(a) Construct, using a compass and straightedge, the midpoint of UV and label it M. Then
draw TM, the median from 2T to side UV.
(b) Prove algebraically that the median TM is not perpendicular to UV. Explain.
Please helpppppp
Answers
Step-by-step explanation:
a) for the first part, you take your compass and stretch it more than halfway on to line UV. Place the fixed point at V and draw a curve. make sure you keep your compass the same size, put the fixed part of your compass on point U and draw a curve again. both curves should go both upward and downward. Now, your curves should meet at two points. use your straight edge to draw the line that meets at both points. I have drawn an example of what it should approximately look like. for the second part you are simply using your straight edge to draw a line from T down to the median M you previously found. I have drawn a second picture to show you.
b) now to check if they are perpendicular, we must find the slope of each line. I will not be able to do this accurately since I didn't use an exact method to find M, so you must follow my steps.
Step 1: find the slope of UV. To do so, we must take two points from the line. I will take points U and V because they are easiest to see. To find the slope, we can use the equation:
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
where m is the slope.
so, let's define our points.
Point V is (4,4), let's call this point one.
Point U is (14,6), let's call this point two.
So,
x1= 4
y1= 4
and
x2= 14
y2= 6
now, we can plug these into our slope equation.
[tex]m = \frac{6 - 4}{14 - 4} = \frac{2}{10} = \frac{1}{5} [/tex]
You must then use the points T and M in order to solve the second slope. Where T is (2,12). I will keep M as (x1, y1) for now.
The equation should then look like:
[tex]m = \frac{2 - y1}{12 - x1} [/tex]
now, in order for it to be perpendicular to our original slope, it must be the opposite reciprocal, which is the number flipped and made negative. The opposite reciprocal of 1/5 will be -5.
It should NOT be, as we have been told. So, we can state:
"I know that TM is not perpendicular to UV because the UV has a slope of 1/5 and TM has a slope of x, which is NOT the opposite reciprocal on 1/5."
Hope this helps! :)
Related Questions
Simplify the left side of equation so it looks like the right side. cos(x) + sin(x) tan(x) = sec (x)
Answers
Step-by-step explanation:
Consider LHS
[tex] \cos(x) + \sin(x) \tan(x) = \sec(x) [/tex]
Apply quotient identies
[tex] \cos(x) + \sin(x) \times \frac{ \sin(x) }{ \cos(x) } = \sec(x) [/tex]
Multiply the fraction and sine.
[tex] \cos(x) + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x) [/tex]
Make cos x a fraction with cos x as it denominator.
[tex] \cos(x) \times \cos(x) = \cos {}^{2} (x) [/tex]
so
[tex] \frac{ \cos {}^{2} (x) }{ \cos(x) } + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x) [/tex]
Pythagorean Identity tells us sin squared and cos squared equals 1 so
[tex] \frac{1}{ \cos(x) } = \sec(x) [/tex]
Apply reciprocal identity.
[tex] \sec(x) = \sec(x) [/tex]
230, 200, 170, 140 __ next number sequence ?
Answers
Answer:
C. 110
Step-by-step explanation:
It decrease each time by 30
230-30=200
200-30=170
170-30=140
So
140-30=110
110 is the correct answer.
Hope this helps!!
Find the value of each variable in the parallelogram
PLEASE HELPPPP!!
Answers
Answer:
m = 35
n = 110
Step-by-step explanation:
70/2 = 35
70 + 70 = 140
360 - 140 = 220
220/2 = 110
Find the value of x.
Answers
Answer:
⏩12°
Step-by-step explanation:
4x + 7° + 35° = 90° {being complementary angles }
4x + 42° = 90°
4x = 90° - 42°
4x = 48°
x = 48° / 4
x = 12°
Hope it will help :)❤
Step-by-step explanation:
35°+4x+7°=90°
or,42°+4x=90°
or,4x=90°/42°
or,x=2.14/4
or,x=0.53
hope this helps
What is the circumference?
(radius = 4)
Answers
Answer:
25.13
Step-by-step explanation:
C = 2πr
C = 2π(4)
C = 25.13
Hope this helps!
i need help and thank you
Answers
Answer:
Hello! answer: 6
Step-by-step explanation:
2 × 3 = 6 12 - 6 = 6 therefore the answer is 6 hope that helps!
Answer:
6
Step-by-step explanation:
Match each interval with its corresponding average rate of change for q(x) = (x + 3)2.
1. -6 ≤ x ≤ -4
2. -3 ≤ x ≤ 0
3. -6 ≤ x ≤ -3
4. -3 ≤ x ≤ -2
5. -4 ≤ x ≤ -3
6. -6 ≤ x ≤ 0
A)-1
B)1
C)3
D)-3
E)0
F)-4
Answers
Answer:
When we have a function:
f(x)
The average rate of change in the interval a < x < b
is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Now for each of the given intervals, let's find the average rate of changes.
q(x) = (x + 3)^2
1) -6 ≤ x ≤ -4
[tex]r = \frac{(-4 + 3)^2 - (-6 + 3)^2}{-4 - (-6)} = \frac{1 - 9}{2} = -4[/tex]
here the correct option is F.
