The coordinates of the vertices of a triangle are E(4,5), F(16,17 and G(10, 5) Let H be the midpoint of segment "EG" and let J be the midpoint of segment "FG".Verify the Triangle Midsegment Theorem by showing that segment "HJ" is parallel to segment "EF" and HJ = 1/2EF.
Answers
The coordinates of the vertices of a triangle are E(4,5), F(16,17 and G(10, 5) Let H be the midpoint of segment "EG" and let J be the midpoint of segment "FG".
Verify the Triangle Midsegment Theorem by showing that segment "HJ" is parallel to segment "EF" and HJ = 1/2EF.
step 1
Find out the midpoint H
The formula to calculate the midpoint between two points is equal to
\((\frac{x1+x2}{2},\frac{y1+y2}{2})\)we have
E(4,5) and G(10, -5)
substitute given coordinates
\(\begin{gathered} H=(\frac{4+10}{2},\frac{5-5}{2}) \\ H(7,0) \end{gathered}\)step 2
Find out the midpoint J
we have
F(16,17) and G(10, -5)
substitute
\(\begin{gathered} J=(\frac{16+10}{2},\frac{17-5}{2}) \\ J(13,6) \end{gathered}\)step 3
Find out the slope HJ
H(7,0) and J(13,6)
m=(6-0)/(13-7)
m=6/6
m=1
step 4
Find out the slope EF
we have
E(4,5), F(16,17)
m=(17-5)/(16-4)
m=12/12
m=1
step 5
Compare slope HJ and slope EF
their slopes are equal
that means
HJ and EF are parallelstep 6
Find out the distance HJ
the formula to calculate the distance between two points is equal to
\(d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}\)we have
H(7,0) and J(13,6)
substitute
\(\begin{gathered} HJ=\sqrt[]{(6-0)^2+(13-7)^2} \\ HJ=\sqrt[]{(6)^2+(6)^2} \\ HJ=6\sqrt[]{2} \end{gathered}\)step 7
Find out the distance EF
we have
E(4,5), F(16,17)
substitute
\(\begin{gathered} EF=\sqrt[]{(17-5)^2+(16-4)^2} \\ EF=\sqrt[]{(12)^2+(12)^2} \\ EF=12\sqrt[]{2} \end{gathered}\)step 8
Verify
HJ = 1/2EF
substitute
\(\begin{gathered} 6\sqrt[]{2}=\frac{1}{2}\cdot(12\sqrt[]{2}) \\ 6\sqrt[]{2}=6\sqrt[]{2} \end{gathered}\)is true
that means
Triangle Midsegment Theorem was verified
Related Questions
(−2k + 3kª + 2k³) − (−12k – k³ + 8)
Answers
The simplified expression of (−2k + 3kª + 2k³) − (−12k – k³ + 8) is 10k + 3kª + 3k³ - 8.
Let's simplify the expression step by step:
(−2k + 3kª + 2k³) − (−12k – k³ + 8)
First, let's distribute the negative sign to the terms inside the second parentheses:
−2k + 3kª + 2k³ + 12k + k³ - 8
Next, let's combine like terms:
(-2k + 12k) + (3kª + k³) + (2k³ - 8)
Simplifying further:
10k + 3kª + k³ + 2k³ - 8
Combining the terms with k³:
10k + 3kª + 3k³ - 8
So, the simplified expression is 10k + 3kª + 3k³ - 8.
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how is the graph of y=(x-1)^2-3 transformed to produce the graph of y=1/2(x+4)^2
Answers
Answer:
To transform the graph of y = (x-1)^2 - 3 to produce the graph of y = 1/2(x+4)^2, we can use the following steps:
Shift the graph of y = (x-1)^2 to the right by 4 units. This can be done by adding 4 to the x-values of every point on the graph.Stretch the graph vertically by a factor of 2. This can be done by multiplying the y-values of every point on the graph by 2.Shift the graph upward by 3 units. This can be done by adding 3 to the y-values of every point on the graph.Applying these transformations to the graph of y = (x-1)^2 will produce the graph of y = 1/2(x+4)^2.
