Answers
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}}[/tex] :
a = dk³ , b = dk² , c = dk[tex] \underline{ \underline{ \text{To \: prove}}} : [/tex]
[tex] \tt{ \sqrt{ab} - \sqrt{bc} - \sqrt{cd} = \sqrt{(a - b - c)(b - c - d)} } [/tex]
[tex] \underline{ \underline{ \text{Solution}}} : [/tex]
Left hand side ( L.H.S ) :
[tex] \tt{ \sqrt{ab} - \sqrt{bc} - \sqrt{cd}} [/tex]
⟶ [tex] \tt{ \sqrt{d {k}^{3} \cdot \: d {k}^{2} } - \sqrt{d {k}^{2} \cdot \: dk } - \sqrt{dk \cdot \: d} }[/tex]
⟶ [tex] \tt{ \sqrt{ {d}^{2} {k}^{5} } - \sqrt{ {d}^{2} {k}^{3} } - \sqrt{ {d}^{2}k } }[/tex]
⟶ [tex] \tt{ \sqrt{ {d}^{2} \cdot \: {k}^{2} \cdot \: {k}^{2} \cdot \: k } - \sqrt{ {d}^{2} \cdot \: {k}^{2} \cdot \: k \: } - \sqrt{ {d}^{2}k } }[/tex]
⟶ [tex] \tt{ \sqrt{ {d}^{2} } \cdot \sqrt{ {k}^{2} } \cdot \: \sqrt{ {k}^{2} } \cdot \: \sqrt{k} } - \sqrt{ {d}^{2} }\cdot \: \sqrt{ {k}^{2}} \cdot \: \sqrt{k} \: - \sqrt{ {d}^{2} } \cdot \: \sqrt{k} [/tex]
⟶ [tex] \tt{d {k}^{2} \sqrt{k} - dk \sqrt{k} - d \sqrt{k} }[/tex]
⟶ [tex] \tt{ d\sqrt{k} \: ( {k}^{2} - k - 1) } [/tex]
Right Hand Side ( R.H.S) :
[tex] \tt{ \sqrt{(a - b - c)(b - c - d)}} [/tex]
⟶ [tex] \tt{ \sqrt{(d {k}^{3} - d {k}^{2} - dk)( d{k}^{2} - dk - d)} }[/tex]
⟶ [tex] \tt{ \sqrt{ \{dk( {k}^{2} - k - 1) \} \: \{d( {k}^{2} - k - 1) \}} }[/tex]
⟶ [tex] \tt{ \sqrt{ {d}^{2}k( {k}^{2} - k - 1) ^{2} } } [/tex]
⟶ [tex] \tt{ \sqrt{ {d}^{2}k } \cdot \: \sqrt{ {( {k}^{2} - k - 1)}^{2} } } [/tex]
⟶[tex] \tt{ \sqrt{ {d}^{2} } \cdot \: \sqrt{k} \cdot \: \sqrt{( {k}^{2} - k - 1) ^{2} } }[/tex]
⟶ [tex] \tt{d \sqrt{k} \: ( {k}^{2} - k - 1) } [/tex]
L.H.S = R.H.S
Hence , Proved !
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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Related Questions
I rly need help! I will mark brainliest if you are correct
Answers
Hope that helps
If an author can type 2500 words in 5 minutes, how many words can he type in 210 minutes?
Answers
Answer:
105,000
Step-by-step explanation:
2500/5 gives you 500 x 210 =105,000
If Mr.John has a new house he want to put mats on the flour the length of the mat is 95cm and the width is 74cm that is the perimeter of the mat Mr.John has?
Answers
Answer:
338cm
Step-by-step explanation:
P= 2( L+W)
P=2(95+74)
P=2(169)
P=338cm
What is the value of x in the figure shown below
Answers
Answer:
x = 34 degrees
Step-by-step explanation:
if this is a parallelogram then Δ ACB ≅ Δ DCB
which means that ∠A = ∠D
Find the value of X.
Answers
Answer:
In My Knowledge
Option G. 10.4cm is the answer
is there more options
if yes please tell me
2*10⁴-7³ please help
Answers
Answer:
19657
Step-by-step explanation:
By PEMDAS, we know we have to calculate the exponents first, then multiply the 2, and then subtract the 7³
2*10⁴ = 20000
20000 - 7³ = 19657
This is the third time I've seen this question. Are you posting this question again and again?
Does anyone know how to do geometry? Please help
Answers
Answer:
No
Step-by-step explanation:
>>>>
Order from least to greatest
1.84, the square root of 5, 2.3,the square root of 3
Answers
Answer:
square root of 3 ,1.84,2.3, square root of 5
What is the measure, in degrees, of the angle marked B?
