The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.
What is? (attached)
Answers
The dashed line segments form 30-degree angles in the given diagram of a regular hexagon and triangle.
In the given diagram, hexagon GIKMPR and triangle FJN are regular. The dashed line segments form 30-degree angles.
Since hexagon GIKMPR is regular, all its interior angles are equal. Each angle of a regular hexagon is 120 degrees, so angle GIK is 120 degrees.
The angle at GIK can be split into two equal angles by the dashed line segment, so each of these angles measures 60 degrees.
Similarly, since triangle FJN is regular, each of its angles measures 60 degrees.
Therefore, the dashed line segments form two 30-degree angles each side of the regular hexagon and triangle.
The correct answer is option d. The image of [tex]\overline{OQ}[/tex] after a rotation of 300 degrees about point O is [tex]\overline{OF}[/tex].
To find the image of line segment [tex]\( \overline{OQ} \)[/tex] after a rotation of [tex]\( 300^\circ \)[/tex] about point O, we need to understand that a rotation of [tex]\( 300^\circ \)[/tex] is equivalent to rotating [tex]\( 60^\circ \)[/tex] clockwise. This is because rotating [tex]\( 360^\circ \)[/tex] would bring us back to the original position, so a rotation of [tex]\( 300^\circ \)[/tex] is the same as rotating [tex]\( 360^\circ - 60^\circ = 300^\circ \)[/tex].
Given that line segment [tex]\( \overline{OQ} \)[/tex] forms a [tex]\( 30^\circ \)[/tex] angle with the dashed lines, after a rotation of [tex]\( 300^\circ \)[/tex], it will form a [tex]\( 30^\circ \)[/tex] angle with the new position of the dashed lines.
Therefore, the image of line segment [tex]\( \overline{OQ} \)[/tex] after the rotation is [tex]\( \overline{OF} \)[/tex].
The complete question
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.
Find the image of [tex]\overline{OQ}[/tex] after a rotation of 300 degree about point O.
a. [tex]\overline{OJ}[/tex]
b. [tex]\overline{OH}[/tex]
c. [tex]\overline{OQ}[/tex]
d. [tex]\overline{OF}[/tex]
Related Questions
what number must you add to complete the square? x^2+6x=15
Answers
Final answer:
To complete the square for the equation [tex]x^2 + 6x = 15,[/tex] you must add 9 to both sides to form the perfect square [tex]trinomial (x + 3)^2 = 24.[/tex]
Explanation:
To complete the square for the equation [tex]x^2 + 6x = 15,[/tex]we need to add a number to both sides of the equation to form a perfect square trinomial on the left side.
Completing the square involves taking half of the linear coefficient (6), squaring it, and adding that value to both sides. Since half of 6 is 3, and 3 squared is 9, we must add 9 to both sides of the equation.
Therefore, our new equation would be[tex]x^2 + 6x + 9 = 15 + 9[/tex] , which simplified to [tex](x + 3)^2 = 24.[/tex]
Determine the ordered pair that lies on the unit circle corresponding to startfraction 5 pi over 4 endfraction .
Answers
A red candle is 8 inches tall and burns at a rate of 710 inch per hour. a blue candle is 6 inches tall and burns at a rate of 15 inch per hour. after how many hours will both candles be the same height? enter your answer in the box.
Answers
Initial height = 8 in
Burn rate = 710 in/h
After x hours, the height will be
h₁ = 8 - 710x
Blue candle:
Initial height = 6 in
Burn rate = 15 in/h
After x hours, the height will be
h₂ = 6 - 15x
When the two heights are equal, then
h₁ = h₂
8 - 710x = 6 - 15x
-695x = -2
x = 0.00288 hours
Answer:
The answer may take one of these forms:
0.003 hours, or
0.0029 hours, or
0.00288 hours.
Answer:
5 hour
Step-by-step explanation:
Hi can I find the missing coordinates of this parallelogram ?
Answers
Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime’s account after his deposit on Thursday?
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To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
At approximately what angle does the wire meet the ground?
Answers
12 feet would be the hypotenuse...
56.4 degrees my friend. That is ur answer.
Think about what you have learned about parallel and perpendicular lines. In what profession might a person rely upon this information? Describe how that person would apply these concepts.
