Answers
[tex] \bold{\underline{\underline{\underbrace{Answer}}}} [/tex]
x = p and y = -q
Step-by-step explanation:
To findThe value of x and y
Givenpx + qy = p² - q²(equation 1)
qx - py = 2py
Solution{Taking equation 2}
[tex] \sf qx - py = 2py[/tex]
{Taking py on RHS}
[tex] \sf qx = 2py \ + py [/tex]
{Dividing both sides by q
[tex] \sf x = \frac{2pq}{q} + \frac{py}{q} \\ \\ \sf x = 2p + \frac{py}{q} (equation \: 3)[/tex]
{Now substituting the value of equation 3 in equation 1}
[tex] \sf p(2p + \frac{py}{q} ) + qy = {p}^{2} - {q}^{2} \\ \\ \sf 2 {p}^{2} + \frac{ {p}^{2}y }{q} + qy = {p}^{2} - {q}^{2} [/tex]
{Taking 2p² on RHS and taking LCM on LHS}
[tex] \sf \frac{ {p}^{2}y + {q}^{2} y }{q} = {p}^{2} - {q}^{2} - 2 {p}^{2} \\ \\ \sf \frac{y( {p}^{2} + {q}^{2} ) }{q} = - ( {p}^{2} + {q}^{2} )[/tex]
{Dividing (p² + q²) both sides}
[tex] \sf \frac{y}{q} = - 1 \\ \\ \red{ \boxed {\bold{y = - q}} }[/tex]
{Now using value of y in equation 3}
[tex] \sf x = 2p - \frac{pq}{q} \\ \\ \sf x = 2p - p \\ \\ \red{ \boxed{ \bold{ x = p}}}[/tex]
Related Questions
An architect is designing a house. She wants the bedroom to have the dimensions of 10 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom?
Answers
The volume of the den ( 2240ft³ ) is 1960ft³ more than the volume of the bedroom ( 280ft³ ).
Hence, the den will not have double the volume of the bedroom.
Does the den have double the volume of the bedroom?Given the dimensions in the question, the bedroom and the den takes the shape of rectangular prism.
Volume of rectangular prism is expressed as;
V = l × b × h
Given that;
Length of the bedroom l = 10ftBreadth of the bedroom B = 4ftHeight of the bedroom h = 7ftLength of the den = 2l = 2×10ft = 20ftBreadth of the den = 2B = 2×4ft = 8ftHeight of the den = 2h = 2×7ft = 14ftFirst we calculate the volume of the bedroom.
V = l × b × h
Vr = 10ft × 4ft × 7ft
Vr = 280ft³
Next, we determine the volume of the den
V = l × b × h
Vd = 20ft × 8ft × 14ft
Vd = 2240ft³
The volume of the den ( 2240ft³ ) is 1960ft³ more than the volume of the bedroom ( 280ft³ ).
Hence, the den will not have double the volume of the bedroom.
Learn more about the volume of rectangular prism here: https://brainly.com/question/27804313.
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Simplify the rational expression
x^4 y^2/xy^7.
Answers
Answer: [tex]x^3y^9[/tex]
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): Dot was discarded near "7.".
STEP 1:
Simplify [tex]\frac{y^2}{x}[/tex]
The equation at the end of step 1:
[tex]((x^4)*\frac{y^2}{x} )*y^7[/tex]
Multiplying exponential expressions:
2.1 [tex]y^2[/tex] multiplied by [tex]y^7[/tex] [tex]=y^(2+7)=y^9[/tex]
Final result is [tex]x^3y^9[/tex]
Nannette buys a $5000 20-year bond that has a coupon rate of 2.5 %. If she keeps the bond to maturity, how much money plus principal interest will she have collected over the life of the bond?
Answers
The total amount collected over the life of the bond is $7,500.
What is the total amount collected?A bond is a debt instrument that entitles its holder to regular interest payments. At the end of the life of the bond, the bondholder receives the amount invested back.
