Given info:- [tex]\textsf{If (√3+√2)/(3√2-2√3) = x+y√6,} [/tex]
[tex]\textsf{then find the value of x and y?}[/tex]
Explanation:-
[tex]\textsf{Consider LHS=}\\[/tex]
[tex] \rm \: \frac{ \sqrt{2 } + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \\ [/tex]
[tex] \rm \: = \frac{ \sqrt{2 } + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \\ [/tex]
[tex] = \rm \: \frac{( \sqrt{2 } + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} )}{(3 \sqrt{2} - 2 \sqrt{3})(3 \sqrt{2} + 2 \sqrt{3}) } \\ [/tex]
[tex] \rm \: = \frac{3 \sqrt{2 \times 2} + 2 \sqrt{3 \times 2} + 3 \sqrt{2 \times 3} + 2 \sqrt{3 \times 3} }{(3 \sqrt{2} {)}^{2} - (2 \sqrt{3} {)}^{2} } \\ [/tex]
[tex] \rm = \frac{3 \times 2 + 2 \sqrt{6} + 3 \sqrt{6} + 2 \times 3}{18 - 12} \\ [/tex]
[tex] \rm \: = \frac{12 + 5 \sqrt{6} }{6} \\ [/tex]
[tex] \rm \: = 2 + \frac{5}{6} \sqrt{6} \\ [/tex]
[tex] \rm \therefore \: 2 + \frac{5}{6} \sqrt{6} = x + y \sqrt{6} \\ [/tex]
[tex]\textsf{On, comparing with RHS we notice that:}\\[/tex]
[tex]\textsf{the value of x = 2 and y = 5/6.}\\[/tex]
[tex]\bf{Read more:}[/tex]
[tex]\textsf{Similar questions}\\[/tex]
[tex] \sqrt{6} + \sqrt{11} \div \sqrt{5} + \sqrt{3} [/tex] A. [tex] \sqrt{30} + 3 \sqrt{2} + \sqrt{55} + \sqrt{33} \div 8[/tex] B. [tex] \sqrt{30} - 3 \sqrt{2} ...
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Write the inequality for the situation. Penny has 7 dollars. Fred has fewer dollars than Penny. Left F=Fred
Answer:
7 > F
Step-by-step explanation:
Penny has 7 dollars. Fred has fewer dollars than Penny. Left F=Fred
7. Fred has fewer dollars than Penny. Left F=Fred
7 > Left F=Fred
7 > F
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
i am very confused amd i also hate math so please help
Answer:
The answer that you put is right
Serena’s average speed during her training run was 8 kilometers per hour over the 2 hours that she ran. What was the total distance that she ran?
Use the formula d = rt, where d represents the distance, r represents the rate, and t represents the time.
4 km
Step-by-step explanation:
so, we just enter the given data into the given formula. and then calculate. it does not get easier than that.
d = 8km/h × 2h = 16km
Serena ran 16km in these 2 hours.
Answer:
the correct answer is 16km
Step-by-step explanation:
pl.z dont delete this
Someone pls pls pls help ASAP
I’ll give brainliest I promise just pls help me
Answer:
Answer attached below.
Evaluate the expression for p = 2.4 and q = 8.
Write your answer as a decimal or whole number.
pq =
Answer:19.2
Step-by-step explanation:
Answer:
19.2
Step-by-step explanation:
pq is the same as p x q.
then substitute into the above equation 2.4 x 8= 19.2 as a decimal and a whole number
Please I help I'll brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
c^2 = a^2 + b^2
a = 4
b = ?
c = 8
8^2 = 4^2 + b^2
64 = 16 + b^2
48 = b^2
b = sqrt(48)
b = 4√3
Please help me with this
Sales tax rate is 8% if Ayana buys a set of spoons price that 17.88 what will be the total cost including tax
Extra:
Percentage = 1% = 0.01, 10% = 0.1 and 100% = 1
Increase in percentage = 1 + percentage eg. (1 + 0.08 = 1.08)
Decrease in percentage = 1 - percentage eg. (1 - 0.08
what is 23 in binary
Answer:
vanadium
Step-by-step explanation:
Answer:
10111Step-by-step explanation:
may it will help you
Next sequence of 1,-2,-5,-8
Answer:
-11,-14,-17
Step-by-step explanation:
Your numbers are decreasing by 3.