Answers
the top of a certain mountain in California has an altitude of 14,721 ft above sea level. The bottom Death Valley is 282 ft below sea level. using 0 as sea level, find the difference between these two elevations. what is the difference between these two elevations?
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EXPERTS/ACE OR PEOPLE THAT KNOW IT QUICK PLZ. !!
Answers
[tex] \frac{y1-y2}{x1-x2} [/tex]
Using that, with the cost being the y values and the amount of pounds being the x values, we have (20, 25) at one point and (50, 40) at another. For our equation, we have
[tex] \frac{40-25}{50-20} = \frac{15}{30} [/tex]
Dividing both the numerator and denominator by 15 (we know they are both factors of 15 with a little guess and check), we have 1/2 or 0.5 as our answer
The product of 19 and a number , subtracted from the reciprocal of the number cubed
Answers
Final answer:
The expression for the product of 19 and a number, subtracted from the reciprocal of the number cubed, is represented as (1/x)³ - 19x. It involves finding the product of 19 and a variable, taking the reciprocal of the variable, cubing it, and then performing the subtraction.
Explanation:
The original question is asking for the expression of a mathematical operation involving a variable and its reciprocal raised to a power. Specifically, the operation is the product of 19 and a number, subtracted from the reciprocal of the number cubed. When constructing this expression, we denote the unknown number as x and perform the following steps:
Identify the product of 19 and x, which is 19x.
Find the reciprocal of x, which is 1/x.
Cube the reciprocal of x to get (1/x)³.
Subtract the product of 19 and x from the cubed reciprocal to get the final expression (1/x)³ - 19x.
This expression represents the mathematical relationship detailed in the question. To simplify or evaluate this expression, additional information about the value of x would be required.
There are 180 pages in the book Diana is reading. Diana has read 90 pages. What percent of the book has she read?
Answers
=90/180×100%
=1/2×100%
=50%
Thus the percentage is 50%
A small airplane used 5 2/3 gallons of fuel to fly 2 hour trip. How many gallons were used each hour
Answers
rewrite the expression as a multiple of a sum of two numbers with no common factor 15+24 _____
Answers
15 + 24 = 3(5 + 8)
To rewrite the expression as a multiple of a sum of two numbers with no common factor, find the prime factorizations of the given numbers and then multiply them together which brings the result as 39.
Explanation:To rewrite the expression as a multiple of a sum of two numbers with no common factor, we need to find two numbers that have no common factors and multiply them together. Let's find the prime factorizations of 15 and 24:
15: 3 × 524: 2 × 2 × 2 × 3Now we can rewrite the expression as:
15 + 24 = (3 × 5) + (2 × 2 × 2 × 3) = 3 × (5 + 8) = 3 × 13 = 39
So, 15 + 24 can be written as a multiple of 3 × 13, which is 39.
Which postulate or theorem can be used to prove that △ABD≅△CBD?
ASA Congruence Postulate
SAS Congruence Postulate
SSS Congruence Postulate
HL Congruence Theorem
Answers
The congruent angles given is the included angle such that the postulate should be named, SAS.
The answer to this item is the second choice.
Answer:
SAS
Step-by-step explanation:
How many complex roots does the polynomial equation have?
−3x^4−7x+17=0
2
3
4
5
Answers
Which is the next number in this pattern. What is the rule ? 0,1,1.5,1.75
A.2
B.1.875
C.1.85
D.1.8
Answers
the table shows the sales of admission tickets to a science museum. A table labeled Science Museum Admission Revenue. It contains a row for Tickets Sold with the amounts 128, 264, 308, 514, 520, 650, 722, and a row for Sales with the amounts 1088, 2244, 2618, 4369, 5525, and 6137. The equation y = 9.75x represents the number of dollars, y, earned by an art museum for selling x tickets. Which statements about the costs of the admission tickets at the museums are true? Select each correct answer. It costs $9.75 per ticket for admission to the art museum. It costs $8.75 per ticket for admission to the science museum. Art museum tickets are more expensive than science museum tickets. Given the same number of ticket sales, the science museum earns more revenue. 1 2 3 4 5
Answers
Answer: It costs $9.75 per ticket for admission to the art museum.
Art museum tickets are more expensive than science museum tickets.
