The pentagon ABCDE has been divided into six isosceles triangles, which all have the same perimeter. The triangle ABC is even equilateral. What is the ratio of the perimeter of the triangle ABC to the perimeter of the pentagon ABCDE?

A) 1:3
B) 4:9
C) 3:7
D) 9:16
E) 5:8​

Answer:

x=5.8

Step-by-step explanation:

a^2+b^2=c^2

3^2+5^2=x^2

9+25 = 34

[tex]\sqrt{34)[/tex] = 5.8

Answer:

[tex]17\sqrt{2}[/tex]  or approximately 5.83

Step-by-step explanation:

The triangle is a right triangle so we use Pythagorean theorem to find the missing side.

[tex]a^{2} + b^{2} =c^{2}[/tex]

x is the hypotenuse so that has to be the value of c but the other two sides are interchangeable.

[tex]3^{2} + 5^{2} = x^{2}\\\\9+25=x^{2} \\\\34=x^{2} \\[/tex]

Square both sides to isolate the x.

[tex]\sqrt{34} =x[/tex]

Simplify

[tex]17\sqrt{2} =x\\[/tex]

The word phrase "negative one fifth is bigger than or equal to the product of negative two thirds" is represented by the inequality "1/5 ≥ (-2/3) x," and its solution is x ≥ 3/10.

The inequality that symbolises the word phrase as supplied in the task content must be determined, as is evident from the assignment's content.

Negative one fifth is more than or equal to the product of negative two thirds and a number, which is how the disparity is expressed.

Therefore,

Let the number = y

- 1 / 5 ≥ - 2 / 3 × y

- 1 / 5 ≥ - 2 / 3 y

Now, multiply both sides of the inequality by - 3 / 2

Therefore,

- 1 / 5 (- 3 / 2) ≤ y

3 / 10 ≤ y

y ≥ 3 / 10

Therefore, y is greater than or equal to three tenths.

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Answer: 54°

Step-by-step explanation: As the sum of all angles in a Pentagon is 540°

so value of X is 540° - 456 = 54°

Using the Pythagorean theorem we know that the length of the given diagonal is 21.25 units respectively.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle.

This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

If a²+b²=c² and c is the triangle's longest side, the triangle is a right triangle.

If a triangle is not a right triangle, there are two additional types that can exist.

So, the formula is:

a² + b² = c²

Now, insert values as follows:

12.75² + 17² = c²

162.5625 + 289 = c²

451.5625 = c²

√451.5625 = c

21.25 = c

Therefore, using the Pythagorean theorem we know that the length of the given diagonal is 21.25 units respectively.

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An angle that is coterminal with -865° and has a measure between 0° and 360° is 75°. Since Angle b is coterminal with this angle, we can conclude that the measure of Angle b is 75°.

We must locate an angle that is coterminal with the -865° angle and has a measure between 0° and 360° in order to determine the size of angle b.

To do this, we can add or remove 360-degree multiples until we have an angle that is coterminal with -865° and is between 0° and 360°.

-865° + 360° = -505° (not between 0° and 360°)

-865° + 2(360°) = -145° (not between 0° and 360°)

-865° + 3(360°) = 75° (between 0° and 360°)

As a result, an angle with a measure between 0° and 360° that is coterminal with -865° is 75°. We can infer that Angle b's measure is 75° because it contaminates with this angle.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

We can use the kinematic equations of motion to solve this problem. Let's assume the initial velocity of the snowball is 16 feet per second and its initial height is 32 feet. Also, we know that the acceleration due to gravity is -32.2 feet per second squared (assuming downward direction as negative).

To find out when the snowball hits the ground, we can use the equation:

h = 32 + 16t - 16t^2

where h is the height of the snowball at time t. We want to find the value of t when h = 0 (since the snowball hits the ground at that point). Therefore, we can rewrite the equation as:

16t^2 - 16t - 32 = 0

Dividing both sides by 16, we get:

t^2 - t - 2 = 0

Solving for t using the quadratic formula, we get:

t = (1 ± √(1 + 8))/2

t = 2 seconds or -1 second

Since time cannot be negative, the snowball hits the ground after 2 seconds.

To find the maximum height the snowball reaches, we can use the fact that the maximum height occurs at the vertex of the parabolic trajectory. The x-coordinate of the vertex is given by:

t = -b/2a

where a and b are the coefficients of the quadratic equation. In this case, a = 16 and b = -16, so:

t = -(-16)/(2*16) = 0.5 seconds

To find the corresponding height, we can substitute t = 0.5 seconds into the equation for h:

h = 32 + 16(0.5) - 16(0.5)^2

h = 36 feet

Therefore, the maximum height the snowball reaches is 36 feet.

