if x/a =y/b=z/c prove the follong photo​

If X/a =y/b=z/c Prove The Follong Photo

Answers

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]\frac{x}{a}= \frac{y}{b} =\frac{z}{c}[/tex]

[tex]Let \: \frac{x}{a}= \frac{y}{b} =\frac{z}{c}=m[/tex]

(where m is any constant)

[tex]\implies[/tex]

[tex]\frac{x}{a}=m\implies x =am[/tex]

[tex]\frac{y}{b}=m\implies y =bm[/tex]

[tex]\frac{z}{c}=m\implies z =cm[/tex]

To Prove:

[tex]\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}=2[/tex]

LHS [tex]=\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}[/tex]

(Plug the values of x, y and z in the form of am, bm and cm respectively in the LHS)

[tex]=\frac{a(am)-b(bm)}{(a+b)(am-bm)}+\frac{b(bm)-c(cm)}{(b+c)(bm-cm)}[/tex]

[tex]=\frac{a^2m-b^2m}{(a+b)m(a-b)}+\frac{b^2m-c^2m}{(b+c)m(b-c)}[/tex]

[tex]=\frac{m(a^2-b^2)}{m(a+b)(a-b)}+\frac{m(b^2-c^2)}{m(b+c)(b-c)}[/tex]

[tex]=\frac{\cancel{m(a^2-b^2)}}{\cancel{m(a^2-b^2)}}+\frac{\cancel{m(b^2-c^2)}}{\cancel{m(b^2-c^2)}}[/tex]

= 1 + 1

= 2

= RHS

[tex]\implies \purple{\bold{\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}}}=\red{\bold{2}}[/tex]

Thus proved


Related Questions

Is –49 − –78 positive or negative?

Answers

Answer:

This is positive

Step-by-step explanation:

A "double negative" will always be positive. The equation should be rewritten as -49+78, the answer is 29.

Answer:

This one will be postive

Step-by-step explanation:

–49 − –78 is positve 29

It comes out to a positive because you are subtracting by a negative.

Hope that helps!

The volume of a paper cone of radius 2.4cm is 95.4 cm3.

The paper is cut along the slant height from O to AB.

The cone is opened to form a sector OAB of a circle with centre O.

Calculate the sector angle x°.

[The volume, V, of a cone with radius r and height h is V= 1/3 x π x r² x h.]

Answers

The sector angle formed by the cone when it is opened is: 54°.

What is the Curved Surface Area of a Cone?

Curved surface area of a cone = πrl, where l is the slant height and r is the radius of the cone.

What is the Area of Sector?

Area of a sector in a circle = ∅/360 × πr², where ∅ is the sector angle.

Step 1: Find the height (h) of the cone using the volume formula, V= 1/3 x π x r² x h:

V = 95.4 cm³

r = 2.4 cm

Plug in the values:

95.4 = 1/3 x 3.14 x 2.4² x h

95.4 = 6.03 x h

h = 15.8 cm

Step 2: Use the pythagroean theorem to find the slant height (l) of the cone

l = √(h² + r²)

Plug in the values

l = √(15.8² + 2.4²)

l = 16 cm.

Step 3: Find the curved surface area of the cone

Curved surface area = πrl = π(2.4)(16) = 120.6 cm².

Step 4: Find the sector angle of the sector formed by the cone when opened

Curved surface area of the cone = area of the sector formed by the cone = 120.6 cm².

Area of a sector in a circle = ∅/360 × πr², therefore:

120.6 = ∅/360 × (3.14)(16²)

120.6 = ∅/360 × 803.84

(120.6)(360) = (∅)(803.84)

43,416 = (∅)(803.84)

43,416/803.84 = ∅

∅ = 54°

Therefore, the sector angle formed by the cone when it is opened is: 54°.

Learn more about cone on:

https://brainly.com/question/6613758

help i am bad at geometry

Answers

Answer:

115.5 cubic meters.

Step-by-step explanation:

First find the are which is 10.5 because are is base times width divided by 2

The multiply the are with the height. 10.5 times 11 equals 115.5 cubic meters.

Please, Help.
the answer isn't 30°

Answers

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A)

How to find a missing angle by triangle properties

Triangles are geometrical figures formed by three sides and whose sum of internal angles equals 180°. There are two kind of triangles existing in this question: (i) Right triangles, (ii) Isosceles triangles.

Right triangles are triangles which one of its angles equals 90° and isosceles triangles are triangles which two of its sides have equal measures.

According to the statement, we know that triangle BQR is an isosceles triangle, whereas triangles ABC, ANB and NBC are right triangles. Based on the figure attached below, we have the following system of linear equations based on right triangles ABC and NBC:

2 · x + 90 + θ = 180   (1)

(90 - x) + 90 + θ = 180   (2)

By equalizing (1) and (2) we solve the system for x:

2 · x = 90 - x

3 · x = 90

x = 30

And by (1) we solve the system for θ:

θ = 180 - 2 · x - 90

θ = 30

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A) [tex]\blacksquare[/tex]

To learn more on right triangles, we kindly invite to check this verified question: https://brainly.com/question/6322314

A watercolor painting is 22 inches long by 8 inches wide. Ramon makes a border around the watercolor painting by making a mat that adds 3 inches to each side of the length and the width. What is the area of the mat?

