Final answer:
The equation m∠DEF = m∠D'F'E' must be true following a 90° clockwise rotation of ∆DEF, because rotations preserve angle measures.
Explanation:
When a geometric figure such as ∆DEF is rotated 90° clockwise about a point A, to create ∆D'E'F, corresponding angles in the two triangles will be equal. This is true because a rotation is a type of rigid motion, which preserves angle measures. The equation m∠DEF = m∠D'F'E' must be true because the angle at F in the original triangle ∆DEF becomes the angle at E' in the rotated triangle ∆D'E'F, given the preservation of angle measures through rotation.
Therefore, for such geometric transformations, it's crucial to understand that rotations do not alter the internal angles of the shape being transformed, which is consistent with the rules of plane geometry. This principle is useful in solving many problems that involve the rotation of figures within a plane.
Cynthia glued a trapezoid with bases of 9 centimeters and 7 centimeters and a height of 6 centimeters onto a rectangular piece of construction paper that measures 20 centimeters by 24 centimeters. How much of the construction paper is not covered by the trapezoid?
Triangle BCD is similar to triangle ACE. If the triangles are isosceles, what is the length of AB?
F.) 16cm
G.) 11cm
H.) 40cm
J.) 35cm
What is the value of x? sin(x+34)°=cos(2x+20)°
Answer:
The value of x is 12
Step-by-step explanation:
What quadrilateral has exactly one pair of parallel sided?
Gigi’s parents pay $1,400 for a mortgage and $250 for a car loan each month. They pay $175 monthly for health insurance and spend about $300 a month on food. Utilities cost about $150 a month. They pay about $100 for the monthly Internet and cell phone plan and set aside $200 per month for retirement.
This month, Gigi’s parents spend $285 on food, $175 on utilities, and $112 on the Internet and cell phone plan. What are her parents’ total fixed and variable expenses this week?
fixed expenses total: $
variable expenses total: $
Use 2 points to write an equation for each function. Exponential functions.
Triangles ABC and DEF are similar. The ratio of the side lengths in triangle ABC to triangle DEF is 1:3. If the area of triangle ABC is 1 square unit, what is the area of triangle DEF?
Answer:
The area of triangle DEF is 9 square units.
Step-by-step explanation:
It is given that triangle ABC and DEF are similar and the ratio of the side lengths in triangle ABC to triangle DEF is 1:3.
Let the length of their sides be x and x respectively.
If two triangles are similar then the ratio of their areas is equal to the square of the ratio of their sides.
Since triangle ABC and DEF are similar, therefore
[tex]\frac{Area(ABC)}{Area(DE F)}=\frac{(x)^2}{(3x)^2}[/tex]
[tex]\frac{1}{Area(DE F)}=\frac{(x)^2}{9(x)^2}[/tex]
Cancel out the common factors.
[tex]\frac{1}{Area(DE F)}=\frac{1}{9}[/tex]
On cross multiplication, we get
[tex]1\times 9=1\times Area(DE F)}[/tex]
[tex]9=Area(DE F)}[/tex]
Therefore the area of triangle DEF is 9 square units.
Casey said 40 people were surveyed. I his answer reasonable?
How do you find the mean and medium of a data set?
Step-by-step explanation:
MEAN
First, add all the values together and divide by the number of values in the set. Imagine 3 people donated money to red cross. Their names are Allisa, John, and Thomas. Allisa gave 20 dollars, John gave 35, and Thomas gave 20. Next, you add the amount of money they donated, which is 70. Then you divide 70, the amount of money, by 3, because thats the amount of people that donated. Then you get a mean of 23.
To put it simpler,
add the values.
then, add the amount of whatever carries that value, such as people.
after, you devide the value and the amount of people or etc.
when you finish, your mean will be what you have divided.
Another example would be this.
There are several whales out in the ocean. One is the Cuvier's beaked whales, which can swim as deep as 2,992 m. Another whale, named the sperm whale, can swim down to at least 1,000 m.
So, what is the mean?
Once again, first, we add the value, which in this case, is how deep the whales can dive. We then get 3992 m.
Next, we add the amount of whatever carries that value, which in this case are whales.
after, you devide the value by the amount of whales.
when you finish, you will get 1996
MEDIAN
Arrange your numbers in numerical order. If they were scrambled like this, 9, 7, 3, 9, 6, 1, 5, rearrange them like this. 1, 3, 5, 6, 7, 9, 9.
When you do this, check how many numbers are in that row. In this case, the amount is 7, which is odd.
If you have an odd number like in the example above, select the number in the middle, which in our case, its 6. ( 1, 3, 5, 6, 7, 9, 9 ) So your median would be six, since median means "the middle number"
If you have an even number, add them together then divide by 2. Heres an example. 1, 3, 5, 6, 7, 9, 9. (1, 3, 5, 8, 12, 9, 9, 12) You would add 8 and 12. Your answer would be 20. So now, you divide 20 by 2. 20 divided by 2 is 10, so your median would be 10.
I did not plagerise this, I made these example up myself and solved them the way they are supposed to be and used these examples on another question similar to this.
