Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2

From the given sequence, it is found that:

a) It is a geometric sequence, as the ratio between consecutive terms is the same.

b) Station 5 will be completed in 48 minutes.

c) Station 9 will be completed in 768 minutes.

In a geometric sequence, 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 the following rule:

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

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

In the context of this problem, the ratio between consecutive terms is given by:

r = 24/12 = 12/6 = 6/3 = 2.

Hence it is a geometric sequence.

Applying the recursive formula, the time for Station 5 is the time for Station 4 multiplied by the common ratio of 2, hence:

24 x 2 = 48 minutes.

The first term of the sequence is of 3, hence the explicit formula is given by:

[tex]a_n = 3(2)^{n-1}[/tex]

Hence the time for the 9th station, in minutes, is given as follows:

[tex]a_9 = 3(2)^{8} = 768[/tex]

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if the two trains are miles apart after hours, then  the rate of the westbound train is 79 miles per hour

two trains leave the station at the same time, one heading west and the other east.

the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours,

what is the rate of the westbound train?

Allow the westbound train to be "w" and the eastbound train to be "e". We can make the following equation:

4 (e + (e - 12)) = 680

4 (2e + 12) = 680

8e - 48 = 680

8e = 728

e = 91 mph

e - 12 = w

91 - 12 = w

79 = w

Therefore, the westbound train travels at 79 miles per hour.

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Answer:

Step-by-step explanation:

Your equation has two complex roots, a=-3/4+sqrt(23)/4*i and b=-3/4-sqrt(23)/4*i. Calculate (x-a³/b³)*(x-b³/a³) and simplify it to get that expression. It will be a bit tedious, but the result is quite nice.

a³/b³=1001/1024+45*sqrt(23)/1024*i

b³/a³=1001/1024-45*sqrt(23)/1024*i

Notice that these are complex conjugates (which isn’t surprising, because a and b were complex conjugates). That’s why the result (x-a³/b³)*(x-b³/a³) will be a polynomial with real coefficients!

If you have complex conjugate roots c+di and c-di, you always get (x-(c+di))*(x-(c-di))=x²-2cx+c²+d², where c and d are real numbers.

It is -2c=-2*1001/1024=-1001/512, and

c²+d²=(1001/1024)²+(45*sqrt(23)/1024)²=1048576/1048576=1.

Answer: 3a

Step-by-step explanation: 4a - 1a = 3a

The distance traveled by the tip of the minute hand in 45 minutes is approximately 256.77 mm, while the distance traveled by the tip of the hour hand in 1 hour is approximately 267 mm.

A) The hour needle completes a complete rotation of 12 hr, in 45 min = 0.75 hours, it will be 0.75 ÷ 12 of a complete rotation.

Given that the hour arrow's tip touches the rim of a clock, the radius of the clock is equal to the distance of the pointer.

The circumference of a circle is:

C=2 × π × radius

The span crossed by the hand in 12 hours is:

2 × 36=76π mm

The space traversed in 45 min is:

0.75 ÷ 12 × 72π=4.5π mm

in 45min, the min hand will make 45 ÷ 60=3 ÷ 4. If the min hand is 150% of the hour hand, then its length is 150 ÷ 100 × 36 = 54 mm.

As a result, the point of the minute will go around the complete circumference of a circle with a radius of 54 mm, implying that for a full circle, we will have:

2 × π × 54mm = 108π mm.

As a result, the minute hand's tip will have moved 45 minutes in 45 minutes, 108 × 3 ÷ 4 × π = 81π mm.

B) The clock's hour hand measures 30 mm.

As a result, the radius of the minute hand is,

1.5 × 30 = 45mm

And the minute hand moves after one hour 2π × ( r )²:

2 × 3.14 × 45 × 45 = 90π mm

And the minute hand moves,

π ÷ 6 × 30 = 5π mm

As a result, the minute hand moves,

90π - 5π = 85π mm

= 267 mm

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Step-by-step explanation:

21+3=24

1/3x+9=24

24-9=13

1/3x=13

13×1=13

3x=13

13/3=4.33

x=4.33

Answer:

x=27

Step-by-step explanation:

Answer:

solving the bracket

x×x = x²

x×-4= -4x

3×x= 3x

3×-4= -12

x²-x-12=0

The constant proportionality is 3

What is Proportionality Constant ?

The proportionality constant is the ratio between two variables that varies directly . For directly proportional variables, their ratio is always a constant and this constant is the proportionality constant.

Now, We have the equation is:

y = 3xy

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k = y/x  or y = kx

To get the constant of proportionality,

we will derive both sides of the equation by x.

y/x = 3x/x

y/x = 3

Hence, The constant proportionality is 3

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not to intrude but is that big ideas math?

Let's call a to the length of a side on the original polygon.

Let's call b to the length of the corresponding side to side a in the first photocopy. The length of b is: 0.3a (30% of a).

Similarly, c the length of the corresponding side in the second photocopy is: 0.3b = 0.3x0.3a = 0.09a

Then, the ratio of the corresponding sides of the second photocopy of the original to the sides of the original is 0.09:1

Answer:

16

Step-by-step explanation:

4/5=0.8

20*0.8=16

The number of distance in feet the driver travel in 52 seconds is 216 feet.

