Step-by-step explanation:
Given that:
{(x²+y²)/(x²-y²)} = 17/8
On applying cross multiplication then
since, (a/b) = (c/d) ⇛a(d) = b(c)
Where, x = x²+y², b = x²-y², c = 17 and d = 8
So,
⇛17(x²-y²) = 8(x²+y²)
Multiply the number outside of the brackets with variables in the brackets on both LHS and RHS.
⇛17x²-17y² = 8x²+8y²
⇛17x²-17y² - 8x²-8y² = 0
⇛17x²- 8x² - 17y² - 8y² = 0
⇛9x² - 25y² = 0
⇛9x² = 25y²
⇛9/25 = y²/x²
⇛25/9 = x²/y²
⇛x/y = √(25/9)
⇛x/y = √{(5*5)/(3*3)}
⇛x/y = 5/3
Therefore, x:y = 5:3
Let x = 5a and y = 3a
Now, (x³+y³):(x³-y³)
= {(x³+y³)/(x³-y³)} = [{(x+y)(x²-xy+y²)}/{(x-y)(x²+x-y+y²)}]
= [{(5a)³ + (3a)³}/{(5a)³ - (3a)³}]
= [{(5*5*5*a*a*a) + (3*3*3*a*a*a)}/{(5*5*5*a*a*a) - (3*3*3*a*a*a)}]
= {(125a³ + 27a³)/(125a³ - 27a²)}
= {(152a³)/(98a³)}
= 152/98
Write the obtained fraction in lowest form by cancelling method.
= {(152÷2)/(98÷2)}
= 76/49
Therefore, , (x³+y³):(x³-y³) = 76/49
Answer: Hence, the required value of (x³+y³):(x³-y³) is 76/49.
Please let me know if you have any other questions.
Answer:
76:49 or 49:76
Step-by-step explanation:
The second relation gives an expression for y in terms of x:
[tex]\dfrac{x^2+y^2}{x^2-y^2}=\dfrac{17}{8}\\\\8x^2+8y^2=17x^2-17y^2\qquad\text{cross multiply}\\\\25y^2=9x^2\qquad\text{add $(17y^2-8x^2)$}\\\\5y=\pm3x\qquad\text{take the square root}\\\\y=\pm\dfrac{3}{5}x\qquad\text{divide by 5}[/tex]
Substituting into the expression we want the value of, we can factor out x^3 to get ...
[tex](x^3+y^3):(x^3-y^3)=(1\pm(3/5)^3):(1\mp(3/5)^3)=(125\pm27):(125\mp27)\\\\=152:98\text{ or }98:152=\boxed{76:49\text{ or }49:76}\m[/tex]
_____
Additional comment
There is nothing in the given requirement that means x and y must have the same sign. If the signs are different, then the value of the expression is less than 1, rather than greater than 1.
Find the area of the rectangle below
length = 11 in
width = 17 in
Answer:187
Step-by-explanation: width multiply by height
=11 times 17
=187
Use the fact that sin 38 ≈ 0.6157 to solve m.
cos m ≈ 0.6157
what is the value of m?
Answer:
52°Step-by-step explanation:
We know that sine and cosine are equal when angles are complementary.
sin 38° = cos msin 38° = cos (90° - 38°) = cos 52°cos m = cos 52°m = 52°sin and cos are equal when their sum is 90°
So
cosm=0.6125=sin38cos(90-38)=sin38cos52=sin38m=52°no links or files please, i just need the answers.. (Worth 25 points)
Answer:
A ,D , F
Step-by-step explanation:
A) x-3=0 , x=3
B 1+x=2 , x=2-1=1 , x=1
C 9-x=3 , x=9-3=6 , x=6
D) 6=2x , x=6/2=3 , x=3
E (1/5)x=3 , x=3*5=15 , x=15
F) x^2=9 x=√9 , x=3
Antonia is saving for a video game. On the first day, she saves two dollars in her piggy bank. Each day after that, she doubles the number of dollars she saved on the previous day. How many dollars does she save on the sixth day?
