistant from the centre.

Answer: [tex]y+5=-2(x+4)[/tex]

Step-by-step explanation:

See attached image.