given: XZ/MZ=YZ/NZ Prove XZ/MZ=XY/MN
Answers
Answer:
By trigonometric ratio;
XZ/sin(b) = XY/sin(c) = YZ/sin(a)
MN/sin(c) = NZ/sin(f) = MZ/sin(d)
∴ XZ/MZ = XY/MN × (sin(b)/(sin(d))
XY/MN = XZ/MZ × (sin(b)/sin(d))
Where (sin(b)/(sin(d)) = V;
(XZ/MZ)/(XY/MN) = (XY/MN × V)/(XZ/MZ × V)
(XZ/MZ)/(XY/MN) = (XY/MN)/(XZ/MZ)
∴ (XZ/MZ)² = (XY/MN)²
∴ XZ/MZ = XY/MN QED
Step-by-step explanation:
Whereby the shapes in the question are triangles ΔXYZ and ΔMNZ, and given that we have;
XZ/MZ = YZ/NZ, and from the attached drawing, we have;
∠XZY = ∠NZM
By trigonometric ratio, we have;
XZ/sin(b) = XY/sin(c) = YZ/sin(a)
∴ XZ = sin(b)×XY/sin(c)
MN/sin(c) = NZ/sin(f) = MZ/sin(d)
MZ = sin(d)×MN/sin(c)
∴ XZ/MZ = sin(b)×XY/sin(c)/(sin(d)×MN/sin(c)) = XY/MN × (sin(b)/(sin(d))
XY = sin(c) × XZ/sin(b), MN = sin(c) × MZ/sin(d)
XY/MN = sin(c) × XZ/sin(b)/(sin(c) × MZ/sin(d)) = XZ/MZ × (sin(b)/sin(d))
Let 'V' represent (sin(b)/(sin(d)), we have;
XZ/MZ = XY/MN × V...(1)
XY/MN = XZ/MZ × V...(2)
Dividing equation (1) by (2) gives;
(XZ/MZ)/(XY/MN) = (XY/MN × V)/(XZ/MZ × V) = (XY/MN)/(XZ/MZ)
(XZ/MZ)/(XY/MN) = (XY/MN)/(XZ/MZ)
∴ (XZ/MZ)² = (XY/MN)²
∴ XZ/MZ = XY/MN
Related Questions
2 birds are building a nest. Bird A is flying toward the nest at the same time bird B is flying away from it
Answers
Answer:
Step-by-step explanation:
is it that 1 bird is at the nest and the other is flying away ?
What is the measure of arc WYZ?
----------
231
255
200
168
Answers
9514 1404 393
Answer:
(a) 231°
Step-by-step explanation:
arc WYZ = arc WX + arc XYZ
arc WYZ = 51° +180° . . . . . XZ is a diameter, substitute known arc measures
arc WYZ = 231°
Ramon drew boxplots to summarize the number of pages in each chapter of two books. The values of the interquartile ranges for these boxplots are the same. Which boxplot could represent this data?
Answers
Answer
look at the ss i sent to see the answer
Step-by-step explanation:
Find the distance between each pair points
Answers
Point J is on line segment \overline{IK} IK . Given IK=5x,IK=5x, IJ=4,IJ=4, and JK=4x,JK=4x, determine the numerical length of \overline{IK}. IK
Answers
Answer:
IK = 20
Step-by-step explanation:
If Point J is on the line segment IK, then;
IK = IJ + JK
Given that
IJ = 4
IK = 5x
JK = 4x
Substitute into the expression
5x = 4 + 4x
5x - 4x = 4
x = 4
Get the value of IK
IK = 5x
IK = 5(4)
IK = 20
Hence the numerical length of IK is 20
Ruth is knitting hats to sell at a local fair. The booth costs her $63 and the materials for each hat cost $10. She plans on selling them for $19. How many hats will Ruth have to make to break even, and how much will sales and costs be at that point?
Answers
Answer: Ruth have to make 7 hats to break even.
Step-by-step explanation:
Break even point is a point where Cost = Revenue.
Let x be the number of hats sold.
Given: Cost of booth = $63
Each hat cost = $10
Selling price for each cost = $19
As per given,
Total cost = Cost of booth+ (Cost of each hat)(Number of hats)
= 63+10x
Total selling price = 19x
For break even,
63+10x=19x
9x=63
x=7
Hence, Ruth have to make 7 hats to break even.
3x + 4y - 7z + 11
Identify constant term
Answers
Answer:
11
Step-by-step explanation:
3x + 4y - 7z + 11
The constant term is the term that has no variables ( letters)
11 is the constant term
Shawn rode his bike 3 miles to the library. He rode 4 miles to his friend’s house. Then, he rode 5 miles home. How many miles in all did Shawn ride his bike?
Answers
Solve the following equation for A. Be sure to take into account whether a letter is
capitalized or not.
q2 = g(-h + A)
Answers
Answer:
A = (q² + gh) / g
Step-by-step explanation:
Given equation:
q² = g(-h + A)
Solve for A
q² = g(-h + A)
q² = -gh + gA
Add -gh to both sides
q² + gh = -gh + gA + gh
q² + gh = gA
Divide both sides by g
(q² + gh) / g = gA / g
A = (q² + gh) / g
find out the shortest distance between the point (3,4) and the line 3x+4y+25=0
Answers
Answer:
Hence, shortest distance is 0
Step-by-step explanation:
4y = -3x+25
y = -3/4x + 25/4
When x = 3,
y = -9/4 + 25/4
y = 4
Hence, when x =3,
Point: (3,4)
Feel free to mark this as brainliest :D
A pair of shoes is 60% off if the sale price is now $33 find the original price
Answers
Answer:
$82.5
Step-by-step explanation:
40%-33
10%-8.25
100%-82.5
Can somebody give me a link to Maths Progress Core 2 active learn
Answers
Please help 7th grade math
Answers
Answer:
d = 67.5
e = 22.5
Step-by-step explanation:
d + e = 90
d = 3e
Therefore, we can simply divide 90 by 4, which gives us 22.5, and also tells us what e equals. Then, multiply that by 3 to get d.