Answers

to find:

the area of the mat.

solution:

22 + 3= 25

8 + 3= 11

= 25 inches long by 11 inches wide.

25 × 11= 275 in^2

the area of the mat is 275 in^2.

write each ratio in the simplest form 35 to 105

Answers

Answer: 35:105=1:3

Hope this helps! Have a good day !!! :)

In the figure below all lines intersect at point W what is the value of angle VWX?

Answers

Answer: 55

Step-by-step explanation:

Angle VWX and the 55 degree angle are vertical angles.

The sum of two numbers is 39. The larger number is 11 more than the smaller number. What are the numbers?

Larger number: ?
Larger number: ?

Answers

Answer:

Larger number = 25

Smaller number = 14

Step 1. Establish variables and system of equations

Larger number = x

Smaller number = y

&

x + y = 39

y + 11 = x

Step 2. Isolate a variable in ONE equation

x + y = 39

y = 39 - x

Step 3. Substitute that into the OTHER equation to find x

y + 11 = x

(39 - x) + 11 = x

50 - x = x

50 = 2x

25 = x

Step 4. Substitute that into the OTHER equation to find y

x + y = 39

(25) + y = 39

y = 14

Hope this helps!
Large: 25
Small: 14


i did. this for test practice in class on Friday!

which answer is right and please explain

Answers

None of them are right, you should email your teacher

What is V=(3.14)(12x12)(12)

Answers

Answer:

5,425.92

Step-by-step explanation:

multiply 12×12

then mulitply 144×3.14×12

Put a circle round the largest number and a square round the smallest number in estha
a) 8 -7 -4 0 7
b) -9 1 0 -1 -4
C) -4 -8 -3. -7 -2

Answers

Answer:

A 406 of answer your question please sorry

: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Answers

Answer:

A rational number: 5.4, which also can be written as 27/5

Irrational number:

sqroot 28

approx= 5.29

Step-by-step explanation:

5.4 is a rational number because it is a terminating decimal. That means it ends after the 4, there are no more numbers. Also it can be written as a ratio (looks like a fraction) 27/5.

Sqroot28 is irrational. Since 28 is not a perfect square, when you squareroot it you get a number with a neverending decimal

sqroot28 = 5.2915026221...

since the decimal does not repeat or end it cannot be written as a ratio, so it is not rational

sqroot28 ~= 5.29

3+x=7 help please I’m so confused

Answers

×=4

Step-by-step explanation:

#CARRY LEARNPA BRAINLIEST PO!

Answer:

[tex]\huge\boxed{\bf\:x = 4}[/tex]

Step-by-step explanation:

[tex]3 + x = 7[/tex]

Bring 3 to the right hand side of the equation and isolate the variable.

[tex]3 + x = 7\\x = 7 - 3\\\boxed{\bf\:x = 4}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

50% is the same as what decimal?

Answers

Answer:

0.5

Step-by-step explanation:

To convert a percentage into a decimal you divide by 100 :

50% ÷ 100 = 0.5

Hope this helped and brainliest please

Answer: 0.5

Step-by-step explanation: 50/100

Help Needed. Please.....!

Answers

Answer:

1  7/8

Step-by-step explanation:

You just have to subtract 2 from 1/8.

Quotient for 7.924/0.7

Answers

Answer:

11.32

Step-by-step explanation:

Help me please I don’t know what to do

Answers

Answer:

You didn't include the question, so people are unable to help you.

Please answer this it would be very helpful if you did.

Answers

Answer:

See below ↓↓↓

Step-by-step explanation:

Probability of getting heads

Outcome (head) = 1Total outcomes = 2P (head) = 1/2

Probability of getting an odd number

Outcome (odd) = {1, 3, 5} = 3Total outcomes = 6P (odd) = 3/6 = 1/2

The outcomes are equally likely because the probabiity of each outcome is the same.

Which number line shows all the values of x that make the inequality -3x + 1 < 7 true

Answers

After solving the equation (work shown in image) your answer would be x > -2. I drew an image of how the number line should look at least similar to, using the solution.

*whenever you divide or multiply with a negative number reverse/flip the sign

< or > signs will always have an open circle

≥ or ≤ signs will have a closed/filled in circle

TIP: To know which way the arrow should point, look at the sign and think of it as an arrow.

< would have the arrow on the number point

this way: <-

or > which would have the arrow on the number line point this way: ->

Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)

Answers

Using the Pythagorean theorem:

X^2 = 10^2 + 24^2

X^2 = 100 + 576

X^2 = 676

X = sqrt(676)

X = 26


answer: 26

Answer:

26 :)

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

Lets solve!!

10^2 + 24^2 = c^2

100 + 576 = c^2

676 = c^2

Now lets find the square root!!

[tex]\sqrt{676}[/tex] = 26

Have an amazing day!!!

Please rate and mark brainliest!!

Refer to the figure below. What are the answers for the four blanks?