Can someone help me please because I have a lot of trouble doing these problems. Please show work so I can see how you did it.
solve the equation -18 +3x = -6
What is the correct meaning of the word foresight?
Kim had the foresight to finish her homework early so she could attend the concert that night.
A) the ability to manage time effectively
B) the inability to see what might happen in the feature
C) a lack of regard for being responsible
D) the ability to look forward and plan ahead
Which of the following equations is the equation of the circle with the diameter AB and points A (0,0) and B (8,6) ?
If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width
If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width
Solution:
Let the length of rectangle=x
Width of rectangle=x/10
Perimeter is 2(Length+Width)
= 2(x+x/10)
Area of Rectangle= Length* Width=x*x/10
As, Perimeter=2(Area)
So,2(x+x/10)=2(x*x/10)
Multiplying the equation with 10, we get,
2(10x+x)=2x²
Adding Like terms, 10x+x=11x
2(11x)=2x^2
22x=2x²
2x²-22x=0
2x(x-11)=0
By Zero Product property, either x=0
or, x-11=0
or, x=11
So, Width=x/10=11/10=1.1
Checking:
So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2
Area=Length*Width=11*1.1=12.1
Hence, Perimeter= 2 Area
As,24.2=2*12.1=24.2
So, Perimeter=2 Area
So, Answer:Length of Rectangle=11 units
Width of Rectangle=1.1 units
Which of the following can be used to prove that triangle EFG is also a right triangle?
Prove that the sum of a and c is greater than b.
Prove that the sum of a and b is greater than c.
Prove that the ratio of EF and KL is greater than 1 and hence, the triangles are similar by AA postulate.
Prove that KL is equal to c by Pythagorean Theorem.
Answer:
Prove that KL is equal to c by Pythagorean Theorem.
Step-by-step explanation:
In the two triangles triangle KLM is a right triangle with sides a and b as the two legs of the right triangle .We can apply Pythagorean Theorem to find KL.
In triangle KGF two sides are a and b .If we prove KL=EF then Pythagorean Theorem will be true for triangle KGF and hence we can prove triangle KGF to be a right triangle.
The correct option to prove triangle KGF to be a right triangle is to Prove that KL is equal to c by Pythagorean Theorem.
Anna mixes the letters S, E, L, E, C, T, E, and D thoroughly. Without looking, Mary draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that E will NOT be the letter Mary selects?
The probability of not drawing an E is 5/8. Expressed as a decimal, it is 0.625, and as a percentage, it is 62.5%.
To determine the probability that the letter E is not selected by Mary, we first look at the total number of E's in the mix and the total number of letters. There are three E's and a total of eight letters. To calculate the probability of not drawing an E, we need to find the number of outcomes that are not E, which is 8 total letters minus 3 E's, leaving us with 5 non-E letters.
The probability of not drawing an E can be calculated as the number of non-E letters over the total number of letters: P(not E) = 5/8. To express this as a decimal, we divide 5 by 8 to get 0.625. To express it as a percentage, we simply multiply the decimal by 100, resulting in 62.5%.
Therefore, the probability that E will NOT be the letter Mary selects is 5/8 as a fraction, 0.625 as a decimal, and 62.5% as a percentage.
What is the MAD of the data set?
{5, 12, 1, 6, 11}
Enter your answer in the box
Answer:
Its 3.6
Step-by-step explanation:
You turn {5, 12, 1, 6, 11} into {2, 5, 6, 1, 4} add them into 18 then divide by 5 into 3.6
One pound of grapes costs $1.55. Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of 3.5 pounds of grapes?
Final answer:
The equation to find the cost of 3.5 pounds of grapes, with one pound costing $1.55, is represented by the proportion 1 pound / 3.5 pounds = $1.55 / x. By solving this equation, we find that x, the total cost for 3.5 pounds of grapes, is $1.55 multiplied by 3.5 = $5.425
Explanation:
The student is asking about the cost of 3.5 pounds of grapes, given that one pound costs $1.55. To find the equivalent ratio that can be used to calculate the cost of 3.5 pounds, we can set up a proportion where the cost of 1 pound is to 3.5 pounds as $1.55 is to the unknown cost (let's call it x). The equation representing the pair of equivalent ratios is:
1 pound / 3.5 pounds = $1.55 / x.
To solve for x, we multiply both sides of the equation by 3.5 pounds, which gives us:
1 pound * ($1.55 / 1 pound) * 3.5 = x
And this simplifies to:
x = $1.55 * 3.5 = $5.425
Therefore, by calculating $1.55 * 3.5, we can find the cost of 3.5 pounds of grapes.
which function represents an initial population that increases 22% per year where A represents the initial value and x represents time in years?
A)y=A(0.22)^x
B)y=A(0.68)^x
C)y=A(1.22)^x
D)A(1.68)^x
The population growth function represented by an initial value A that increases 22% per year with x representing time in years is y=A(1.22)^x.
Explanation:The function which represents an initial population that increases 22% per year, where A is the initial value and x is time in years, is given by y=A(1.22)^x. This formula calculates the future value (y) based on the premise of exponential growth, which embodies a continual increase year after year. The rate of growth is 22%, therefore we add this to 100% to get 122% (1.22). This entire value is raised to the power of x, representing the number of time periods (years).
