Answer:
The length of EF is [tex]4\sqrt{17}[/tex] units.
Step-by-step explanation:
The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1).
Using distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]BC=\sqrt{(3+1)^2+(1-2)^2}=\sqrt{17}[/tex]
It is given that ΔDEF ∼ ΔABC.
If two triangles are similar then the corresponding sides are proportional.
[tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]
[tex]\frac{AB}{4AB}=\frac{BC}{EF}[/tex] (DE = 4AB)
[tex]\frac{1}{4}=\frac{BC}{EF}[/tex]
[tex]EF=4\times BC[/tex]
[tex]EF=4\times \sqrt{17}[/tex]
[tex]EF=4\sqrt{17}[/tex]
Therefore the length of EF is [tex]4\sqrt{17}[/tex] units.
Describe a way you can use graham crackers to demonstrate the division problem 3 divided by 1/4 . Include the result in your description.
Matthew walks 5/8 mile to the bus stop each morning. how far will you walk in 5 days
If a piece of cardboard is 6 in long and I line up a hundred and ten of them what would be the length of my row and feet
How to do this cause I am confused
how much should Lauren, earning 7.80 an hour, make working a 44-hour week?
Answer:
343.2
Step-by-step explanation:
7.8*44=343.2
Victor Hernandez has a credit card that bases its finance charge on the average-daily-balance method-new purchases included. His monthly periodic rate is 2.9% and his finance charge for the most recent billing cycle was $37. Find his average daily balance.
How many different triangles can be constructed with side measurements 6 centimeters, 9, centimeters, and 13 centimeters?
1.exactly one triangle
2.more than one triangle
3.no triangles
If you could answer as fast as you can that would be great please
Pink, purple, red. If these colors would go in order, each used twice, what are all the possible combinations that can be made??
Which orderer pair can be removed so that the resulting graph represents a function? (-2,2) (1,3) (5,-4) or (-4,-4)
It will be B. (1,3)
Hope this helps!
A student attempted to generate an equivalent expression using the distributive property, as shown below:
4(x + 2) = x + 8
What was the mistake made?
4 was not multiplied by x
4 was not multiplied by 2
Incorrect sign was used for the first term
Incorrect sign was used for the second term
Answer:
4 was not Multiplied By X
Step-by-step explanation:
I need help simplifying this: √289
When you take the square root of a positive integer, how many possible answers are there? When you take the cube root of a positive or negative integer, how many possible answers are there?
What is the circumference of a circle with a radius of 6.1 centimeters?
Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth.
cm
please help
how to find the height of a cylinder knowing the volume
PLZ HELP FAST!!!!!!!
The triangles are similar. The area of the larger triangle is 729 cm².
What is the area of the smaller triangle?
10.5 cm²
31.5 cm²
67 cm²
81 cm²
Justin drove at a steady speed of 60 miles/hour. Write an equation to represent the relationship between the total distance Justin drove, 'd', in a certain amount of time, 't'. Which value is the dependent variable? Which is the dependent variable? Which is the independent variable? Explain.
Answer:
60d+t=
Step-by-step explanation:
what the answer
Select the statement that correctly describes the solution to this system of equations.
–3x + 2y = –22
–5y = –4x + 27
A
There is no solution.
B
There are infinitely many solutions.
C
There is exactly one solution at (8, 1).
D
There is exactly one solution at (1, 8)
Please solve this problem (surface area). With work bc my teacher said I need to show work with my answer
Write a trinomial of degree 35
which equation represents the pattern in the table below?
[tex]s = c + 4[/tex]
[tex]s = 4c[/tex]
[tex]c = s + 4[/tex]
[tex]c = 4s[/tex]
Answer:
[tex]c=s+4[/tex]
Step-by-step explanation:
We are given that a pattern in the table
We have to find which equation represents the pattern in the table.
Sail=3
Carrie's age=7
Let s be the sale's and c be the carrie's age
Sail=3
Carrie's age=7
Carrie's age=3+4
Sail=5
Carrie's age=9
Carrie's age=5+4
Sail=8
Carrie's age=12=8+4
Sail=13
Carrie's age=13+4
Sail=15
Carrie's age=19=15+4
Hence, [tex]C=S+4[/tex] is an equation which represents the pattern in the table.
Answer:[tex]c=s+4[/tex]
A right circular cylinder has a height of 19 3/4 ft and a diameter 1 2/5 times its height.
What is the volume of the cylinder?
Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
Height of cylinder = [tex] 19\frac{3}{4} =19.75 [/tex]ft
Diameter of cylinder = [tex] 1\frac{2}{5} [/tex]times its height = [tex] 1.4 * 19.75=27.65 [/tex]ft
Now Radius = half of diameter = [tex] \frac{27.65}{2} =13.825 [/tex]ft
Now we have to find the Volume of cylinder
formula for Volume of cylinder is
Volume of cylinder = [tex] \pi r^2 h [/tex]
let's plug the values
Volume of cylinder = [tex] (3.14)*(13.825)^2 *(19.75) [/tex]
Plug the values in calculator
= 11852.9657 cubic feet
Round off the answer to two decimal places(i.e. hundredth)
= 11852.97 cubic feet
Using the given points, determine the slope. (5,-6)and(2,15)
if f(x)= 2x^2+5sqrt(x-2), complete the following statement: The domain for f(x) is all real numbers _____ than or equal to 2. (fill in the blank)
Answer:
Greater.
Step-by-step explanation:
The in the function [tex]f(x)=2x^2+5\sqrt{x-2}[/tex], the square root term [tex]\sqrt{x-2}[/tex] has to give a real number if [tex]f(x)[/tex] is to be real. This can only happen if [tex]x\geq 2[/tex] because if [tex]x<2[/tex] then [tex]\sqrt{x-2}[/tex] will give a complex number and therefore [tex]f(x)[/tex] will not be real.