The race car driver travels 34 feet in the first second of a race.

The driver travels 3.5 additional feet each subsequent second.

The number of feet the driver travel in 52 seconds can be solved as follows:

Therefore,

the distance travel = 34 + 3.5x

where

Therefore,

the distance travel  = 34 + 3.5(52)

the distance travel  = 34 + 182

the distance travel  = 216 feet

Therefore, if the driver travels 34 feet in the first seconds of the race and travels an additional 3.5 feet each subsequent second, the number of distance in feet the driver will travel in 52 seconds is 216 feet.

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y < 2

can't be y <= 2 or y<=1 because the dot is open meaning the point is not included.

the range is talking about the y value, the point is at y = 2. The graph is also negative; therefore, range will be anything less than y = 2

Answer:

A = 127.251 cm²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( where r is the radius )

the area (A) of a semicircle is then

A = [tex]\frac{1}{2}[/tex] πr²

given diameter = 18 then r = 18 ÷ 2 = 9 cm , so

A = 0.5 × 3.142 × 9² = 0.5 × 3.142 × 81 = 127.251 cm²

Probability is the quantitative measure of the likelihood of the occurrence of an event.

It is mathematically expressed as:

We can decide to call the set of numbers below 7 "A".

A = {1, 2, 3, 4, 5, 6}

|A| = 6

We call the universal set, the set containing all the numbers rollable "U"

|U| = 12

Our probability is therefore:

Answer: 89%

[tex]\frac{0.89}{1}*\frac{100}{100} = \frac{89}{100}[/tex]

We can represent the length in Zach's car model by x

Since we have been given that Ginny's car is 2 more than 3 times the length of Zach's car, then we can get the expression as follow

Therefore,

Ginny's model will be 2 + 3x

Next, we are told that the sum of the lengths of both cars is 30 inches

Then

Therefore,

The answer is

Thus, the answer is Option B

Answer:

800000

Step-by-step explanation:

(1 x 10^1) = 10

(8 x 10^4) = 80000

10 x 80000 = 800000

Sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.

So, as in the description, it is given that A literal equation is one that is mostly made up of letters.

Therefore, sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.

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The correct question is given below:

Which best describes why you might want to rewrite a literal equation?

(A) To solve for a different indicated variable.

(B) To solve for the variable x.

(C) To solve for a different number.

(D) To solve for the variable y.

Answer:

y = 14

Step-by-step explanation:

2y - 16 = 12

add 16 to both sides:

2y - 16 + 16 = 12 + 16

2y = 28

divide both sides by 2:

2y/2 = 28/2

y = 14

Answer: y = 14 is the solution.

Following is the proof of BC||ED using alternate interior angles.

According to the alternate angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent.

We are given the ∠ABD = ∠FDB

and

∠1 = ∠4

using the above-given conditions we need to prove that line BC is parallel to line BD (i.e. BC || BD)

∠ABD = ∠FDB...................................(i)

∠ABD= ∠1 +∠2

and

∠FDB= ∠3+∠4

now subsituting these values of ∠ABD and ∠FDB in equation(i)

we get,

∠1 +∠2=∠3+∠4

we are also given that ∠1 = ∠4,  substituting that,

∠1 +∠2=∠3+∠1

= ∠2=∠3+∠1-∠1

= ∠2=∠3

through the given fig we know,

∠2=∠CBD

and

∠3=∠EDB

i.e.

∠CBD=∠EDB

∠CBD and ∠EDB make alternate interior angles of the lines BC and ED,

and since both the alternate interior angles are equal(∠CBD and ∠EDB) both the lines are parallel (||).

therefore we have BC||ED, hence proved.

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Answer:

92 public transit

23 bike

Step-by-step explanation:

460 / 5 = 92

460 / 20 = 23

The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex].

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Given Data

Function

8x-5x+21 = 36-6y

6y = 36 - 21 - 8x +5x

6y = -3x + 15

y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]

The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]

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Answer:

it should be in the ratio of 3:4

Step-by-step explanation:

100w= 75f

w/f = 75/100

 = 3/4

 = 3:4

The probability that none of the employees in the sample work at the plant in hawai is 0.0112

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

PH= 20/60 = 1/3

P(T) = 2/3

It is hypergeometric distribution

P(X=k)={\frac {{\binom {K}{k}}{\binom {N-K}{n-k}}}{\binom {N}{n}}},

where

N = 60

K = 20 for Hawai; 40 for Texas

n = 10

P(X=0) = 0.0112

Hence The probability that none of the employees in the sample work at the plant in hawai is 0.0112

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4) The reason for the second step is division property of equality.

5) The reason for the second step is Multiplication property of equality.

6) The reason for the third step is because of substitution property of equality.

4) We are given that;

4x = -24

x = -6

Thus, the reason for the second step is division property of equality because both sides were divided by 4.

5) We are given;

(3x + 5)/2 = 7

Multiply both sides by 2 to get;

3x + 5 = 14

The reason is due to Multiplication property of equality.

6) We are given;

x = 4

y = 3x + 7

y = 3(4) + 7

The reason is because of substitution property of equality.

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Answer:

$142.80

Step-by-step explanation:

smarts

Answer:

5

Step-by-step explanation:

155-18=137

137/24=5.70833333

5 people are able to join max