Answer:
64
Step-by-step explanation:
so each day you times the amount of money by two
1=2
2=4
3=8
4=16
5=32
6=64
7=128
$13.56 is what percent of $16.95?
Answer:
$13.56 is 80% of $16.95.
Darren is finding the equation in the form y = m x b for a trend line that passes through the points (2, 18) and (–3, 8). Which value should he use as b in his equation? –34 –19 2 14.
what were the most important people for mary eliza mahoney
Answer:
African American and women
Step-by-step explanation:
Mary Eliza Mahoney was eager to encourage greater equality for African Americans and women
hope this helps!
the length of a quarter is .955. Round .955 to the nearest tenth of an inch
Answer:
1.0 inch
Step-by-step explanation:
Round the 9 in 0.955, this turns it into 1.0, Since you said an inch, the value will be in inches.
Answer:
1.0in is your answer!
Step-by-step explanation:
the person above me explained it good enough
The edge of a cube is (5x+2) mm long. What is its volume?
Answer:
(125x+8)cm^3
Step-by-step explanation:
Volume= (5x+2)^3 = (125x+8)cm^3
Hey!
Answer:
125x^3+ 150 x^2+ 60x +8.
Formula of the volume of the cube = v=a^3
Substitute:
v=(5x+2)^3
=125x^3+ 150 x^2+ 60x +8.
Admission to the school dance is $4.00. There is a picture booth at the dance, and each picture costs $1.50. Maria has $10.00. Which inequality represents the number of pictures, p, that Maria can purchase at the dance with admission?
A. 4.00p + 1.50 ≥ 10.00
B. 4.00 + 1.50p ≤ 10.00
C. 4.00p + 1.50 ≤ 10.00
D. 4.00 + 1.50p ≥ 10.00
Explain Direct Variation. What does “k” equal?
Answer:
In y = kx, where k is the constant of proportionality.
Answer:
k is the constant
Step-by-step explanation:
Direct variation is simply explained as when a number is directly proportional to another number. For example, when 8 is directly proportional to 4 then it will result to
=> 8= k4, where k is the constant
=> divide both sides by 4 to get k
=> k= 2
A 48°
B (6x−28)°
C (2x)°
Find the value of x. Then find the measures of angles B and C.
Enter your answers in the boxes.
x =
m∠B=
º
m∠C=
º
Answer:
x = 20, angle B = 92 and angle c = 40
Step-by-step explanation:
3 angles in a triangle adds up to 180, and since A is 48, we have B + C = 132
6x - 28 + 2x = 132
=> 8x - 28 = 132
=> 8x = 160 and x = 20
B = 6 x 20 - 28 = 92
C = 2 x 20 = 40
Work out the value of angle marked b
Answer:
22
Step-by-step explanation:
180-90-68=22
Answer:
180 - (90+68) = 22
B =22
Hope this helps!
Which expression is equivalent to -6(-2/3+2x)?
plss hurry im timed
-4-12x
-4+2x
4-12x
4÷12x
Answer:
4 - 12x
Step-by-step explanation:
-6(-2/3 + 2x)
we can distribute by multiplying -6 by whats inside of the parenthesis ( -2/3 and 2x )
-6 * -2/3 = 4
-6 * 2x = -12x
4 - 12x would be the equivalent expression
Given expression to us is ,
→ -6( -2/3 +2x)
Simplify by multiplying each terms inside the brackets by -6 .
→ -6*-2/3 + 2x*(-6)
Simplify,
→ 4 -12x
Hence option 3 is correct .
I hope this helps .
The ratio of boys to girls at a camp is 4:5. If there are 75 girls, how many boys are there? I NEED AN ANSWER ASAP PLEASE
Answer:
60 boys
Step-by-step explanation:
To find how many boys, you need to find how many times more than 75 is than five. To do that, divide 75 by 5 and you'll get 15. Multiply 4 by 15 and you get 60 boys. (i'm guessing bc im in middle school lol)
Please answer these thank u
1. 3*3 + 3*8 = 9+24=33
2. 4*4+.5*2*4+5*5= 16+4+25=45
3. 5*10+4*10= 90
4. 24+.5*4*4 = 32
Which expressions are equivalent? chose all that apply.