Which number produces a rational number when added to 0.25?
Answers
___________________________________________________________
Answer:
2/9 produces a rational number when added to 0.25
___________________________________________________________
Q10.
What is the area of the shaded part?
Q 10.
25 m
k
25 m
A. 42.5sq m B.212.5sq m
C.225sqm
D.5312.5sq m
NIA
Answers
Answer:
ok so we need to first find the amount of black squares vs white squares
top row: 2 black 3 white
2nd top row: 1 black 4 white
middle row: 3 black 2 white
2nd bottom row: 1 black 4 white
bottom row: 2 black 3 white
so lets add that up
9 black 16 white
so then each one is 5 meters so
9*5=45
45m^2
Hope This Helps!!!
You have two numbers if you double the first number and add it to the second number the sum is 10
Answers
Answer:
first number = 4
second number = 2
Step-by-step explanation:
4x2=8
8+2=10
Please Help Geometry Question, I will mark brainliest, also answer is a simplified fraction or whole number
Answers
hope u get it!!!!
btw please check the answer whether it is 3 or 2÷7
use the figure to find x
Answers
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
The given side is opposite the angle, and the unknown is the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(30°) = (5/2)/x
x = (5/2)/sin(30°) = (5/2)/(1/2) = 5/1
x = 5
__
Additional comment
In this 30°-60°-90° "special" right triangle, the long leg is √3 times the short leg, so ...
y = (5/2)√3
1.Use the Pythagorean Theorem to find AD and DC. Then find AC using addition. Show your calculations.
Answers
Answer:
c=a2+b2=102+172≈19.72308
Step-by-step explanation:
a calculator bro its easy
Please helpppppppppppppppppppppppppppppppppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
60
Step-by-step explanation:
a tringle always adds ups to 180 add them then subtract.
find the domain of the function, picture included
Answers
Answer:
[4,∞)
Step-by-step explanation:
x≥4
[4,∞)
a. Find the atmospheric pressure in Boston, MA which is at sea level
Answers
Calculate how many cups of butter your new recipe will need.
What is 1 and 1/2 cups x 1 and 1/2?
Answers
The surface area of a sphere is 900pi cubic cm. What is the length of its diameter.
Answers
The length of the diameter of the sphere is 30 cm.
The surface area of a sphere is given by the formula:
\(A = 4\pi r^2\)
where A is the surface area and r is the radius of the sphere.
We are given that the surface area of the sphere is 900π cubic cm. Therefore:
\(A = 4\pi r^2 = 900\pi\)
Dividing both sides by 4π, we get:
\(r^2 = 225\)
Taking the square root of both sides, we get:
r = 15
The diameter of the sphere is twice the radius, so:
d = 2r = 30
Therefore, the length of the diameter of the sphere is 30 cm.
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Which of the following equations has infinitely many solutions?
A.
b+2=b+2
B.
b= -b+2
C.
b+2=b-2
D.
b+b=2
Answers
Answer:
A
Step-by-step explanation:
Equation A is true for all real numbers. It says the quantity b + 2 is equal to itself!
Equation B, solved for b, gives b = 1, so the equation is true only for b = 1.
Equation C, solved for b, gives 2 = -2, which is absolutely false, so the equation has no solutions.
Equation D, solved for b, gives b = 1, so only one solution
How much would you have to deposit today to accumulate the SAME AMOUNT OF MONEY that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn?
Answers
Answer:
7606.62
Step-by-step explanation:
Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.
\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)
Now just equate this to a time 0 payment at the same rate
\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)
As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.