Answers

Answer:

see explanation

Step-by-step explanation:

the figure is an isosceles trapezium

The legs are congruent , that is

BC = AD = 15 units

The upper base angles are congruent , so

∠ B = ∠ A = 145°

Any lower base angle is supplementary to any upper base angle, that is

∠ C + ∠ B = 180°

∠ C + 145° = 180° ( subtract 145° from both sides )

∠ C = 35°

The lower base angles are congruent , so

∠ D = ∠ C = 35°

Help me please so i can get points real quick!!

Answers

Area = πr2

Area of shaded part
= π(8^2) - π(5^2)
= π[(8^2)-(5^2)]
= π(64-25)
= π x 39
= 122.52 yard squared

If X=25 when y=125, what is the value of x when y=25?

Answers

Answer:

5

Step-by-step explanation:

x=1/5y

what is the area of this shape?

Answers

130.5 I think because top triangle is 9 by 3 middle rectangle is 12 by 9 and bottom square is 3 by 3

Answer:

130.5 mi sq

Triangle: A = bh/2

A = ((21 - 12) x (3))/2

A = (9 x 3)/2 = 13.5 mi sq

Middle rectangle: A = bh

A = (6 + 3)(15 - 3)

A = (9)(12) = 108 mi sq

Last rectangle: A = bh

A = 3 x 3 = 9 mi sq

TOTAL: 13.5 + 108 + 9 = 130.5 miles sq

Have a good night!

simplify the following quadratic expressions
1) 2x^2 -3x -9
2) 3x^2 +5x +2​

Answers

Answer:

Below in bold.

Step-by-step explanation:

1) 2x^2 -3x -9

 2 * -9 =  -18. We need 2 numbers whose product is -18 and whose sum     is -3. They are -6 and + 3. So:

= 2x^2 - 6x + 3x - 9

= 2x(x - 3) + 3(x - 3)

= (2x + 3)(x - 3)

2) 3x^2 + 5x +2​

Now 3 * 2 = 6   We need to numbers whose product is + 6 and whose  sum is +5.  Theres are + 3 and + 2>

= 3x^2 + 3x + 2x + 2

= 3x(x + 1) + 2(x + 1)

= (3x + 2)(x + 1)

=

what is the slope of (2,5) (-6,-3)

Answers

Answer:

m=1

Step-by-step explanation:

(2,5);(−6,−3)

(x1,y1)=(2,5)

(x2,y2)=(−6,−3)

Use the slope formula:

m=

y^2−y^1

x^2−x^1

=

−3−5/−6−2

=

−8/−8

=1

Answer:

m=1

Answer:

[tex]\boxed{\sf{1}}[/tex]

Step-by-step explanation:

To solve this problem, you have to use a slope formula.

Slope formula:

[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{Rise}{run} }[/tex]

[tex]\sf{y_2=(-3)}\\\\\sf{y_1=5}\\\\\sf{x_2=(-6)}\\\\\sf{x_1=2}[/tex]

Rewrite the problem down.

[tex]\sf{\dfrac{(-3)-5}{(-6)-2} }[/tex]

Solve.

[tex]\sf{\dfrac{(-3)-5}{(-6)-2}=\dfrac{-8}{-8}=\boxed{\sf{1} }[/tex]

Therefore, the slope is 1, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

What is the volume of a right circular cylinder with a diameter of 19.6 yd and a height of 23.52 yd?

Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.

Answers

Answer:

7092.82 cubic yards

Step-by-step explanation:

The volume of a right circular cylinder is given by:

V represents the volume of a cylinder.

r represents the radius of a cylinder.

h represents the height of a cylinder.

As per the given statement:

Diameter(D) = 19.6 yd and height(h) = 23.52 yd.

Diameter = 2r where r is the radius of the cylinder

Substitute these given values in [1] we have cubic yard

Simplify:

V = 7,092.82291 cubic yard.

Hope this helps!

A) not periodic
B) periodic with a period of 6 and an amplitude of about 12.5
C) periodic with a period of 6 and an amplitude of about 25
D) periodic with a period of 12 and an amplitude of about 12.5​

Answers

Answer:    A) not periodic

Explanation:

Plot all of the data points on the same xy grid as shown below.

I used GeoGebra to make the diagram.

The points seem to be randomly scattered about without any apparent pattern (though there might be some symmetry going on). The data does not seem to be periodic.

Periodic data repeats itself at some point in time, for example like a waveform pattern, which unfortunately these data points don't reflect.

give me the full working and I give you stars ​

Answers

→ Area of rectangle = Length * Width

Here given:

Length = 63 mWidth = 17 m

Here area:

L * W63 * 17 1071 m²

Answer:

1071 m²

Step-by-step explanation:

The area of a rectangle is basically the length multiplied with the width. The length can be any side length, but the width must be the adjacent to the length. Thus, we can let the length be 63 meters and the width be 17 meters as the width is adjacent to the length.

⇒ Area of rectangle = Width × Length

⇒ Area of rectangle = 17 × 63

Area of rectangle = 1071 m²

I Need help asap!!!!!!!!!!!!!!!!!!

Answers

Answer:

The answer of how many cars is 23

The answer would equal to 23 cars rented
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