2) -3 ≤ x ≤ 0
[tex]r = \frac{(0 + 3)^2 - (-3 + 3)^2}{0 - (-3)} = \frac{9}{-3} = -3[/tex]
Here the correct option is D.
3) -6 ≤ x ≤ -3
[tex]r = \frac{(-3 + 3)^2 - (-6 + 3)^2}{-3 - (-6)} = \frac{9}{3} = 3[/tex]
Here the correct option is C
4) -3 ≤ x ≤ -2
[tex]r = \frac{(-2 + 3)^2 - (-3 + 3)^2}{-2 - (-3)} = \frac{1}{1} = 1[/tex]
Here the correct option is B.
5) -4 ≤ x ≤ -3
[tex]r = \frac{(-3 + 3)^2 - (-4 + 3)^2}{-3 - (-4)} = -1/1 = -1[/tex]
Here the correct option is A
6) -6 ≤ x ≤ 0
[tex]r = \frac{(0 + 3)^2 - (-6 + 3)^2}{0 - (-6)} = \frac{9 - 9}{6} = 0[/tex]
Here the correct option is E.
What is the radius of a sphere with a volume of 12,348 π cubic feet?
Answers
Answer:
Radius = 21
Step-by-step explanation:
Volume of a sphere = 4/3 * pie * radius^3
12,348 pie = 4/3 * pie * radius ^3
12,348 = 4/3 * radius^3
(12,348 * 3)/ 4 = radius^3
9261 = radius^3
radius = [tex]\sqrt[3]{9261}[/tex]
radius = 21
THIS IS exact and approximate pi PLS HELP ME BEFORE I FAIL
Answers
Answer:
Approximate: C ≈ 50.27
Exact: C = 16π
Step-by-step explanation:
C = 2πr
We know that r is 8
C = 2π8
C = 16π
C ≈ 50.27
The circumference of a circle is 16π unit²
What is circumference of a circle?The circumference of a circle is defined as the linear distance around of circle.
Formula of circumference of a circle (C) = 2πr
Where r is radius of circle
Given radius of circle (r) = 8,
Substitute the value of r,
C = 2π(8)
C = 16π unit²
Substitute π = 3.14,
C ≈ 50.27 (approximate)
Thus, the circumference of a circle is 16π unit²
Learn more about Circles
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Find all solutions to the equation. cos x = -1/2
Answers
Answer:
^^
Step-by-step explanation:
Answer:
You didn't add the range. I'll use (0<x<2π)
cosx = -1/2
x=-cos-¹(1/2)
x= -60°
Cosine is negative in the second and 3rd quadrants
180-x ---- Second quadrant
x+180 ----- 3rd quadrant
So
Our answer
180-(-60)=240° or 4π/3 second quad
180+(-60) = 120° or 2π/3---- 3rd quad
PLEASE ASAP ILL GIVE BRAINLIEST.
Answers
Answer:
It would be the fourth one
Step-by-step explanation:
Amy has a box that is 6 1/2 feet long, 3.25 feet wide, and 2 feet high. What is the volume of the box? V=lwh
Answers
Answer:
42.25 feet ³
Step-by-step explanation:
Volume of the box = length × width × height
Length = 6 1/2 feet = 6.5 feet
Width = 3.25 feet
Height = 2 feet
Volume of the box = length × width × height
= 6.5 feet × 3.25 feet × 2 feet
= 42.25 feet ³
Volume of the box = 42.25 cubic foot
BRAINLIEST! hello please help i’ll give brainliest
Answers
Answer:
the bin, 60-69 has the most data values
Step-by-step explanation:
since it has the highest frequency it has the most data values
Answer:
Step-by-step explanation:
The bin 60-69, contains the most data 100% positive that this is correct
what is this
Writing State the Pythagorean Theorem. Describe how you determine where
the lengths of the sides of a right triangle get substituted into the equation.
Answers
Answer:
In mathematics, the Pythagorean theorem, or Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the si…
Step-by-step explanation:
Answer: Hope This Helps!
Step-by-step explanation:
Pythagoras Theorem Statement Pythagoras theorem states that “ In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides “. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse.
please help :) find the area of the regular polygon
Answers
9514 1404 393
Answer:
3√3 square units
Step-by-step explanation:
The area of a regular n-sided polygon with radius r is given by the formula ...
A = (n/2)r²·sin(360°/n)
For n=3 and r=2, the area is ...
A = (3/2)(2²)·sin(360°/3) = 6·sin(120°) = 6(√3/2)
A = 3√3 . . . . square units
_____
Alternate solution
The center of this polygon is the centroid, which divides each median into parts with the ratio 2:1. This means the given radius is 2/3 of the height of the triangle. The base of the triangle is 2/√3 times the height, so is ...
b = (2/√3)(3) = 2√3
The area using these dimensions is calculated as ...
A = 1/2bh
A = 1/2(2√3)(3) = 3√3 . . . . square units
Please help, sorry if it’s blurry.
Answers
Answer:
0.35
Step-by-step explanation:
j.g susghe yo s9ss9sssisjwus
Answer: D) 385.2
What you give me in the comments 1,540.7......789.4.....1,155.5.....385. I think that was the choice for me to put what kind of answer you want!