Step-by-step explanation:
From the given table of Science Museum Admission Revenue, we can see that the sales amount by selling 128 tickets = $1088
Therefore, the cost of each ticket for science museum =[tex]\frac{1088}{128}=\$8.5[/tex]
∴ It costs $8.5 (not 8.75) per ticket for admission to the science museum.
Also,The equation [tex]y = 9.75x[/tex] represents the number of dollars, y, earned by an art museum for selling x tickets.
At x=1, y=9.75
∴ It costs $9.75 per ticket for admission to the art museum.
Clearly, 9.75>8.5
∴ Art museum tickets are more expensive than science museum tickets.
If the number of ticket sales will be same then art museum will earn more revenue.
Since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
Price per ticket to a science museum:
Given the table showing the sales of admission tickets to a science museum:
Thus,
The unit rate/price per ticket sold at the science museum using a pair of values from the table, say, (128, 1088) is: y/x
Thus:
unit rate/price per ticket = [tex]\frac{1088}{128} = 8.5[/tex]That is, a ticket to a science museum costs $8.5.
Price per ticket to an art museum:
The equation, y = 9.75x is given as the equation modelling the situation.
Where x = number of tickets soldy = amount in dollarsThus, this means that the price per ticket to the art museum is: $9.75.
Therefore, since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
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Solve. 5m+72=−2m+52 Drag and drop the answer into the box.
Answers
5m + 72 + 2m = -2m + 52 + 2m
7m + 72 = 52
7m + 72 - 72 = 52 - 72
7m = -20
7m/7 = -20/7
m = -20/7
If ST=3x, TU=7x, and SU=10, what is ST?
Answers
Final answer:
To find the value of ST, we set up the equation 3x + 7x = 10, solve for x, and then calculate ST as 3(1), which gives us ST = 3.
Explanation:
The student is asking to solve for ST, given that ST=3x, TU=7x, and SU=10. This is a segment addition problem, where ST and TU make up the whole segment SU. To solve it, you would first set up the equation ST + TU = SU. Substituting the given values, we get:
3x + 7x = 1010x = 10x = 1After finding the value of x, we substitute it back into the expression for ST:
ST = 3xST = 3(1)ST = 3So, the segment ST is 3 units long.
Decide which of the two points lies on the graph of the line
X+y=6
A. 2,2
B. 5,1
Answers
x = 5
y = 1
plug in 5 and 1 to x and y
5 + 1 = 6
True
your answer is B
hope this helps
Max rented a motorbike at $465 for 5 days. If he rents the same motorbike for a week, he has to pay a total rent of $625.
Write an equation in the standard form (Ax + By = C) to represent the total rent (y) that Max has to pay for renting the motorbike for x days.
Answers
For a normal distribution, the z value for an x value that is to the right of the mean is always:
Answers
In a normal distribution, the Z value for an X value that is to the right of the mean is always positive. It indicates how many standard deviations X is larger than the mean. Conversely, Z values are negative for X values to the left of the mean because they are smaller than the mean.
Explanation:In a normal distribution, the Z value corresponds to the number of standard deviations a value X is from the mean. Specifically, for an X value that is to the right of the mean, the Z score will always be positive. This is because values to the right of the mean are larger than the mean.
For example, if X = 10 and the mean is 5, and this corresponds to a Z score of 2.5, it means that X is 2.5 standard deviations to the right of the mean. In other words, X is larger than the mean by 2.5 times the standard deviation. The actual Z score, such as 2.5 in this example, indicates how far the score is from the mean, with greater Z scores indicating values further to the right of the mean.
In contrast, X values to the left of the mean have negative Z scores, indicating they are smaller than the mean. Finally, if X equals the mean, then X has a Z score of zero. This basic understanding of Z scores and their relation to the mean in a normal distribution is crucial in many statistical analyses.
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Which transformations are needed to change the parent cosine function to y=3cos(10(x-pi))
Answers
The parent cosine function is transformed [tex]y=3cos(10(x-\pi ))[/tex] by vertically stretching it by a factor of 3 (amplitude), horizontally compressing it by a factor of 10 (frequency), and shifting it to the right by [tex]\pi[/tex] units (horizontal shift or phase shift).