Total earnings = interest + amount invested
(20 x 0.025 x 5000) = $2500
Amount invested = $5000
= 2500 + 5000 = $7,500
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Add 3/4 + (−2 1/2) using the number line.
Select the location on the number line to plot the sum.
Answers
Answer:
Heyyy!!!!
Alrighty... here it goes....
Step-by-step explanation:
3/4 + (-2 1/2)
okay... the first thing you have to do is convert 1/2 into fourths. that'll make it way easier to solve..... like way easier.....
then rewrite the expression to get 3/4 + (-2 2/4)
now we know that + - = -
basically you subtract since adding a negative makes you subtract...
3/4 - 2 2/4 gives you - 1 3/4
all you have to do is plot that on the number line and you should be good to go
state the value of factorial 6 !
[tex] \\ [/tex]
ty! ._.
Answers
hope this helps!
──────⊹⊱✫⊰⊹──────
What is the State the value of factorial 6 ?
Aɴsᴡeʀ :-
720
✔︎ Expʟaɴaᴛiᴏn :
Because we have to do first !
ɴ = ɴ × (ɴ - 1) × (ɴ – 2) × (ɴ – 3) = 6
So your factorial will be 6.
Oʀ, ʏᴏᴜ ᴄᴀɴ ᴅᴏ ɪs:-
6 = 6 × (6 -1) × (6 – 2) × (6 – 3) × (6 – 4) × 1
720.
Aɴᴅ, ʏᴏᴜ ᴄᴀɴ ᴅᴏ ɪs.
6 × 5 × 4 × 3 × 2 × 1
= 720
Thus, your factorial will be 6 is 720.
Hope It Helps! ~
Aɴsᴡeʀ :-
Sxɴɴʏsᴏᴜʟ
.
[tex]x^{2} +x = 12[/tex]
answer ?
Answers
Answer:
x = 4 and x = -3
Step-by-step explanation:
⇒ x² + x = 12
⇒ x² + x - 12 = 0
⇒ x² + 3x - 4x - 12 = 0
⇒ x(x + 3) - 4(x + 3) = 0
⇒ (x - 4)(x + 3) = 0
⇒ x = 4 and x = -3
Hey there!
x^2 + x = 12
SUBTRACT 12 to BOTH SIDES
x^2 + x - 12 = 12 - 12
SIMPLIFY IT!
x^2 + x - 12 = 0
SET the FACTORS to EQUAL to 0
x - 3 = 0 OR x + 4 = 0
SIMPLIFY IT!
x = 3 or x = -4
Therefore, the answer is:
x = 3 or x = -4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Evaluate 6ab + 2c if a = 3, b = 10, and c = 7
Answers
Answer:
6 (3 ×10 ) + 2 (7)
6(30) + 14
180 + 14
= 194
Answer: 194
Step-by-step explanation:
Given:
6ab + 2c
a = 3, b = 10, c = 7
Solve:
1. Plug in what you know and solve for your answer
⇒ 6(3)(10) + 2(7)
⇒ 6(30) + 14
⇒ 180 + 14
⇒ 194
What is the slope of the line that
passes through these two points?
(2, 3)
(2,9)
Answers
Answer:
Slope = undefined.
Step-by-step explanation:
Given two points:
(2,3) & (2,9)To Find:
The slopeSolution:
Using slope's formulae,
[m denotes slope]
[tex] \boxed{ \rm{m = \cfrac{y_2 -y_1 }{x_2 - x_1} }}[/tex]
According to the question,here:
(y_2,y_1) = (9,3)(x_2,x_1) = (2,2)Substitute them onto the formulae:
[tex] \rm \: m = \cfrac{9 - 3}{2 - 2} [/tex]
Simplify.
[tex] \rm \: m = \cfrac{6}{2 - 2} [/tex]
[tex]\rm \: m = \cfrac{6}{0} = \boxed{ \rm \: undefined}[/tex]
if an expression contains division by 0 , then It's undefined.
So, slope(m) = undefined.
How much would you have to
deposit today to have an
accumulated amount of
$20,000 in 20 years if yearly
interest is 4.75% compounded
continuously?
