Answers
Step-by-step explanation:
The given expression is :
[tex]\dfrac{2-\sqrt5}{2+3\sqrt5}=\sqrt5 x+y[/tex] ....(1)
Taking LHS of the above expression
[tex]\dfrac{2-\sqrt5}{2+3\sqrt5}[/tex]
Rationalizing both denominator and numerator.
[tex]\dfrac{2-\sqrt5}{2+3\sqrt5}\times \dfrac{2-3\sqrt5}{2-3\sqrt5}=\dfrac{4-6\sqrt5-2\sqrt5+15}{2^2-(3\sqrt5)^2}\\\\=\dfrac{19-8\sqrt5}{4-45}\\\\=\dfrac{19-8\sqrt5}{-41}\\\\=\dfrac{\sqrt5 \times 8}{41}+(\dfrac{-19}{41})[/tex]
Equation (1) becomes,
[tex]\dfrac{\sqrt5 \times 8}{41}+(\dfrac{-19}{41})=\sqrt 5\ x+y[/tex]
Equating both sides,
[tex]x=\dfrac{8}{41}[/tex] and [tex]y=\dfrac{-19}{41}[/tex]
Hence, this is the required solution.
Related Questions
Need help take your time and thx
Answers
Answer:
-1 and -3
Step-by-step explanation:
(x+1) (x+3)
what is the answer of -13=15+d ?
Answers
Answer:
d= -28..................
Casho has a bag that contains pineapple chews, lemon chews, and lime chews. She performs an experiment. Casho randomly removes a chew from the bag, records the result, and returns the chew to the bag. Casho performs the experiment 54 times. The results are shown below:
A pineapple chew was selected 9 times.
A lemon chew was selected 15 times.
A lime chew was selected 30 times.
Based on these results, express the probability that the next chew Casho removes from the bag will be pineapple chew as a percent to the nearest whole number.
Answers
Answer:
17% the next chew Casho pulls out is pineapple
Step-by-step explanation:
pineapple chew 9/54
lemon chew 15/54
lime chew 30/54
9/54 = 0.1666666... make this a percent and you get 17% of the time Casho will pull out a pineapple chew.
Answer:
...................................................................
Step-by-step explanation:
The dimensions of this screen are 10 inches by 10 inches. What is the screen size? Round your answers to the nearest whole number. Remember, the screen size is the same as the hypotenuse of the triangle whose legs are the width and height of the screen.
Answers
Answer:
14.14inches
Step-by-step explanation:
Given data
Length L= 10 inches
Width W= 10 inches
The size of the screen is described by the lenght of the diagonal
Applying the Pythagoras theorem we have
D^2= L^2+ W^2
D^2= 10^2+ 10^2
D^2= 100+100
D^2= 200
D= √200
D= 14.14 inches
Hence the size of the screen is 14.14inches
Answer:
A. 14
Step-by-step explanation:
hey can someone please help me solve this you will get 10 pioints!!
Answers
Answer:
area of triangle will be same as parallelogram
second one is 12unit^2.
5. Area of parallelogram = Area of rectangle
6. 12unit^2
What is the value of 3/5 divide 2/5
A. 6/25
B. 2/3
C. 6/5
D. 3/2
E.25/6
Answers
Help!I need also the slope and yint and equation for this!!
Answers
slope : 0.25
equation : 0.25x+3
and what is the yint
An engineer is designing a fountain that shoots out drops of water. The nozzle from which the water is launched is 3 meters above the ground. It shoots out a drop of water at a vertical velocity of 14 meters per second. Function h models the height in meters, h, of a drop of water t seconds after it is shot out from the nozzle. The function is defined by the equation h(t)=−5t2+14t+3. How many seconds until the drop of water hits the ground?
Answers
Answer:
After 3 seconds
Step-by-step explanation:
Given
[tex]h(t) = -5t^2 + 14t + 3[/tex]
Required
Time the drop will hit the ground
When the drop hits the ground,
[tex]h(t) = 0[/tex]
So, we have:
[tex]0 = -5t^2 + 14t + 3[/tex]
Rewrite as:
[tex]5t^2 - 14t - 3 = 0[/tex]
Expand
[tex]5t^2 + t - 15t - 3 = 0[/tex]
Factorize
[tex]t(5t + 1) -3(5t + 1) = 0[/tex]
Factor out 5t + 1
[tex](t -3)(5t + 1) = 0[/tex]
Split
[tex]t -3 = 0[/tex] or [tex]5t + 1 = 0[/tex]
Solve for t
[tex]t = 3[/tex] or [tex]5t = -1[/tex]
Time cannot be negative.