133
65
68
47
Answers
All triangles are 180 degrees. Add the 2 numbers given to get a number. Take 180 and subtract it from that number to get 47
Answer:
[tex]\boxed {\boxed {\sf 133 \ degrees }}[/tex]
Step-by-step explanation:
According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the 2 remote and opposite interior angle.
[tex]d=a+b[/tex]
In this triangle, angle B is the exterior angle (d). The two interior angles are 68 degrees and 65 degrees ( a and b).
[tex]\angle B=68 \textdegree +65 \textdegree[/tex]
Add.
[tex]\angle B= 133 \textdegree[/tex]
This can also be solved using triangles and supplementary angles.
The angles in a triangle must add to 180 degrees. We have three angles: 68, 65, and an unlabeled angle we can call x.
[tex]68+65+x=180 \\133+x=180[/tex]
Subtract x from both sides.
[tex]133+x=180-133 \\x=47[/tex]
x is on a straight line with B, so they are supplementary and add to 180 degrees.
[tex]47+ \angle B= 180[/tex]
Subtract 47 from both sides.
[tex]47-47+ \angle B= 180-47\\\angle B= 133[/tex]
Angle B is equal to 133 degrees.
A theater has 384 seats. Each row has 16 seats. The area model represents this situation. Area model showing 2 areas. The first is16 high and 20 wide, with a total of 320. The second is 16 high and x wide, with a total of 64. Part A What is the value of x in the area model? Enter your answer in the box. x = 4 I already answer part A what is the answer for part B?? Part B How many rows of seats are inside the theater? Enter your answer in the box. rows
Answers
Answer:
x=4
Rows = 24
There are 24 rows each having 16 seats making a total of 384.
Step-by-step explanation:
Part B
Total number of seats = Total of rows* Number of seats in each row
Let the total number of rows be y. The theater has 384 seats and each row has 16 seats. Putting the values
384= y * 16
y= 384/16= 24
There are 24 rows each having 16 seats making a total of 384.
Part A:
Area= length * width
Area 1= 320= 16 *20
Area 2 = 64
64 = 16 x
x= 64/16= 4
Need a little help here pls
Answers
Answer:
The statements that must be true are:
XY and JK form four right angles ⇒ B
XY ⊥ JK ⇒ C
JP = KP ⇒ E
m∠JPX = 90° ⇒ F
Step-by-step explanation:
From the given figure
∵ Line XY is the perpendicular bisector of the line segment JK
→ That means line XY is the line of symmetry of the line segment JK
∴ XY ⊥ JK ⇒ C
∵ XY ∩ JK at point P
∴ P is the midpoint of JK
∵ XY ⊥ JK
∴ ∠JPX, ∠KPX, ∠JPY, and ∠KPY are right angles
∴ XY and JK form four right angles ⇒ B
∵ The measure of the right angle is 90°
∴ m∠JPX = m∠KPX = m∠JPY = m∠KPY = 90°
∴ m∠JPX = 90° ⇒ F
∵ P is the midpoint of JK
∴ JP = KP ⇒ E
(5x - 2y = 22
8x - 2y = 28
Please!! Urgent
Answers
9514 1404 393
Answer:
(x, y) = (2, -6)
Step-by-step explanation:
Subtract the first equation from the second.
(8x -2y) -(5x -2y) = (28) -(22)
3x = 6
x = 2
Substitute this into either equation and solve for y.
8(2) -2y = 28
8 -y = 14 . . . . . . . . divide by 2
y = 8 -14 = -6 . . . . add y-14 to both sides
The solution is (x, y) = (2, -6).
_____
I like a graphing calculator for a quick solution to such problems.
2x-4=x+6 how solve this
Answers
Answer:
x = 10
Step-by-step explanation:
1. Add 4 to both sides of the equation
2. Simplify
3. Subtract x from both sided of the equation
4. Simplify
Therefore, x = 10
Hope this helps :)
Answer:
=10
Add 4
to both sides of the equation 2−4=+6
2x-4=x+6 2−4+4=+6+4
turquoise paint is made by mixing blue, green and yellow paint in the ratio 2.5 : 1.4 : 0.1 . how much of each colour is needed to make 1.5 litres of turquoise paint? write answers in the same order as the ratio (eg, blue, green, then yellow)
Answers
Answer: Blue color = 937.5 ml
green color = 525 ml
Yellow color= 37.5 ml
Step-by-step explanation:
Let the quantity of all kinds of paint required to make turquoise paint be 2.5 x(blue), 1.4 x( green), 0.1 x.(yellow).
