Where is the blue dot on the number line?

The exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

The exterior angle adjacent to the largest interior angle in a triangle is equal to the sum of the other two interior angles.

Let's call the measures of the angles in the triangle x, x, and 2x. Then,

x + x + 2x = 180 degrees,

so 4x = 180 degrees, and

x = 45 degrees.

The largest interior angle is 2x, or 90 degrees. The exterior angle that is adjacent to this angle is equal to 180 degrees minus the interior angle, which is 180 - 90 = 90 degrees.

So the exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

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False. If you double your speed, you quadruple your kinetic energy.

False. If you double your speed, you quadruple your kinetic energy. This is because kinetic energy is directly proportional to the square of the velocity. When you increase your speed from 30 miles per hour to 60 miles per hour, you are actually doubling your speed, not quadrupling it. Therefore, you will be doubling your kinetic energy, not quadrupling it. This is an important concept in physics and it shows the relationship between speed and kinetic energy. It's always important to understand how speed affects different physical quantities like kinetic energy. I hope this explanation helps!

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Answer:

D) 4  E) 15  F) 30  G) 30  H) 70

Step-by-step explanation:

D) the square root of 4 is 2. We do 2 x 2 = 4.

E) the square root of 9 is 3. We do 3 x 5 = 15.

F) the square root of 25 is 5. We do 5 x 6 = 30.

G) the square root of 36 is 6. We do 6 x 5 = 30.

H) the square root of 100 is 10. We do 10 x 7 = 70.

I hope this helped and please mark me as brainliest!

Answer:

x = number of hours = 8 hours

Step-by-step explanation:

Let

x = number of hours

There are 3 people who rented bicycle from each shop

Ace bicycle shop:

Total cost = 3(4 + x)

= 12 + 3x

Best bicycle shop:

Total cost = 3(8 + 0.50x)

= 24 + 1.5x

Equate both equations and solve

12 + 3x = 24 + 1.5x

12 - 24 = 1.5x - 3x

-12 = -1.5x

x = -12/-1.5

x = 8 hours

x = number of hours = 8 hours

The coordinate of point X is 14 in the number line.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.

To determine the coordinate of point X such that the ratio of MX to XJ is 3:1

Refer to the number line,

The distance between M and J = 18 - 2 = 16

Since the ratio of MX to XJ is 3:1

So the distance of point X from M is 12 and from J is 4.

Point X's coordinate on the number line = 14.

Hence, the coordinate of point X is 14 in the number line.

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Remember that the general formula of an arithmetic sequence is:

Where:

• An is the n-term

• d is the common difference

• n is the number of the step

Using the given data,

Therefore, the 13th term of the arithmetic sequence is 73

Answer:

0.5

Step-by-step explanation:

0.472    look at the digit to the RIGHT of the 10ths place if it is >=5   round the 10ths up one    ....    o/w leave it as is

0.472 = 0.5   rounded to nearest tenth

Answer:0.5

Step-by-step explanation: Find the number in the tenth place 4 and look one place to the right for the rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5.0.472 = 0.5

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π               → A = π - (B + C)

                                               → B = π - (A + C)

                                               → C = π - (A + B)

Use Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Use the following Cofunction Identity: cos (π/2 - A) = sin A

Proof LHS → RHS:

LHS:                        sin A - sin B + sin C

                             = (sin A - sin B) + sin C

\(\text{Sum to Product:}\quad 2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Given:}\qquad 2\cos \bigg(\dfrac{\pi -(B+C)}{2}+\dfrac{B}{2}}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi -C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(.\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2} -\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Cofunction:} \qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Factor:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\bigg]\)

\(\text{Given:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad =2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi}{2} -\dfrac{(A+B)}{2}\bigg)\bigg]\)

\(\text{Cofunction:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)\bigg]\)

\(\text{Sum to Product:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ 2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{LHS = RHS:}\quad 4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)=4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\quad \checkmark\)

Answer:

is finding the square root

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number.

When a number is squared, it is multiplied by itself. For example, squaring the number 4 gives 4^2 = 16.

The inverse operation undoes the effect of squaring and returns you to the original number. In this case, finding the square root of a number is the inverse operation of squaring.

The square root of a number "x" is a value that, when squared, gives the original number. It is denoted by the symbol √x.

For example, if you have the number 25 and you want to find its square root, you calculate:

√25 = 5

5 is the square root of 25 because when you square 5 (5^2), you get 25.

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number. The concept of square root and squaring are inverse operations that are used in various mathematical calculations and problem-solving.

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Answer:

A slope of 0.5.

Step-by-step explanation:

Each coin toss has a 50% probability of being heads.  Therefor, the histogram plot should have a slope of 0.5.  To illustrate, graph the predicted probabilities of at least two sets of coin tosses, such as 6 and 16.  The probable number of heads would be 3 and 8.  Plot those two points and draw the line.  The slope of that line will be 0.5.

See the attachment.  I graphed more than two points, since it was easy.  But you really only need two if you know it is a straight line function.  Graph a third just to be certain.