So:
[tex]t = 3[/tex]
answer for brainilest and 11 points
Answers
Answer:
[tex]16 \times 10 = 160 {in}^{2} \\ 160 \div 16 = 10 {ft}^{2} [/tex]
You have 4 pounds of peanuts. You want to put it in the bags so that there is 2/3 pounds in each bag. How many bags can you fill ?
Answers
Answer:
6 bags
Step-by-step explanation:
This problem is essentially asking how many ([tex]\frac{2}{3}[/tex]) peanut bags can one fill with ([tex]4[/tex]) pounds of peanuts. This problem can be solved by divided ([tex]4[/tex]) by ([tex]\frac{2}{3}[/tex]). Set up the problem,
[tex]4[/tex] ÷ [tex]\frac{2}{3}[/tex]
In order to divide by a fraction, one must change the multiplication sign to a division sign, then take the reciprocal of the second number, the fraction. In order to take the reciprocal of a fraction, switch the numerator (number on top) and the denominator (number on the bottom).
[tex]4 * \frac{3}{2}[/tex]
Multiply,
[tex]\frac{12}{2}[/tex]
Simplify,
[tex]6[/tex]
HELP ME PLEASE! I need to figure out the median and Interquartile of : 0,0,0,1,1,3,3,3,4,4,4,6,6,7,7,7,8,8,9,10
Answers
Answer:
The median is 8
Step-by-step explanation:
4+4=8
It is 8 because the middle numbers there are 4 and 4
Pls explain so I can show my work!!
Answers
Answer:
He spends 20 percent of his free time reading so I think its 1 hour and 48 minutes.
A rectangular piece of paper with length 35 cm and a width 18 cm has two semicircles cut out of it as shown below
Answers
Answer:
375.66 cm²
Step-by-step explanation:
The two semicircles add to a full circle.
For the circle, d = 18 cm.
r = d/2 = 9 cm.
A = LW - πr²
A = (35 cm)(18 cm) - 3.14(9 cm)²
A = 375.66 cm²
What is the radius of the circle with equation (x+1/5)^2+(y-2/5)^2=1/25
Answers
Answer:
r = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + [tex]\frac{1}{5}[/tex] )² + (y - [tex]\frac{2}{5}[/tex] )² = [tex]\frac{1}{25}[/tex] ← is in standard form
with r² = [tex]\frac{1}{25}[/tex] , then
r = [tex]\sqrt{\frac{1}{25} }[/tex] = [tex]\frac{1}{5}[/tex]
The radius of the circle is, r = 1/5 units.
What is equation of circle?An equation of circle with center (h, k) and radius 'r' is,
(x - h)²+(y - k)² = r²
For given example,
the equation of the circle is, (x+1/5)^2+(y-2/5)^2=1/25
By comparing with standard equation of circle (x - h)²+(y - k)² = r²,
we have h = -1/5, k = 2/5 and r² = 1/25
We need to find the radius of the circle,
r² = 1/25
By taking square-root,
we have r = 1/5 units
Therefore, the radius of the circle is r = 1/5 units.
Learn more about equation of circle here:
https://brainly.com/question/10618691
#SPJ2
Find the area and circumference of a circle with the
radius of 8.5 cm.
Answers
Answer:
Area: 226.98
Circumference: 53.41
Step-by-step explanation:
Answer:
Area = 72.25π ≈226.98 cm
Circumference = 17π ≈ 53.41 cm
Step-by-step explanation:
Area formula for a circle = πr²
Circumference formula = 2πr
r = 8.5cm
Mr. Winkleman , a professional wine taster, made $32,800 last year . This year he had a raise of $2,132 . what was the percent of the raise? PLEASEE ALSO show work , i will try and mark brainliest
Answers
Answer:
0.65
Step-by-step explanation:
Answer:
Step-by-step explanation:
2,142/32,800 ≈ 0.065 = 6.5%
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is
viable solution if x represents the number of days that a library book is late and y represents the total fee?