The question asks which transformations are required to alter the parent cosine function to [tex]y=3cos(10(x-\pi ))[/tex]. The transformations involved in this equation are:
Amplitude modification: The coefficient '3' indicates that the amplitude of the cosine function is scaled by a factor of 3.Frequency adjustment: The factor '10' inside the cosine function affects the function's frequency, indicating the function has 10 complete cycles within the interval of [tex]2\pi[/tex] radians. This is a horizontal scaling transformation.Horizontal shift (or phase shift): The subtraction of [tex]\pi[/tex] within the argument of the cosine function translates the function [tex]\pi[/tex] units to the right along the x-axis.No vertical shift is present because there is no addition or subtraction outside the cosine function.
To transform the parent cosine function [tex]\(y = \cos(x)\) to \(y = 3 \cos(10(x-\pi))\)[/tex], apply a vertical stretch by 3, horizontal compression by 1/10, and a right shift by [tex]\(\pi\)[/tex] units.
To transform the parent cosine function[tex]\(y = \cos(x)\)[/tex] to the function [tex]\(y = 3 \cos(10(x-\pi))\)[/tex], we need to apply the following transformations:
1. Amplitude change: Multiply the function by [tex]\(3\)[/tex], which increases the amplitude.
2. Horizontal compression: Multiply the input of the cosine function by [tex]\(10\),[/tex]which compresses the graph horizontally.
3. Phase shift: Shift the graph to the right by [tex]\(\pi\)[/tex]units, indicated by the term [tex]\(x - \pi\).[/tex]
So, the transformations needed are:
- Amplitude change: Vertical stretch by a factor of [tex]\(3\).[/tex]
- Horizontal compression: Compression by a factor of [tex]\(1/10\).[/tex]
- Phase shift: Right shift by [tex]\(\pi\)[/tex] units.
Which of the following has the ability to turn light energy into chemical energy? A. a generator B. an automobile C. a tree D. water
Answers
Find an equation for the horizontal line that passes through the point (10 , -13 )
Answers
A painter uses 1.2 liters of the paint to cover 1m2 of the wall. How many square meters he can cover with (1)12 liters; (2)6.6 liters; (3)4.8 liters of paint?
Answers
Answer:
He can cover 10 sq. meters using 12 liters, 5.5 sq. meters using 6.6 liters, and 4 sq. meters using 4.8 liters of paint.
Step-by-step explanation:
1. 12 LITERS/ 1.2 LITERS = 10 SQ. METERS
2. 6.6 LITERS/ 1.2 LITERS = 5.5 SQ. METERS
3. 4.8 ITERS/ 1.2 LITERS = 4 SQ. METERS
Explain how the common difference in an arithmetic sequence is like the slope of a linear function. read more >>
Answers
[tex]T_n=a+(n-1)d[/tex]
For a linear function with y-intercept, c, and slope, m, the linear function is given by:
[tex]y=mx+c[/tex]
Comparing the equation of the arithmetic sequence and that of the linear function, we can see that y is compared to Tn, a is compared to c, m is compared to d, and x is compared to n - 1.
Therefore, the common difference in an arithmetic sequence is like the slope of a linear function as both are multiple of a variable.
A circle with radius 5 and a center at (2, 3) was transformed to a circle with radius 10 and a center of (‒1, 4).
Show that the two circles are similar by describing the transformations that would have to be performed.
Answers
Answer:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
Let the origin in first case(radius 5) be at (0,0) , so if we shift the origin to (2-(-1),3-(4)) = (3,-1) {shifting origin to shift the first circle to second's place}. So, we arrive at a circle of radius 5 and center (-1,4).
Since similarly has no constraints on size comparison increase the radius to 10 units. Thus we arrive at the circle of radius 10 and center (-1,4).
Step-by-step explanation:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
What is the significance of the mean of a probability distribution? choose the correct answer below.
a. it gives information about how the outcomes vary.
b. it represents the most likely possible outcome.
c. it is the expected value of a discrete random variable.
d. it can never be negative?
Answers
Answer:
Step-by-step explanation:
ANSWER C : It is the expected value of a discrete random variable
2 people are going to equally share 5 kg, of chocolate. how many kilograms of chocolate should each person get?
Answers
5 kilograms divided by 2 is 2.5 kilograms