Hope that this helps!
Simplify the following expression as much as possible.
(4+1)-(3-51)(-2+57)
O A. -15-241
O B. 35-241
O C. -15+ 261
O D. 35+261
Answers
I did the problem...
Find the slope from the two points given: (-4, 2) and (5, 6) *
Answers
Answer:
Slope = 4/9
Step-by-step explanation:
x1(-4,2)
x2(5,6)
Slope,
m = (y2-y1)/(x2-x1)
= (6-2)/(5--4)
=4/9
I NEED HELP ITS ALMOST DUE!!
Answers
Answer:
B) 9
Step-by-step explanation:
rise over run and simplify
Solve the problem. A room in the shape of a triangle has sides of length 7 yards, 8 yards, and 11 yards. If carpeting costs $13.50 per square yard and padding costs $2.25 per square yard, how much to the nearest dollar will it cost to carpet the room, assuming there is no waste? $426 $419 $440 $377
BRAINLIEST TO FIRST CORRECT ANSWER
HELP ASAP!
Answers
27.928 times 15.75
439.866 rounds to 440
Which of the following best describes the equation below? 3(x + 9) + 6x = 9x - 27 A. no real solutions B. exactly one real solution, x = -1 C. exactly one real solution, x = D. infinite real solutions
Answers
Answer:
no solutions
Step-by-step explanation:
3(x + 9) + 6x = 9x - 27
Distribute
3x+27 +6x = 9x -27
Combine like terms
9x +27 = 9x -27
Subtract 9x from each side
27 = -27
This is never true so there are no solutions
pls help i am really struggling at this it is a vector question
Answers
Answer:
Step-by-step explanation:
PQ = q-p
PQ = q-p, therefore PS = (2/3)(q-p)
OS = p + (2/3)(q-p) = (2q+p)/3
OR = q + p/2
To make new vectors, chain vectors, follow arrow directions.
The sum is the line joining the beginning and end points.
If you need to reverse the direction of a vector, simply put a negative sign.
Which of the following points are in the second quadrant of the xy-plane? Check all that apply. O A. (-4,2) O B. (-7, 6) O C. (4,8) O D. (2,2) O 6 E. (6,-2) O F. (-2,-8)
Answers
Answer:
a and b bc that are in the negative-positive quad
PLS HELPP ASAP
Plss help me
Answers
Answer:
a. 42
Step-by-step explanation:
10.5x4=42
Helppppppppppppppppp
Answers
Answer:37.7825
Step-by-step explanation: all you really need to do is find the percentage of 595 of 6.35 which is 37.7825
PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEE easdyfhrdfghfchdfchfch
Answers
857,963 five has a value of
Answers
Answer: 5 has a value of 50 000 2.
Hope this helps ;)
A circle has a radius of 3. An arc in this circle has a central angle of 340°. What is the length of the arc? Either enter an exact answer in terms of or use 3.14 for and enter your answer as a decimal. 340tom
Answers
Step-by-step explanation:
length of arc=2πr(340/360)
= 2x3.14x3(0.944)
=17.78 approximately 17.8
length of wall is 13.5m calculate the area in cm2
Answers
Answer:
15 Apr 2018 — Area of path parallel to the remaining length of ... Area of parallelogram ABCD = AB × AE = 8 × 4 cm2 ... We can also calculate area of shaded portion by using area of..
Answer:
185.25 cm^2
Step-by-step explanation:
since only length is given i considered the wall as square shape. So given :
length = 13.5 cm
area of the wall = l^2
= 13.5^2
=182.25 cm^2
What is the least common multiple of these two denominators? 3/6 , 2/12
A: 18
B:12
C:6
D:15
Answers
Step-by-step explanation:
simple
multiples of 6= 1, 2, 3, 6
multiples of 12= 1, 2, 3, 4, 6, 12
.L.C.M of 12 and 6= 12
someone plz help with dis
Answers
If one zero of the polynomial 5z2 + 13z – p is reciprocal of the other, then find p.
Answers
Step-by-step explanation:
Please mark as brainlist !!!!!!(☆^ー^☆)
Estimate the sum by rounding each number to the nearest half or whole
Answers
Answer:
8 1/2
Step-by-step explanation:
I do not have much of an explanation but here it is:Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2
To find new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2
b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.
Two and one half is five halfs
Conversion a mixed number 5 5/8 to a improper fraction: 5 5/8 = 5 5/8 = 5 · 8 + 5/8 = 40 + 5/8 = 45/8
To find new numerator:
a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
b) Add the answer from previous step 40 to the numerator 5. New numerator is 40 + 5 = 45
c) Write a previous answer (new numerator 45) over the denominator 8.
Five and five eighths is forty-five eighths
Add: 5/2 + 45/8 = 5 · 4/2 · 4 + 45/8 = 20/8 + 45/8 = 20 + 45/8 = 65/8
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - five halfs plus forty-five eighths = sixty-five eighths.