By answering the presented question, we may conclude that Therefore, trigonometry the given identity is true.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.  

= 1/sin x

= √(1/sin²x - 1) / (1/sin²x)

= √(1 - sin²x) / sin x

= √(cos²x) / sin x

= √(1 - sin²x) / cos x

= √(csc²x - 1) / cos x

cos x = √(csc²x - 1) / cos x

cos²x = csc²x - 1

cos²x + sin²x = csc²x

1 = csc²x

Therefore, the given identity is true.

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The answer of the given question is the solution to the inequality h(t) > 9 is any value of t that makes h(t) greater than 9.

An inequality is a mathematical statement that shows a relationship between two values or expressions that are not equal. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to express the relationship between the two values. Inequalities are often used in algebra, geometry, calculus, and other areas of mathematics to represent constraints or limits on values or to compare two different sets of values. For example, an inequality might be used to determine if a certain number falls within a certain range, or to find the maximum or minimum value of a function given certain constraints.

The solution to the inequality h(t) > 9 is any value of t that makes h(t) greater than 9.

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The power from the main engines, P = 0.

What is power?

Let P be the power from the main engines. Then, the total power of the space shuttle during launch is:

Total power = Power from solid rocket boosters + Power from main engines

Total power = 9,750,000,000 watts + P

We can isolate P by subtracting the power from the solid rocket boosters from both sides:

P = Total power - Power from solid rocket boosters

P = (9,750,000,000 watts + P) - 9,750,000,000 watts

P = P

Simplifying, we get:

P = 0

This means that the power from the main engines is zero. However, this result is not realistic since the space shuttle requires power from both the solid rocket boosters and the main engines to launch. Therefore, there may be an error in the given information or additional information is needed to accurately solve the problem.

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When Gracie distributes her carrots equally among the 5 bunnies, each bunny gets 7,878 whole carrots, and 3,939 whole carrots remain without being given to a bunny. These figures are whole numbers.According to the statement, Gracie has 5 pet bunnies that love to eat whole carrots. Gracie has 3,939 carrots to feed the bunnies, and she will use as many carrots as she can and give each bunny the same number.

To calculate the number of carrots each bunny will get:Total number of whole carrots ÷ Total number of bunnies = Number of whole carrots each bunny gets Gracie distributes the 3,939 carrots equally among the 5 bunnies, with each bunny getting 7,878 carrots. This is illustrated in the calculation below:3,939 ÷ 5 = 7,878Hence, the number of whole carrots each bunny gets is 7,878.

When it comes to the number of carrots that remain without being given to a bunny, we need to calculate it using the following formula:Total number of whole carrots − (Number of whole carrots each bunny gets × Total number of bunnies) = Number of whole carrots that remain without being given to a bunnyUsing the figures from the above calculations, the computation will be as follows:3,939 − (7,878 × 5) = 3,939 − 39,390 = -35,451. Therefore, the number of whole carrots that remain without being given to a bunny is -35,451. However, since the answer must be a whole number, we can round this up to 0 carrots. This implies that all of the carrots were given to the bunnies.

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The new coordinates for point D after the rotation are (-4, 3).

To find the coordinates of each point after quadrilateral ABCD is rotated 270° counterclockwise about the origin, we can use the following formula:

(x', y') = (-y, x)

where (x, y) are the original coordinates of the point and (x', y') are the new coordinates after the rotation.

Starting with point A, which has coordinates (2, 1), we plug in the values into the formula:

(x', y') = (-y, x)
(-1, 2)

So the new coordinates for point A after the rotation are (-1, 2).

Moving on to point B, which has coordinates (4, 3), we apply the same formula:

(x', y') = (-y, x)
(-3, 4)

Therefore, the new coordinates for point B after the rotation are (-3, 4).

For point C, which has coordinates (5, 6), we get:

(x', y') = (-y, x)
(-6, 5)

Hence, the new coordinates for point C after the rotation are (-6, 5).

Finally, for point D, which has coordinates (3, 4), we have:

(x', y') = (-y, x)
(-4, 3)


So, the coordinates of each point after quadrilateral ABCD is rotated 270° counterclockwise about the origin are:

A' = (-1, 2)
B' = (-3, 4)
C' = (-6, 5)
D' = (-4, 3)

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Answer:

1, 2, 3, 5

Step-by-step explanation:

Answer:

To find the cubic function with the given roots, we can use the factored form of a cubic function:

f(x) = a(x - r1)(x - r2)(x - r3)

where r1, r2, and r3 are the roots of the function.