Answers
Liability charges $0.30 dollars as a fee for being 1 day late,
For being 1 day late, fee charge is: 1* $0.30
So, for X days the charge would be: X*$0.30.
Total charge for being X days late is Y, Which means: Y= 0.30 * X.
Now We would have to check all the viable solutions in the answer to see if they satisfy the equation Y= 0.30 * X
Option one(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solution because the value of number of days can not be negative and in option one and two, value of days -3 and -2.5 is negative.
Option three(4.5, 1.35) can not be correct because library charges fee for a full day so the number for days would be a whole number. Library would not charge for 4.5 days, they would either charge of 4 days or 5 days because 4.5 is not an whole number.
Option four(8, 2.40) is the correct answer because it satisfies our equation;
Y= 0.30 * X
2.40= 0.30 * 8
2.40 = 2.40.
Fourth option (8, 2.40) is the only viable solution to this question.
The probability that Scott will win his next tennis match is \frac{3}{5}
5
3
What is the probability that he will not win?
Write the answer as a percentage
Answers
3/5 is the probability that he will win, you must find a fraction which adds to make 100%.
2/5 would be the fraction for his probability to lose.
0.4 or 40%.
A quantity with an initial value of 2000 grows exponentially at a rate of 0.35% every
2 days. What is the value of the quantity after 73 days, to the nearest hundredth?
Answers
Answer:
2272.03
Step-by-step explanation:
Write the equation of the circle graphed below
Answers
Answer:
there isnt any image
Step-by-step explanation:
Brad and sally made a total of 31 cakes for the school bake sale. Sally made 7 fewer cakes than brad. How many cakes did brad make?
Answers
Answer:
brad made 19 cakes, sally made 12
Step-by-step explanation:
what is the mean of 83, 92,47, 78, 80?
Answers
Blah blah blah blah blah blah
The dimensions of a triangular prism are shown in the diagram.
What is the volume of the triangular prism in cubic centimeters?
A
1,360 cm3
B
C
D
408 cm3
1,632 cm3
816 cm3
Answers
Answer:
B
Step-by-step explanation:
your welcome
help with this ill give brainlest
Answers
16. On June 8, 1992, a crop circle with an 18-meter radius was found in a wheat field near Szekesfehervar,
43 miles southwest of Budapest, Find its circumference,
a. 112.06
b. 113.04 m
C, 124,45 m
d116,34 m
Answers
Factor the expression completely. 60x^3+50x^5
Answers
Answer: 10x^3(6+5x^2)
I don’t know this and I need help it’s due tomorrow just got it today
Answers
Answer:
x = 9
Step-by-step explanation:
The top shape's side values are 3 times larger than the side values of the bottom shape, so x + 15 = 3(8).
Solve for x and you get x = 9.
Answer:
x = 9
Step-by-step explanation:
9 / x = 3 -> x = 3
(x+15) / 3 = 8
x + 15 = 8*3
x+15 = 24
x = 24 - 15
x = 9
BRAINIEST ANSWER
:)) please help me out!
Answers
Answer:
1,296 cm³Step-by-step explanation:
Now the formula to find the volume of a pyramid is [tex]V=\frac{lwh}{3}[/tex]
We know the length, width and height so let´s get started!
First let´s multiply to find the base. To do so, we will do length × width.
18 × 18 = 324
Now multiply by the height
324 × 12 = 3,888
After you multiply all length, width and height, we need to divide by three.
3,888 ÷ 3 = 1,296
Before we finish, we need to do the last two steps
First we need to add the measurement unit which is centimetres or cm.
We also need to add ³ since it is volume
1,296 cm³ is our final answer
Answer the question in the picture?
Answers
Which is f(6) for the quadratic function graphed?
-2.
-0.5
1.5
4
Answers
Answer:
D. 4Step-by-step explanation:
f(6) is the intersection of vertical line going through x = 6 and the graph of the quadratic function.
By tracing the line we find the intersection is the point (6, 4)
Correct choice is D