Thus, the domain for f(x) is all real numbers greater than or equal to 2.
The domain for f(x) is all real numbers greater than or equal to 2.
This is because the square root function is undefined when its argument is less than or equal to 0. So, the expression 5sqrt(x-2) is defined only when x-2 is greater than or equal to 0. This means that x must be greater than or equal to 2.
The domain of f(x) is all real numbers x such that x ≥ 2.
Here is a table that shows the values of f(x) for different values of x:
x | f(x)
2 | 20
3 | 29
4 | 42
5 | 57
6 | 74
As you can see, the values of f(x) are defined for all real numbers x such that x ≥ 2.
To learn more about domain here:
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A piece of wood is 3/4 meter long is being cut into smaller pieces that are each 1/10 meter long. Which expression is one of the steps in determining how many pieces can be cut?
A. 3/4 • 1/10
B. 3/4 • 10/1
C. 10/1 • 4/3
D. 1/10 • 3/4
At the library you find nine books on a certain topic the librarian tells you that 55% of the books on this topic have been signed out how many books does the library have available on the topic
Kim and her two brothers each use 1 1/2 cups of milk for breakfast how many fluid ounces of milk do they use in 4 days?
87.5% of what number is 49?
Mr. Malloy wants to make sure Amo and Javier get the best possible grade after five tests and can either give a grade based on the median or the mean.
Test
Number
Amo’s Scores
Javier’s Scores
1
97
68
2
92
97
3
89
65
4
55
92
5
90
65
What measure of center should Mr. Malloy use for Amo and for Javier for the best possible grade?
The teacher should use the mean for both Amo and Javier.
The teacher should use the median for both Amo and Javier.
The teacher should use the median for Amo and the mean for Javier.
The teacher should use the mean for Amo and the median for Javier.
Answer:
C: The teacher should use the median for Amo and the mean for Javier 2022
Step-by-step explanation:
I took the test and please mark brainly
AND PLEASE SCROLL DOWN WHENEVER YOUR LOOKING FOR ANSWERS BECAUSE THERE'S A REASON IT SOMETIMES SAYS 2 ANSWERS and if you see this please copy and paste this because some people are to lazy to scroll down and do work
For Amo, the median (89) is higher than the mean (84.6), and for Javier, the mean (77.4) is higher than the median (68). Thus, Mr. Malloy should use the median for Amo and the mean for Javier for the best possible grades.
Explanation:To determine the best possible grade for both Amo and Javier, we first need to calculate their mean and median scores. The mean is calculated by adding all the test scores together and dividing by the number of tests. The median is the middle score when all scores are listed in ascending order. If there is an even number of scores, the median is the average of the two middle scores.
Amo's Scores: 97, 92, 89, 55, 90
Javier's Scores: 68, 97, 65, 92, 65
For Amo, we calculate the mean as follows:
(97 + 92 + 89 + 55 + 90) / 5 = 84.6
The median for Amo would be the third score since there are five tests, which is 89.
For Javier, we calculate the mean as follows:
(68 + 97 + 65 + 92 + 65) / 5 = 77.4
The median for Javier would also be the third score, which is 68.
Now, comparing Amo's mean and median, we see that the median (89) of Amo's test scores is higher than the mean (84.6). Therefore, for Amo, Mr. Malloy should use the median.
Looking at Javier's mean and median, we see that the mean (77.4) of Javier's test scores is higher than the median (68). So, for Javier, Mr. Malloy should use the mean.
The teacher should use the median for Amo and the mean for Javier for the best possible grade.
What is the arm span of a 74 inch tall person
Final answer:
The arm span of a person is typically about equal to their height; therefore, a 74 inch tall person is likely to have an arm span of approximately 74 inches.
Explanation:
The arm span of a 74-inch tall person can be estimated based on certain proportions. In general, a person's arm span is approximately equal to their height. This means that a 74-inch tall person would have an arm span close to 74 inches.
The arm span of a person is generally very close to their total height. Based on anatomical studies and the concept that human body proportions tend to be relatively consistent regardless of overall size, a person who is 74 inches tall is likely to have an arm span that is also approximately 74 inches. However, it is important to note that while this is a common correlation, individual variations do exist and a precise measurement would require actual measurement rather than estimation.
A family reunion of 27 decided to go to Six Flags Magic Mountain. Adult tickets cost $40 each and child tickets cost $30 each. The total cost of all tickets was $930. Use the SUBSTITUTION METHOD to determine how many adults and how many child tickets were purchased?
To solve the problem, set up a system of equations with 'a' representing the number of adult tickets and 'c' representing the number of child tickets. Use the substitution method to solve for the variables. The solution is 12 adult tickets and 15 child tickets.
Explanation:To solve this problem using the substitution method, we need to set up a system of equations. Let's use the variables 'a' to represent the number of adult tickets and 'c' to represent the number of child tickets.
The cost equation can be expressed as: 40a + 30c = 930. This equation represents the total cost of all the tickets.
The quantity equation can be expressed as: a + c = 27. This equation represents the total number of people attending the reunion.
We can solve this system of equations using the substitution method. Multiply the second equation by 30 to get 30a + 30c = 810. Now subtract this equation from the first equation: 40a + 30c - (30a + 30c) = 930 - 810. Simplifying, we get: 10a = 120. Divide both sides by 10 to get a = 12.
Now that we know the number of adult tickets, we can substitute this value back into one of the original equations to solve for the number of child tickets. Using the second equation, we have: 12 + c = 27. Subtracting 12 from both sides, we get c = 15.
Therefore, 12 adult tickets and 15 child tickets were purchased.