Step-by-step explanation: Hope this help :D
Write the equation of the parallel line - x + 2y = 12 that goes through the
point (10,8).
Write your answer in in slope-intercept form,
y = m x +
b
slope
y-intercept
Answers
Answer:
Step-by-step explanation:
What single decimal multiplier would you use to increase by 4% followed by a 3% increase?
Answers
Help me with this question
Answers
Answer:
24
Step-by-step explanation:
41-17=24
The boys basketall team averages 52 points per game with a standard deviation of 7.0 points. What is the probability that the boys will score between -1.2 and 2.0 standard deviations of their average?
Answers
Answer:
0.6832
Step-by-step explanation:
Given :
Mean, m = 52
Standard deviation, s = 7
-1.2 standard deviation of average = 57 - 1.2(7) = 57 - 8.4 = 48.6
2 standard deviations of average = 57 + 2(7) = 57 + 14 = 71
Zscore = (48.6 - 52) / 7 = - 0.486
Zscore = (71 - 52) / 7 = 2.714
P < -0.486) = 0.31348
P < 2.714 = 0.99668
P < 2.714 - P < -0.486 = (0.99668 - 0.31348) = 0.6832
If a bracelet costs $50 and there is a 25% off sale, what is the sale price?
Answers
50 - 12.5 = 37.5
So the answer is $37.50
Name all asymptotes: y =x−3/2x+8
Answers
Answer:
x=0
y= x + 8
Step-by-step explanation:
find the oblique asymptotes using long polynomial divison
what does 4(15w) + 90 =
Answers
Answer:
110
Step-by-step explanation:
Answer:
60w+90
Step-by-step explanation:
That would be the simplified expression
Mila graphs the point A (5, 0) on a coordinate plane.
Which of the following statements are true?
Select all that apply.
Point A is 5 units to the________(Please fill this box any of these choices in A-E)
A. right of the origin and up 1 unit.
B. The x-coordinate of point A is 5.
C. The y-coordinate of point A is 5.
D. Point A is on the y-axis.
E. Point A is on the x-axis.
Answers
Answer:
B,E
Step-by-step explanation:
(5,0) (5=x, 0=y)
A is false because y = 0
B is true because x=5
c is false because y = 0
D is false because again y = 0
E is true because 5,0 is on the x axis
- Gage Millar, Algebra 2 tutor
Which choice is equivalent to the expression below
5x sqrt2 - 3 sqrt2 + x sqrt2
Answers
Answer:
answer is D I think
Step-by-step explanation:
.............
For the pair of coordinates, describe the translation rule: A(-2,-6) to A'(-5, -9).
Answers
Answer: a=0 hope that helps sorry i don't have time to explain bye !
Step-by-step explanation:
If you show steps i will give BRAINLIEST
Petra gives Ian the clue below to help him guess a
number.
When the number ( x ) is doubled and the product
is reduced by five, the final result is less than 23.
Which inequality correctly represents this clue?
A. 2x - 5 < 23
B. 2 (x-5) < 23
C. 2x - 5 > 23
D. 2 (x-5) > 23
Answers
Answer:
2x - 5 < 23
2x < 28
x < 14
Step-by-step explanation:
Petra gives Ian the clue below to help him guess a number.When the number (x) is doubled and the product is reduced by five, the final result is less than 23.Which inequality correctly represents this clue?
Answer:
2x - 5 < 23
Step-by-step explanation:
2x - 5 < 23
2x < 28
x < 14
10. Find the total surface area of the triangular prism
shown below.
Answers
Answer:
I think its 132.
The total surface area of the triangular prism is 200 cm².
Triangular prism surface areaSurface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
How to find the surface area of the triangular prism?First, find the height of the prism.
Let h is the height of the prism
Use the pythagoras theorem
then
5² = (6/2)² + h²
5² = 3² + h²
25 = 9 + h²
h² = 25 - 9
h² = 16
h =4
Now apply the surface area formula
total surface area = ( 5 + 5 + 6) 11 + 6×4
= 16 × 11 + 24
= 176 +24
= 200 cm²
Hence the surface area is 200 cm²
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Keisha has been given a List of 5 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different bands are possible ? Please help me
Answers
Answer:
2
Step-by-step explanation:
because she hast to pick her favorite and second favorite
If APML - ATRO, find QR.
P
35
T
.
14
14
و - r
R
Answers
The value of QR in the triangle is 16 units
What is congruent triangle?Recall that Congruence of triangles represents the similarity of triangles. Two triangles are congruent if their corresponding sides and angles are congruent
The question states that ΔPML≅ΔTRQ
This implies that ML/QR = PM/TR
⇒(7x-9)/2x+2 = 35/14
Cross and multiplying we have
14(7x-9) = 35(2x+2)
=98x-126 = 70x +70
98x-70x = 70+126
⇒28x = 196
Making x the subject of the formula
x= 196/28 = 7
Recall that the side QR = 2x+2
Then by substitution,
2(7) +2
14+2 =16
This therefore keeps the side QR as 16 units.
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