Total turquoise color required =2.5x+1.4x+0.1x
[tex]\Rightarrow (2.5+1.4+01)x=1.5\\\\\Rightarrow\ 4x = 1.5\\\\\Rightarrow x=\dfrac{1.5}{4}\\\\\Rightarrow\ x=0.375[/tex] = 1.5 liters [given]
Blue color = 2.5 x 0.375 = 0.9375 liters = 937.5 ml [1 liter = 1000 ml]
green color = 1.4 x 0.375= 0.525 l = 525 ml
Yellow color= 0.1 x 0.375= 0.0375 =37.5 ml
solve for x, tan 12 = 22 over x
Answers
Answer:
tan 12=22/x
x=22/tan 12
x=103.77.................
You mix 1/3 teaspoon of baking soda with 3 teaspoons of salt. What is the value of the ratio of baking soda to salt?
Answers
NEED AN ANSWER SOON
Find the slope of the line that contains the points named. A(3, 2), B(7, 8) 5/2 3/2 2/3
Answers
Answer:
3/2
Step-by-step explanation:
To find the slope you would use the slope formula which is (y2-y1) / (x2-x1).
(8-2) / (7-3)
m = 3/2
When you add a positive number and a negative number, how can
you tell whether the sum will be positive or negative?
Answers
Answer: By looking at which one is bigger
Step-by-step explanation:
if the negative number is a bigger number than the positive your answer will be negative, if the positive number is larger than the negative your answer will be positive if your negative and positive numbers are the same your answer will be zero, hope this helps <3
Answer:
+ - = -
Step-by-step explanation:
+ (+) = +
+ (-) = -
- (-) = -
- (+) = -
Two like signs become a positive sign
Two unlike signs become a negative sign
I neeed help it’s a word problem
Answers
Answer:
12.50
Step-by-step explanation:
62/5=12.4
60/2=30
5/2=2.5
I NEED HELP ASAP IT'S DUE IN 40 MINUTES!!! I'LL GIVE BRAINLIEST!!!
Answers
Answer:
Transversal
Step-by-step explanation:
Sultan needs enough tents for 28 people to sleep in. Each tent can fit 6 people. How many tents does he need?
Answers
Answer:
5 tents
Step-by-step explanation:
1 tent = 6 people
x tent = 28 people
Cross product
1 * 28 = 6 * x
28 = 6x
x = 28/6
= 4.67
Approximately x = 5 tents to an whole number
Therefore, he needs 5 tents for 28 people to sleep in
Can someone help me, if u can ty bless you.
Answers
Answer : 2/3 or 0 R 6
Step-by-step explanation:
hope it helps
Could you guys help me again?
Answers
Answer:
1. n power of 25
2.x power of 5
22 Solve. Type the correct numeric answer in the space provided.
3 1/2 divided by 4 3/8
Answers
Answer:
0.8
Step-by-step explanation:
3 1/2 = 3.5.... 4 3/8 = 4.375
so 3.5 Divided by 4.375 is 0.8
please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!
Answers
Answer:
60
Step-by-step explanation:
I'm taking a test and it's really important that I pass it because I'm already failing the class. Please help me I have no idea how to do it. The test has a time limit, everything has to be submitted by 12:25 at the latest. Please show the work if you can.
Simplify the expressions
1. (1+2i)(5-5i)
2. (1+2i)-(-2-2i)
3. (1+2i)+(2-i)
4. (6i)(-5i)
Answers
Answer:
1. 15+5i
2. 3+4i
3. 3+i
4. 30
Step-by-step explanation:
the base of a pyramid has n sides
write an expression for the number of faces on the pyramid
Answers
Answer: The expression for number of faces of a pyramid =1+n
Step-by-step explanation:
A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .
Its base describe the number of other faces of it.
For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....
So the total number of faces in a pyramid = base + lateral faces
If a pyramid has n sides therefore it give rise to n lateral faces such that
The total number of faces in a pyramid= 1+n .
Read the caption! Thanks, if you can helps thank you
Answers
Step-by-step explanation:
For a triangle, any 2 side lengths of the triangle must be greatee than the 3rd side.
Given a triangle with side lengths 11, 23 and x,
we have:
11 + 23 > x,11 + x > 23, and23 + x > 11.Therefore 34 > x and x > 12. => 12 < x < 34.
Answer:
second option
Step-by-step explanation:
Given 2 sides of a triangle then the third side x is
difference of 2 sides < x < sum of 2 sides , that is
23 - 11 < x < 23 + 11, thus
12 < x < 34
function or not a function?
Answers
What is the solution to this system of equations?
4y + x = 5
x + 4y = 10
Answers
It won’t let me post
the equation doesn't have a solution lol