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Reggie earns $12.65 per hour and works 38 hours per week. How much does he earn in a week before taxes are taken out?
In 1918, the temperature in Alaska dropped from 52 degrees to -23 degrees in 15 hours. What was the average hourly change in temperature?
what is the mean of 54,48,52,56,55
Please help asap will give brainliest!!!
Hello? How do you make a scatter plot?
Zöe schedules advertising for a radio station. She must fill 12 minutes each hour with 30 second ads and 60 second ads. Zöe sold twice as many 60 second ads as she did 30 second ads. She defines x as the number of 30 second ads and y as the number of 60 second ads that she sold. Zöe writes the system and . Which statement identifies Zöe’s error and the correction that is needed? Zöe used seconds to measure time for each ad, but she used minutes for the total. She should have used . Zöe set up an equation that would translate to “twice the number of 30 second ads = the number of 60 second ads.” She should have used . Zöe compared the number of 30 second ads to the number of 60 second ads without including the total number of ads. She should have used . Zöe did not include the whole hour in the total time. She should have used .
Zöe's error is in mixing units of seconds and minutes in her measurements. Her total time of 12 minutes should be converted into seconds (720 seconds) to match the 30 and 60 second ad times. The correct equations for her problem are x + 2y = 720 and y = 2x.
Explanation:The given question relates to system of linear equations and misunderstandings in time measurements. The discrepancy in Zöe's equations relates to the units she used for the ad times and the total time. She was dealing with 30 second and 60 second ads (measuring them in seconds), but she attempted to balance this against a total time of 12 minutes (measured in minutes).
The correct approach would be to ensure that all the times are using the same units. Since there are 60 seconds in a minute, Zöe's total time should be expressed as 720 seconds. Additionally, she sold twice as many 60 second ads as 30 second ads. Therefore, her equations should be: x + 2y = 720 and y = 2x.
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The question relates to formulating equations based on given constraints. Zöe's error is in not taking into account that the sum of the times for the 30 and 60-second ads should be 12 minutes. Moreover, the relation between the quantities of the 30 and 60-second ads should be such that the latter is double the former.
Explanation:The question presents a situation where Zöe has to schedule ads for a radio station with a fixed time frame. The constraints are that she has 12 minutes every hour to fill with either 30 second ads or 60 second ads, and that she sold twice as many 60 second ads as she did 30 second ads. Here, x represents the number of 30 second ads and y represents the number of 60 second ads.
Given these criteria, Zöe should set up two equations. The first equation will express the total time consumed by ads: (0.5x + y) minutes = 12 minutes. The second equation represents the relationship of the number of ads: y = 2x.
The error in the way the problem is stated seems to revolve around Zöe's representation of the constraints. She should consider the fact that the total time occupied by the 30 and 60-second ads must equal 12 minutes. Furthermore, the relationship between the number of 30 and 60-second ads should be factored into the equations, with the 60-second ads being twice the number of 30-second ads.
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talia has 2 red,1 blue and 4 green balls of the same size in the bag talia pulls one ball out of the bag without looking what is the probability that talia will pull a red ball out of the bag 2/2,5/7,2/5,2/7??
Final answer:
The probability that Talia will pull a red ball out of the bag is 2/7, given she has 2 red, 1 blue, and 4 green balls in the bag making a total of 7 balls.
Explanation:
The question you have asked is related to the subject of probability in mathematics. Specifically, it is about the probability of drawing a red ball from a bag containing red, blue, and green balls. To calculate this probability, you need to know the total number of balls and the number of red balls in the bag. Then, you use the formula for probability which is the number of favorable outcomes divided by the total number of possible outcomes.
In Talia's bag, there are 2 red, 1 blue, and 4 green balls, making a total of 2+1+4=7 balls. The probability of pulling a red ball out of the bag is the number of red balls divided by the total number of balls, which gives:
Probability of red ball = Number of red balls / Total number of balls = 2/7.
So, the correct answer to the probability that Talia will pull a red ball out of the bag is 2/7.
A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder
Given two terms from a geometric sequence, identify the first term and the common ratio: a5= 48 and a11= 3,072.
The first term of the geometric sequence is 3 and the common ratio is 2.
Explanation:To identify the first term and the common ratio of a geometric sequence, we can use the formula: an = a1 * r^(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term.
Given a5 = 48 and a11 = 3,072, we can substitute the values into the formula:
48 = a1 * r^(5-1)
3,072 = a1 * r^(11-1)
By dividing the second equation by the first equation, we can eliminate a1:
64 = r^6
Taking the sixth root of both sides gives:
r = 2
Substituting this value back into the first equation, we can solve for a1:
48 = a1 * 2^4
a1 = 3
So, the first term (a1) is 3 and the common ratio (r) is 2.
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Use geometry words to describe a way to separate triangles into other triangles?
Let us suppose we have a triangle ABC as shown in the attached image.
Now, let us we draw a perpendicular line from the vertex A to the base BC. Let the line meets the base BC at D.
Then, this perpendicular line AD will separate the triangle ABC into two right angle triangle ADB and triangle ADC.
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Help please