Write an equation of a line through the point (-5, -2)that is perpendicular to the x-axis. Also state the slope of the line. A. x = -5, m = 0B. y = -2, m = 0C. x = -5, m = undefinedD. y = -2, m = undefined
Answers
First let's take a look at the point (-5,-2) in the plane:
since we want an equation of a line that is perpendicular to the x-axis, it should look like this:
Therefore, the equation is x = -5. Now for the slope, we can easily see that the line passes through the points (-5,-2) and (-5,-3), so, if we calculate the slope we get something like this:
\(\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}_{} \\ \Rightarrow m=\frac{-3.-(-2)}{-5-(-5)}=\frac{-3+2}{-5+5}=-\frac{1}{0} \end{gathered}\)which clearly is undefined.
Joe is asked to prove that the sum of the interior angles (, , and ) of the triangle he has drawn equals 180°. His triangle is represented in the diagram above, and his work is shown below.
Answers
The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.
What is angle sum property of triangle?The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.
To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.
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which of the following functions represent the graph g(x) above
Answers
The function represented by the graph given is equivalent to -
g(x) = (x - 4)².
The function plotted represents a quadratic equation. A quadratic equation has a degree of 2. The given function is shifted to the left by 4 units. This means that the following transformation will take place on the x - coordinate of each and every point lying on the graph -
f(x, y) → f(x - 4, y)
So, we can write the function as -
g(x) = (x - 4)²
So, the function represented by the graph given is equivalent to -
g(x) = (x - 4)²
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Solve the inequality.
2(4+2x)25x+5
Answers
Answer:
\(100x^{2} +200x+5\)
Step-by-step explanation:
Answer:
x ≤ 3
Step-by-step explanation:
A certain list of movies were chosen from lists of recent Academy Award Best Picture winners, highest grossing movies, series movies (e.g. the Harry Potter series, the Spiderman series), and from the Sundance Film Festival and are being analyzed. The mean box office gross was $138.64 million with a standard deviation of $11.2526 million. Given this information, 98.49% of movies grossed greater than how much money (in millions)
Answers
Alice used a $250 cash advance from her credit card company to get cash while on a trip. The company charges a daily finance fee of 0.047%. She reported the advance plus the finance fee 40 days later. What amount did Alicia repay the company?
Answers
you do 0.047×40 and what ever that gives you you add it to 40 and it will give you the answer
The amount Alicia repaid to the company after 40 days is $254.7.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Advance cash = $250
Daily finance fee = 0.047%
The daily finance fee for 40 days.
= 40 x (0.047% x 250)
= 40 x 0.1175
= $4.7
The total amount paid after 40 days.
= 250 + 4.7
= $254.7
Thus,
The amount paid to the company is $254.7.
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ab-c/d has a value of 24. write the values if :-
1- a, b, c, d are all positive.
2- a, b, c, d are all negative.
3- a, b, c, d are mixed of negative and positive.
WRITE ANSWERS FOR 1, 2 AND 3
Answers
The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24
Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.
Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9
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What is the name of the property for : a + ( − a ) = 0 ?
Answers
Answer:
Inverse Property of Addition
Step-by-step explanation:
monday , jay earned $14 per hour for m of hour, thursdays earned $22 per hour for t hour of work. he also got a $100 bonus. which expression shows how much jay earned in total
A. (14 + 22)(m+t)+100
B.14t+22m+100
c, 14m + 22 + 100
D. 14m(22t)(100)
Answers
Answer:
B
Step-by-step explanation:
14t +22m+100
There's no number of hours
The expression of Jay earned in total is;
14m + 22t + 100
Here,
On Monday, Jay earned $14 per hour for m of hour.
On Thursday, Jay earned $22 per hour for t hour of work.
He also got a $100 bonus.
We have to find the expression of Jay earned in total.
What is Mathematical expression?
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Now,
On Monday, Jay earned $14 per hour for m of hour.
Total earned on Monday = $14m
On Tuesday, Jay earned $22 per hour for t hour of work.
Total earned on Tuesday = $22t
He also got a $100 bonus.