We can start by finding the time it takes for Gill to travel the first 27km:

Time taken = Distance / Speed = 27km / 96 km/h = 0.28125 hours

Next, we need to account for the 3-minute stop in Lens. Since 1 hour has 60 minutes, 3 minutes is 3/60 = 0.05 hours.

The total time taken for the journey from the start to Lens is:

0.28125 hours + 0.05 hours = 0.33125 hours

Now we need to find the time it takes for Gill to travel the final 29km:

Time taken = Distance / Speed = 29km / 96 km/h = 0.30208 hours

Adding the time taken for the first part of the journey to the time taken for the second part gives the total time taken for the journey:

0.33125 hours + 0.30208 hours = 0.63333 hours

Finally, we can add this time to the departure time of 09:00 to find the arrival time:

09:00 + 0.63333 hours = 09:38 (rounded to the nearest minute)

ANSWER IS B

Okay, here are the steps to solve this problem:

1) Gill leaves Lille by train at 09:00.

2) The train travels 27km at 96km/h. 27km / 96km/h = 0.2833h = 17min

3) So the train will arrive at Lens at 09:17 (09:00 + 17min)

4) The train stops at Lens for 3 minutes. 3min = 0.05h

5) So the train leaves Lens at 09:22 (09:17 + 3min = 0.05h)

6) The train then travels 29km at 96km/h. 29km / 96km/h = 0.3021h = 18min

7) So the train will arrive at Lillers at 09:40 (09:22 + 18min)

Therefore, the answer is C 09:40

Let me know if you have any other questions!

Answer: I can’t help with that because there should be a graph

Step-by-step explanation:

Answer:

I think the answer is 7.9

Step-by-step explanation:

u can change them into a mixed number and divide them

Answer:

18

Step-by-step explanation:

You have 25 when you are done, but you made 7, so subtract that from 27.

25-7 equals 18.

The given equation is 4sin²() - 3 = 0. Solving for sin(), we get sin() = ±√(3/4) = ±0.866. Since sin() has a period of 2π, we can write the solutions in terms of k as follows:

() = sin⁻¹(0.866) + kπ or () = sin⁻¹(-0.866) + kπ.

Rounding to two decimal places, we get () = 1.05 + kπ or () = -1.05 + kπ.

Therefore, the solutions to the given equation are () = 1.05 + kπ or () = -1.05 + kπ, where k is any integer.

To solve the equation, we first isolate the term containing sin²() by adding 3 to both sides of the equation. We then divide both sides by 4 to get sin²() = 3/4. Taking the square root of both sides gives us sin() = ±√(3/4) = ±0.866. We then use the inverse sine function to find the angles corresponding to these values of sin(). Since sin() has a period of 2π, we add kπ to the solutions to account for all possible angles. Finally, we round the solutions to two decimal places.

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The group of participants who are not exposed to the independent variables are the known as the control group.

Good luck! :)

The graph is attached below which represents the inequality < -1 + 2x

The linear inequality has the form y =b + m x, where m is the slope of the line and b is the y-intercept, or the point at which the line intersects the y-axis (0, b)

The area under the line provides the answer to the inequality.

Identifying the graph that best depicts the inequality y < -1 + 2x\s→ With b = -1, determine the y-intercept, or the value of y at x = 0. It is the y-intercept (0, -1)

We have two graphs from the provided graphs where the line intersected the y-axis (0, -1)

The second graph in row one

Second graph in second row The manifestation of inequality is The shaded region has to be below the line. Our response is the second graph in the first row.

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Answer:

nope sorry man

Step-by-step explanation:

Answer:

3. y = 2x - 2

4. y = \(\frac{4}{3}x-1\)

Step-by-step explanation:

3. Slope = 2

Y-intercept = -2

4. Slope = \(\frac{4}{3}\)

Y-intercept = -1

Answer:

3). y = 2x - 2

4). y = (4/3)x - 1

Step-by-step explanation:

3).

First find the slope

(y2 - y1) / (x2 - x1)  or rise/run

(0 - (-2)) / (1 - 0) = 2

2 is your slope

Now use the equation below for using coordinates for finding slope intercept form.

y - y1 = m(x - x1)

y1 = y number of given coordinate

x1 = x number of given coordinate

m = slope

y - 0 = 2(x - 1)

Distribute

y - 0 = 2x + (-2)

Get y by itself by adding 0 to both sides.

y - 0 = 2x + (-2)

  +0           +0

y = 2x - 2

4).

Repeat the same process for 4 as done in 3

Find the slope

(y2 - y1) / (x2 - x1)  or rise/run

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

4/3 is your slope

Now use the equation below for using coordinates for finding slope intercept form.

y - y1 = m(x - x1)

y1 = y number of given coordinate

x1 = x number of given coordinate

m = slope

y - 3 = (4/3)(x - 3)

Distribute

y - 3 = (4/3)x + (-4)

Get y by itself by adding 3 to both sides.

y - 3 = (4/3)x + (-4)

  +3                  +3

y = (4/3)x - 1

To find the points where the height of the Gateway Arch is 100 meters, we need to solve the equation y = 100 for x.