Substituting the given roots, we get:

f(x) = a(x + 9)(x + 5)(x - 3)

To find the leading coefficient a, we need to use the y-intercept of the function, which is given as -27.

When x = 0, the function becomes:

f(0) = a(9)(5)(-3) = -27

Simplifying and solving for a, we get:

a = -27 / (9)(5)(-3) = 0.6

Rounding to two decimal places, the leading coefficient of the cubic function is a = 0.60.

Answer:

[tex]81 {d}^{4} {e}^{7} [/tex]

Step-by-step explanation:

Use properties of degrees:

1. When multiplying different degrees on one term, the degree indicators must be multiplied, for example:

[tex]( { {x}^{2}) }^{3} = {x}^{2 \times 3} = {x}^{6} [/tex]

2. When dividing like terms (with the same base) with different degrees, the degree indicators must be subtracted, for example:

[tex] \frac{ {x}^{5} }{ {x}^{2} } = {x}^{5 - 2} = {x}^{3} [/tex]

3. When squaring a negative term in parentheses, the minus is eliminated, for example:

[tex]( { - 3x})^{2} = 9 {x}^{2} [/tex]

.

[tex] \frac{ {(( { - 3d})^{2} \times {e}^{4} )}^{3} }{ {9d}^{2} \times {e}^{5} } = \frac{729 {d}^{6} \times {e}^{12} }{9 {d}^{2} \times {e}^{5} } = 81 {d}^{4} \times {e}^{7} [/tex]

The solution to the system of Equations is x = 1 and y = -2.

Binh was solving a system of equations using the graphing method. This method involves graphing the given equations and finding the point where the graphs intersect. In this case, Binh incorrectly graphed the equation y = x - 3.

To solve the system correctly, Binh should follow these steps:

1. Rewrite the equation, if needed, in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The given equation, y = x - 3, is already in this form.

2. Determine the slope (m) and the y-intercept (b) of the equation. For the equation y = x - 3, the slope (m) is 1 and the y-intercept (b) is -3.

3. Graph the equation by first plotting the y-intercept on the y-axis and then using the slope to find additional points on the graph.

4. Repeat steps 1-3 for the second equation in the system.

5. Observe where the graphs intersect. This point represents the solution to the system of equations.

In this case, Binh should have found the point of intersection to be (1, -2). This means that the solution to the system of equations is x = 1 and y = -2. By accurately graphing the equations and finding the correct point of intersection, Binh can ensure that they have solved the system of equations correctly.

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Answer: 61.56%

Step-by-step explanation:

To find what percent 39.4 is of 64, we can use the following formula:

(percent / 100) * 64 = 39.4

Solving for percent, we get:

percent = (39.4 / 64) * 100

percent = 0.615625 * 100

percent = 61.56 (rounded to the nearest hundredth)

Therefore, 39.4 is approximately 61.56% of 64 when rounded to the nearest hundredth.

We can conclude that Bus 14 typically has the faster travel time since its median is lower than that of Bus 47.

When data are sorted in ascending or descending order, the median, a measure of center, indicates the dataset's middle value. Extreme numbers or data outliers have no impact on it.

From the given information, we know that the median travel time for Bus 47 is 16 and the median travel time for Bus 14 is 14.

What is median?

When values are arranged in order of magnitude, the median, a measure of central tendency, indicates the midpoint of the dataset. You must organise the values in ascending order from smallest to largest before determining the middle value to determine the median.

The mean, on the other hand, is affected by extreme values or outliers in the data, which can skew the value. Therefore, we cannot solely rely on the mean to compare the travel times of the two buses. However, for completeness, we also have the mean travel times of Bus 47 and Bus 14, which are both given as 16 and 14, respectively.

Therefore, we can conclude that Bus 14 typically has the faster travel time since its median is lower than that of Bus 47.

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Answer:

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{JK}\\ a=\stackrel{adjacent}{5}\\ o=\stackrel{opposite}{49} \end{cases} \\\\\\ JK=\sqrt{ 5^2 + 4.9^2}\implies JK=\sqrt{ 25 + 24.01 } \implies JK=\sqrt{ 49.01 }\implies JK\approx 7[/tex]

Answer:

y = x - 5

Step-by-step explanation:

y = x -6

y = MX +C

.: m = 1 ( where m is the gradient of the line)

Let gradient = gradient 2 ( because the lines are parallel to each other)

m1= m2

1= y- y1 / x - x1

( 9,4) = ( x1 , y1 )

.: 1= y - 4 / x - 9

Cross multiply

1( x -9) = y - 4

x - 9 = y - 4

y = x - 9 + 4

y = x - 5

.: The equation of the line is y = x -5

The answer can also be written as y - 4 = 1( x -9)

Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

P(X=k) = [tex]C(n,k)[/tex][tex]* p^k * (1-p)^{n-k}[/tex]

Where:

P(X=k) is the probability of getting k successes

n is the total number of trials

k is the number of successful trials

p is the probability of success in one trial

(1-p) is the probability of failure in one trial

here, in the question given that

n = 30 (total number of rolls)

k = 3, 4, 5, 6, or 7 (number of times rolling a 4)

p = 1/6 (probability of rolling a 4 on one roll)

Now we can calculate the probability of rolling a 4 between 3 and 7 times:

P(3<=X<=7) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)

now for  each value of k, we get:

[tex]P(X=3) = C(30,3) * (1/6)^3 * (5/6)^{27} = 0.182[/tex]

[tex]P(X=4) = C(30,4) * (1/6)^4 * x)5/6)^{26} = 0.106\\P(X=5) = C(30,5) * (1/6)^5 * (5/6)^{25} = 0.035\\P(X=6) = C(30,6) * (1/6)^6 * (5/6)^{24} = 0.008\\P(X=7) = C(30,7) * (1/6)^7 * (5/6)^{23} = 0.001[/tex]

Adding these probabilities , we get:

P(3<=X<=7) = 0.182 + 0.106 + 0.035 + 0.008 + 0.001 = 0.332

Therefore, the probability that Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

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If an acute angle increases, then its supplement decreases.

To give you a short quick answer, the supplement is going to have to decrease or get smaller.

Example

Suppose the acute angle is 10 (anything under 90 will do).

Then the supplement is going to be 180 - 10 = 170

Now suppose the acute angle increase to 50 degrees.

That means the supplement will go from 180 - 50 = 130

Conclusion

As the acute angle gets bigger, the supplement gets smaller. This is an important idea to get clear. Bigger and Smaller or More or Less can be ugly little words, so anytime you come across them, pay attention. It will make your life in science so much easier

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Answer:

The cost of 4 dozen eggs is 4 * $1.25 = $5.

The cost of half a gallon of milk is $2.97.

The total cost of the eggs and milk is $5 + $2.97 = $7.97.

Since Chase has only $10, the minimum price for a dozen eggs is $10 - $7.97 = $2.03.

So the answer is 2.03

Step-by-step explanation:

The range of the parabola is (-∞, -2). So correct option is A.

A parabola is a U-shaped curve that is defined by a quadratic equation of the form y = ax² + bx + c, where a, b, and c are constants. The graph of a parabola is symmetric around a vertical line called the axis of symmetry, which passes through the vertex of the parabola. The vertex is the point on the parabola where it changes direction.

The shape and position of a parabola depend on the values of the coefficients a, b, and c. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The value of b determines the horizontal position of the vertex, and the value of c determines the vertical position of the vertex.

Parabolas have many applications in mathematics, physics, engineering, and other fields. For example, the trajectory of a projectile launched into the air can be modeled by a parabolic curve, and the reflector dish of a satellite dish antenna is shaped like a parabolic curve to focus incoming signals at a single point.

The range of the parabola is (-∞, -2). So correct option is A.

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Answer:

158

Step-by-step explanation:

If a person has a slow reaction time that puts them in the top 10% of responses, it means that their reaction time is slower than 90% of the population.

The value that separates the top 10% of responses from the bottom 90% is determined by the distribution of reaction times in the population.

Assuming a normal distribution of reaction times, the value that separates the top 10% of responses from the bottom 90% is the 90th percentile. This means that 90% of the population has a reaction time below this value, while the top 10% have a reaction time equal to or above it.

The specific value that separates the top 10% from the bottom 90% can vary depending on the population being studied and the task being performed. However, in general, a value around 1.5 standard deviations above the mean reaction time would be a reasonable estimate for the 90th percentile.

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Answer:

6000

Convert 8 and 10 to a decimal

8=0.8

10=0.1

0.1*0.8=0.8

4800/0.8=6000

Step-by-step explanation:

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The average speed of the bus is 600 meters / 900 seconds = 2/3 meters/second, or approximately 0.67 meters/second.

To find the average speed of the bus, we need to follow these steps:
1. Determine the total distance traveled:

Since each block is 100 meters long and the bus travels 6 blocks, the total distance is 6 blocks * 100 meters/block = 600 meters.
2. Determine the total time taken: .

The bus travels this distance in 15 minutes, so we need to convert this time to seconds.

Since there are 60 seconds in a minute, the total time taken is 15 minutes * 60 seconds/minute = 900 seconds.
3. Calculate the average speed:

The average speed is the total distance traveled divided by the total time taken.

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