Hence, Total earned = 14m + 22t + 100
So, The expression of Jay earned in total is;
⇒ 14m + 22t + 100
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A solar panel dealer acquires is used panel for $9,000, with terms FOB shipping point. Compute total inventory cost assigned to the used panel if additional costs include $1,500 for sales staff salaries. $280 for transportation-in by train. $110 for online advertising. $135 for shipping insurance. $550 for used panel restoration. $300 for lawn care.
Answers
Answer:
Total inventory cost is $9,965.
Step-by-step explanation:
The terms free on board FOB shipping point implies that the delivery of a good is taken by the buyer after it left the supplier's shipping dock. Therefore, any other relevant cost incurred afterwards will be paid by the buyer.
From the all the cost listed in the question, the $1,500 for sales staff salaries, $110 for online advertising, and $300 for lawn care are NOT related to the inventory cost because they are administrative and sales expenses.
Therefore, the total inventory cost can be calculated using the following relevant cost:
Acquisition cost = $9,000
Transportation-in by train = $280
Shipping insurance = $135
Used panel restoration = $550
Therefore, we have:
Total inventory cost = Acquisition cost + Transportation-in by train + Shipping insurance + Used panel restoration = $9,000 + $280 + $135 + $550 = $9,965.
This is breakdown of attendees at an event
Men 153
Women 357
Boys 153
Girls 187
What percentage of the attendees are men?
What percentage are children?
Answers
Answer:
Men: 18%
Women: 42%
Boys: 18%
Girls: 22%
Children: 40%
Step-by-step explanation:
Choose the true statement about virtue-based ethics.
i. According to the principles of virtue-based ethics, character is more important than actions.
ii. According to the principles of virtue-based ethics, right and wrong are assessed using culture as a guide.
iii. According to the principles of virtue-based ethics, the consequences of actions are very important.
iv. According to the principles of virtue-based ethics, rules are used to evaluate actions.
Answers
Virtue based ethics holds that character is more important than actions.
Virtue based ethics is the aspect of ethics that holds that the moral character of a person if of more paramount importance than the person's actions and its consequences.
Hence, the true statement about virtue based ethics from the options is that; "according to the principles of virtue-based ethics, character is more important than actions."
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Plzzzzzz help right answer gets brainly
Answers
Answer:
3 * 3 * 3 * 3
=> \(3^{4}\)
If my answer helped, then kindly mark me as the brainliest!!
Thank You!!
The ratio of girls to boys in a class with 300 girls and 250 boys
Answers
Step-by-step explanation:
A ratio is a simple way to express the relationship between two quantities (numbers).
A ratio can also show how much greater a quantity is to another.
Express the ratio as 300:250.
This ratio can be simplified by dividing each quantity by 50.
6:5
Multiple choice: which function has an amplitude of 5 and a period of π/3 ?
A) f(x)=5 cos 6x
B) f(x)=1/5 cos6x
C) f(x)=5 cos 2/3 x
D) f(x)=3 cos5x
Answers
The correct answer is C) f(x) = 5 cos 2/3 x, as it has an amplitude of 5 and a period of π/3. To determine which function has an amplitude of 5 and a period of π/3, we need to analyze the properties of the trigonometric functions presented in the options.
The general form of a cosine function is f(x) = A cos(Bx), where A represents the amplitude and B represents the frequency or period of the function.
Option A) f(x) = 5 cos 6x: This function has an amplitude of 5, but its period is 2π/6, which is not equal to π/3. So, this option is not the correct answer.
Option B) f(x) = 1/5 cos 6x: This function has an amplitude of 1/5, which is not 5 as required. Therefore, this option is not the correct answer.
Option C) f(x) = 5 cos 2/3 x: This function has an amplitude of 5, which matches the given condition. Moreover, its period is 2π/((2/3)x) = π/3, which is the desired period. Hence, this option satisfies both conditions.
Option D) f(x) = 3 cos 5x: This function has an amplitude of 3, which is not 5 as required. Thus, this option is not the correct answer.
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