Substituting y = 100 into the equation for the central curve of the arch, we get:

100 = 211.49 - 20.96 cosh (0.03291765x)

Rearranging the equation, we get:

cosh (0.03291765x) = (211.49 - 100) / 20.96

cosh (0.03291765x) = 5.21

Taking the inverse hyperbolic cosine of both sides, we get:

0.03291765x = acosh(5.21)

x = (1/0.03291765) acosh(5.21)

Solving for x using a calculator, we get:

x = ± 64.975

Therefore, the height of the Gateway Arch is 100 meters at the points (64.975, 100) and (-64.975, 100).

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Answer:

56 music files

Step-by-step explanation:

From the above question:

Let the number of music files

Arely has = x

Valerie has = y

Arely has 4 fewer than twice as many music files as Valerie.

x = 2y - 4

They have a combined number of 86 music files.

x + y = 86

We substitute 2y - 4 for x in the above equation

2y - 4 + y = 86

3y - 4 = 86

3y = 86 + 4

3y = 90

Divide both sides by 3

3y/3 = 90/3

y = 30

Hence, Valerie has 30 music files.

The number of music files that Arely has is calculated as:

x = 2y - 4

x = 2(30) - 4

x = 60 - 4

x = 56

Arely has 56 music files

Answer:

11 years 7 months 7 days(if 31 days a months) and change 7 days to 9 days if assuming 30 days a moths

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

\(Distance = r\times time\)

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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Answer: this was confusing but she has  :

(2) $10 bills

(2) $5 bills

(3) $1 bills

10 * 2 = 20

5 * 2 = 10

1 * 3 = 3

20 + 10 + 3 = 33

(1) 25c

(2) 10c

(1) 5c

(4) 1c

.25 + .20 + .05 + .04 = 0.54

dollars + cents = total

so 33 + 0.54 = $33.54

The probability of event B, P(B), is 0.1667.

To find the probability of event B, we can use the formula for the probability of the intersection of two independent events:

P(A and B) = P(A) * P(B)

We are given that P(A and B) = 0.10 and P(A) = 0.6.

Let's substitute these values into the formula:

0.10 = 0.6 * P(B)

To solve for P(B), we divide both sides of the equation by 0.6:

0.10 / 0.6 = P(B)

Simplifying the division:

P(B) ≈ 0.1667

Therefore, the probability of event B, P(B), is approximately 0.1667.

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Answer:

D.

Step-by-step explanation:

To find the equation of g(x), we can substitute the point into each of the equations.

A. g(x) = (1/4x)^2

1 = (1/4 * 2)^2

1 = (1/2)^2

1 = 1/4

This statement is false, so this is not the equation.

B. g(x) = 1/2 * x^2

1 = 1/2 * (2)^2

1 = 1/2 * 4

1 = 2

This statement is false, so this is not the equation.

C. g(x) = 2x^2

1 = 2 * 2^2

1 = 2 * 4

1 = 8

This statement is false, so this is not the equation.

D. g(x) = (1/2x)^2.

1 = (1/2 * 2)^2

1 = 1^2

1 = 1

This statement is true, so this is your answer.

Hope this helps!

Listing all the elements in {α, β} × N × {w, z}. Since we can assign a unique natural number to each element, we have shown that the set {α, β} × N × {w, z} is countably infinite.

To prove that the set {α, β} × N × {w, z} is countably infinite, we need to show that its elements can be listed in a sequence indexed by the natural numbers.

Let's construct a sequence that lists all the elements of {α, β} × N × {w, z}:

Start with the element (α, 1, w).

Move to the next element by changing the second component:

(α, 2, w).

Continue this process for all natural numbers, always alternating between the elements {w, z}:

(α, 1, z), (α, 2, z), (α, 3, z), ...

Once all the elements with α as the first component and {w, z} as the third component are listed, move on to the next element with β as the first component and repeat the process:

(β, 1, w), (β, 2, w), (β, 1, z), (β, 2, z), (β, 3, z), ...

By following this sequence, we can list all the elements in {α, β} × N × {w, z}. Since we can assign a unique natural number to each element, we have shown that the set {α, β} × N × {w, z} is countably infinite.

Therefore, we have proved that the set {α, β} × N × {w, z} is countably infinite by describing a way to list its elements in a sequence indexed by the natural numbers.

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A pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions. Option D is the correct answer.

The dimension of an item in mathematics is, approximately speaking, the quantity of degrees of freedom of a moving point on the object. To put it another way, a dimension is indeed the amount of distinct factors or coordinates required to define the location of a point that must be on an object. For instance, a point has a dimension of zero; a line has a size of one since a point can only move along a line in one direction (or its opposite); a plane has a dimension of two; etc.

The volume of the wooden board is given by the formula:

V = (l)(b)(h)

V = (2)(6)(14)

V = 168 cubic inches.

The volume of pile of 3 boards has dimensions:

l = 14

b = 6

h = 3(2)

V = 3(168) = 504 cubic inches.

Similarly, piling the boards and changing the height.

The volume of pile of four boards = 4(168).

The volume of pile of 5 boards = 5(168)

The volume of pile of 6 boards = 6(168) = 2(3(168))  = 2(Volume of pile of 3 boards)

Hence, a pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions.

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