Answers
Answer:
If it went up it would be: 50596.35 and if it went down it would be: 7556.66
Step-by-step explanation:
Here will be the function if it went up:
20000(1+0.0475)^20
Here’s if it went down:
20000(1-0.0475)^20
What is the area of the triangle Base is 6 ft height is 5 ft.
Answers
Answer:
Area of a triangle = 0.5 * base * height = 0.5 * 6 * 5 = 15 sq. ft
Answer:
Area = 0.5 * base * height
0.5 * 6 * 5 = 15
Area = 15 sq ft
How to find area of a composite figure PLS HELP
Answers
Answer:
5×5=25
8×5÷2=20
25+20= 45
area of a composite 45
Assume you are going to buy a new Nissan Rouge priced at $38250.00 and after the deal you have found out that the sales tax is 9%. Estimate the answer
Answers
On a map, 1 inch equals 25 miles. Two cities are 3 inches apart on the map. What is the actual distance between the cities?
Answers
Answer:
75 Miles apart
Step-by-step explanation:
I = inches on a map
I=25
3I=75
75 miles apart
Which graph shows the solution to the system of linear inequalities?
Answers
Answer:
this is answer
Step-by-step explanation:
To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line. If the inequality is strict ( < or > ), graph a dashed line.
Find the median, first quartile, third quartile, and interquartile range of the data.
14,25,97,55,66,28,92,38,94
Find the median, first quartile, third quartile, and interquartile range of the data.
14,25,97,55,66,28,92,38,94
Answers
Answer:
BELOW IN BOLD.
Step-by-step explanation:
14,25,97,55,66,28,92,38,94
Arrange these in ascending order:
= 14 25 28 38 55 66 92 94 97
The median = middle number = 55.
First quartile = (25+28)/2 = 26.5.
Third quartile = (92 + 94)/2 = 93.
Interquartile range = 93 - 26.5 = 66.5.
Please helppppppppppp
Answers
Steven is puiting a design that contains two repeating patterns that start in the same place. One pattern repeats every 12 inches and the other repeats every 18 inches. How many inches will it take for the patterns to begin together again?
Answers
Answer:
36
Step-by-step explanation:
So, taking 12 inches and 18 inches, we can figure out where they both meet. To do this, you want to change these number into a fraction (12/18). Simplifying this gives you 2/3. So if you flip this fraction (3/2) and then use these number and multiply them with the first numbers (so we do 3*12 and 2*18, they both equal 36, so they would both meet at 36, our final answer. they would also meet at 72, 108, 144, etc. if you were to keep going.
Evaluate the difference quotient
f(x)-f(1)/X-1, where f(x)=X +5/x+1
Answers
Answer:
C) [tex]\displaystyle\frac{-2}{(x+1)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{f(x)-f(1)}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{1+5}{1+1}}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{6}{2}}{x-1}\\\\\frac{\frac{2(x+5)}{2(x+1)}-\frac{6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2(x+5)-6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2x+10-6x-6}{2(x+1)}}{x-1}\\\\\frac{\frac{-4x+4}{2(x+1)}}{x-1}\\\\\frac{\frac{-4(x-1)}{2(x+1)}}{x-1}\\\\\frac{-4}{2(x+1)}\\ \\\frac{-2}{(x+1)}[/tex]
6) What time will it be 17 hours and 53 minutes before 4:37 a.m.? Military time
Answers
Answer:
17:53=5:53pm
Step-by-step explanation:
33. Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
505 m² :519 m ²
505 m ²: 533 m ²
497 m ²: 519 m ²
497 m ²: 533 m ²
Answers
Answer: ⬇️⬇️⬇️⬇️
Lateral area = 505 m² ; Surface area = 519 m²
Hope I helped
Lateral area = Perimeter x height
Lateral area = (2 + 7 + 7.28) x 31 = 16.28 x 31 = 505 m²
Surface area = 2(1/2 x 2 x 7) + 505 = 519 m²
Answer: Lateral area = 505 m² ; Surface area = 519 m²
What is the median of this data set?