Answer:
7.7.7.7 and 7^4 and seven to the fourth power
Step-by-step explanation:
They all equal 2401.
They are all the same but in different forms:
(7.7.7.7- expression)
(7^4 - exponential form)
(seven to the fourth power-word form of exponent)
The tables show the height in
centimeters each plant grew during
a week. Assume the patterns continue.
Compare the growth in height of
each plant.
Answer:
Plant B grows 3 times as fast as Plant A
Step-by-step explanation:
Both plants start at 0 height on Day 1 and grow the same amount each day. Plant A grows 2 cm each day; Plant B grows 6 cm each day. The growth rate of Plant B is 3 times the growth rate of Plant A.
The hot cocoa stand uses 65 spoons each day. If the stand is open for 30 days, how many spoons are uses?
Answer:
1950
Step-by-step explanation:
i got to this by multiplying 30 and 65
1,950
Step-by-step explanation:
it's 65 x 30 which equals 1,950
Evaluate the algebraic expression when b = 3, d = 12, h = 2 and r = 7.
A. 8
B. 16
C. 24
D. 32
Answer:
24
Step-by-step explanation:
the answer is 24 because the 3 and 12 u divide
Answer: the answer is choice c which is 24 .
Step-by-step explanation: HOPE IT IS CORRECT .THANKS .
Elisabeth reads 15 of her book in 112 hours. Elisabeth continues to read at this pace. How long does it take Elisabeth to read 3/4 of the book?
Enter your answer as a mixed number in the simplest form by filling in the boxes.
The number of hours it takes Elisabeth to read 3/4 of the book is; 5³/₅ hours
What are mixed numbers?We are told that she reads 15 of her books in 112 hours.
Thus, number of hours to read one book is;
112/15 hours per book
Therefore, number of hours to read ³/₄ of the book is;
³/₄ * ¹¹²/₁₅ = 28/5
As a mixed number is 5³/₅ hours per book
Read more on mixed numbers at; https://brainly.com/question/10225
Answer:
5 5/8 h
Step-by-step explanation:
took the test and got it right :)
x − y = 4 y − 8 = -x At which point do the given equations intersect each other?
Answer:
(6,2)
Step-by-step explanation:
Graph is below
Please help Mandy took out a $35,000 loan to buy a car. What is the principal?
The principal of a loan is the amount of money they took out as a loan.
Principal = $35,000
Lesson 8-2
In Items 15-18, identify the transformation from the
graph of f(x) = 2* to the graph of g(x).
15. g(x) = 2* – 3
16. g(x) = 2(x – 3)
17. g(x) = 2* + 4
18. g(x) = 2(x+4)
A rectangle is 10 feet long by 2 feet wide.
If 3 feet are removed from the length of t
would be the area, in square feet, of the
You can earn 1 coin
Answer:
14 ft²
Step-by-step explanation:
To find the area of a rectangle you multiply the length and width. Sense the length is 10 feet but 3 feet was removed it is now 7 feet. Now you multiply that 7 feet by the width of 2 feet to get
7×2=
Area= 14 ft²
6.
A swimmer plans to swim at least 100 laps during a 6-day period. During this period,
the swimmer will increase the number of laps completed each day by one lap. What
is the least number of laps the swimmer must complete on the first day?
Answer:
I think 15
Step-by-step explanation:
15+16+17+18+19+20=105
if it was 14 it would equal to 99
I need help with 13 on both pictures. The first picture is the answer and the second picture is the question not getting the answer at all
Problem 13
If we want to multiply (x^3-3x^2+2x) with (x^3-2x^2+x), then we can set up a diagram shown below. The terms are along the outside. The stuff inside is the result of multiplying each pair of outer terms.