{16, 16, 16, 19, 20, 22, 23, 24, 24}
Answers
Answer:
The median is 20
Step-by-step explanation:
They are already in order so you would just have to find the middle.......
Hope this helps.......if not then sorry for wasting your time and may God bless you
which ordered pair in the form (x,y) is a solution of this equation?
7x-5y=28
(-3,-2)
(-2,-3)
(0,4)
(4,0) will give brainly to who ever gets it right please and thank you
Answers
Answer:
I think is 4,0
Step-by-step explanation:
if u divide 28 by seven u would get 4 and u cant divide 28 by 5 sooo it would be a decimal but that isnt an option so imma say its the last one
Please help I put 50 points into this
Answers
Answer:
B,C,E
Step-by-step explanation:
Answer:
A, C, D
Step-by-step explanation:
A ray can have 2 endpoints
And because of that it can be named more than one way.
That means that B&E are wrong
22% of what amount is $88?
Answers
Answer: The final cost would be 68.64
Explanation: Step 1) Convert 22% to a decimal: 0.22
Step 2) Multiply that by the amount (0.22×88=19.36)
Step 3) Subtract from the amount (88−19.36)=$68.64
Answer $68.64
At a Forex Bureau, one US dollar costs Ug.sh.2800. How much Ugandan shillings will a tourist who has US dollars 600 get?
Answers
Answer:
1,680,000 shillings
Step-by-step explanation:
As one US dollar is 2800, and the dollar is repeated 600 times. You multiply Both
=2,800×600
=1,680,000 shillings
--~Hope you understood~--
Helppp I need this asap
Answers
Answer:
[tex]x = 35[/tex]
Step-by-step explanation:
We can use Similar Triangles Ratios to solve for the missing side length. First setup your ratios:
[tex]\frac{42}{6} = \frac{x}{5}\\x = \frac{42}{6} \times 5\\x = 35[/tex]
Answer:
35
Step-by-step explanation:
The sides are in proportion.
[tex]\frac{AB}{PQ} =\frac{AC}{PR}[/tex]? / 5 = 42 / 6? = 5 × 7? = 35This table represents a proportional relationship between x and y.
x 1.3 1.6 1.9 2.2
y 1.82 2.24 2.66 3.08
What is the constant of proportionality?
Enter your answer as a decimal in the box.
ill give brainliest this is for k12
Answers
The table is an illustration of a linear table, and the constant of proportionality is 1.4
How to determine the constant of proportionality?The table is given as:
x 1.3 1.6 1.9 2.2
y 1.82 2.24 2.66 3.08
The constant of proportionality (k) is calculated using:
k = y/x
Using the values on the table, we have:
k = 1.82/1.3
Divide
k = 1.4
Hence, the constant of proportionality is 1.4
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if n varies directly with m and m=-12 when n=4 what is the value when n=-3
Answers
Step-by-step explanation:
m and n are directly linked to each other by a factor.
m×k = n
-12×k = 4
k = 4/-12 = -1/3
m×-1/3 = -3
m = 9
A regular-size box of dog treats measures 314 inches by 712 inches by 12 inches. The manufacturer also sells a small-size box that has a volume that is 310 of the volume of the regular-size box.
What is the volume of the small-size box of dog treats?
Enter your answer as a mixed number in simplest form by filling in the boxes.
(its going to be a mixed number) in³
Answers
The volume of the small-size box of dog treats will be equal to V=8654.24 In³
What is volume?Volume is defined as the space occupied by any body in the three-Dimensions. All three parameters are required for the volume like length,width and height of the cube or Cuboid
The volume of the rectangular box will be:-
V=LxWxH
V=314x712x12
So the volume of small size box will be:-
V=2682816÷310=8654.24
Hence the volume of the small-size box of dog treats will be equal to
V=8654.24 In³
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Round off 380•59 to the nearest whole number easy 5points
Answers
Answer:
381
Step-by-step explanation:
that's the nearest whole number