Example: x^3 times x^3 = x^6 in the top left cornerAnother example: 2x times x = 2x^2 in the bottom right corner.This is known as the box method to keep track of all the terms multiplied.
Once the table is filled out, we add up each term inside the boxes. Combine like terms if possible. Notice that I color-coded the like terms (eg: the x^3 terms are in green boxes).
The final answer is x^6 - 5x^5 + 9x^4 - 7x^3 + 2x^2
A saving account pays a 3% simple annual interest rate. How much must you put in the saving account to earn $100 in interest in 6 months?
HELP PlS
Step-by-step explanation:
Solution
Interest =100
Rate=3•/•
Time =0.5
principal =?
Now
p=I×100÷T×R
p=100×100÷0.5×3
P= 10000÷1.5
P=6666.66
Explain how to find a probability of an event
Answer:
what event there is no picture or words to tell me please explain
Step-by-step explanation:
help with part b pls thank u
Answer:
See belowStep-by-step explanation:
speed = distance / timetime = distance / speeda)
i)
Time taken at the first part:
105 / xii)
Time taken at the second part:
(190 - 105) / (x + 12) = 85/(x + 12)b)
If time is 3 hours and 15 minutes = 3 1/4 hours = 13/4 hours, the equation is:
105/x + 85/(x + 12) = 13/44(x + 12)*105 + 4(85x) = 13x(x + 12)13x² - 604x - 5040 = 0c)
Solve the equation:
13x² - 604x - 5040 = 0x = [604 ± √((-604)² + 4*13*5040) ]/26 = [604 ± √626896]/26 = [604 ± 791.77]/26x = (604 + 791.77)/26 = 53.68 km/h (taking positive root only)d)
105/x = 105/53.68 h = 1.956 h = 1 h 0.956*60 min = 1 h 57 min (rounded)85/(53.68 + 12) = 85/65.68 = 1.294 h = 1 h 0.294*60 min = 1 h 18 min (rounded)Answer:
see below
Step-by-step explanation:
Let t = time (in hours)
a) i) First 105 km of journey
[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]
[tex]\implies x=\dfrac{105}{t_1}[/tex]
[tex]\implies t_1=\dfrac{105}{x}[/tex]
ii) Rest of journey
distance = 190 - 105 = 85 km
speed = [tex]x+12[/tex] km/h
[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]
[tex]\implies x+12=\dfrac{85}{t_2}[/tex]
[tex]\implies t_2=\dfrac{85}{x+12}[/tex]
b) 3 hours 15 minutes = 3.25 hours
[tex]\implies[/tex] total time = [tex]t_1+t_2=3.25[/tex]
[tex]\implies \dfrac{105}{x}+\dfrac{85}{x+12} =3.25[/tex]
[tex]\implies \dfrac{105(x+12)+85x}{x(x+12)} =3.25[/tex]
[tex]\implies 105(x+12)+85x =3.25x(x+12)[/tex]
[tex]\implies 105x+1260+85x =3.25x^2 +39x[/tex]
[tex]\implies 3.25x^2-151x-1260=0[/tex]
multiply by 4:
[tex]\implies 13x^2-604x-5040=0[/tex]
c)
[tex]\textsf{quadratic formula} \ x=\dfrac{-b \pm\sqrt{b^2-4ac} }{2a}}[/tex]
[tex]\implies x=\dfrac{604 \pm\sqrt{(-604)^2-4(13)(-5040)} }{2(13)}}[/tex]
[tex]\implies x=\dfrac{604 \pm\sqrt{626896} }{26}}[/tex]
[tex]\implies x = 53.68, x=-7.22[/tex]
(to 2 decimal places)
d) time ≥ 0, therefore, x = 53.68 only
Substitute x = 53.68 into the expression for [tex]t_1[/tex] and solve for [tex]x[/tex]:
[tex]\implies t_1=\dfrac{105}{53.68}=1.955912... \textsf{hours}=\textsf{1 hr 57 min}[/tex]