Volume=1210 ft radius of 11 find the height
Answer: 12.73 feet
Step-by-step explanation: We aren't told the type of vessel. I'll assume a cylindrical tank.
Volume of a cylindrical tank is V = πr²h
I'm assuming the 1210 is in units of volume, such as ft^3
1210ft^3 = πr²h
h = (1210ft^3 )/(π(5.5)²)
h = 12.73 ft
Viable what is the definition
Answer:
capable of working successfully; feasible.
or
Step-by-step explanation:
(of a plant, animal, or cell) capable of surviving or living successfully, especially under particular environmental conditions.
If the output number y is -52 (y=5x-2) what is the input number? SHOW WORK
Answer:
the input number is -10
Step-by-step explanation:
output is always y
input is always x
so instead of y, put -52
-52=5x-2 add 2 to each side to ger 5x by itself
-50=5x divide both sides by 5 to get x by itself
-10=x
x is the input so the input is -10
6x + 19y = –10 in slope intercept form
Answer:
y = (-6/19)x - 10/19
Step-by-step explanation:
Solving 6x + 19y = –10 for y, we get 19y = -6x - 10, or y = (-6/19)x - 10/19.
This is in slope-intercept form.
Explain what the point (6,2) represents.
Answer: 6 is the 1st term, 2 is the common ratio
Step-by-step explanation: T = 6(2d-1)
Molly can received her weekly paycheck and she earned a total of $339.25. If she makes
$14.75 per hour, how many hours, h. did she work?
Answer:
2267.25
Step-by-step explanation:
add that fisrt one
Randall purchased a flat screen tv for $1089.the tax rate was 8.75%
Answer:
9528.75
Step-by-step explanation:
1089x8.75, or 1089x8 and 3/4 which is 9528.75
I need help finding surface area
Answer:
[tex]603.2km^{2}[/tex]
Step-by-step explanation:
sale 90%Luca buys a swing set during the sale. If the original price was $270, how much does Luca pay?
Answer:
$243
Step-by-step explanation:
Solve for x in ½ logx64 = 3
(A)
2
(B)
1
(C)
4
(D)
3
Answer:
A
Step-by-step explanation:
Using the rules of logarithms
log[tex]x^{n}[/tex] = n logx
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
Given
[tex]\frac{1}{2}[/tex][tex]log_{x}[/tex] 64 = 3
[tex]log_{x}[/tex][tex]64^{\frac{1}{2} }[/tex] = 3
[tex]log_{x}[/tex] 8 = 3
8 = x³
2³ = x³ , then
x = 2
There are 199 green marbles and 199 red marbles in a bag. How many marbles must be chosen to be certain we have the following. Four red or three green?
Answer:
203 for four red and 202 for three green.
Step-by-step explanation:
Consider the worst possible choice. If you want four red then imagine the worst possible case. That'd be picking all 199 marbles before any red, and after you pick all 199 green marbles you still need four red, and 199+4=203. For green, do the same thing and you get 199+3=202
There are 203 for four red and 202 for three green.
Given that,
There are 199 green marbles and 199 red marbles in a bag.Based on the above information, the calculation is as follows:
Since there is 4 red or three green.
So,
We can solve like
= 199 + 3
= 202
And,
= 199 + 4
= 203
Therefore we can conclude that there are 203 for four red and 202 for three green.
Learn more: brainly.com/question/16115373
Surface area I need help
Answer:
100 + 100 + 40 + 40 + 40 + 40 = 360 yd^3
Decrease £5480 by 10%
Step-by-step explanation:
the currency does not matter (only if we get into any fractions of the main unit and have to name the fractions properly). % is usually about the number itself.
so,
5480 = 100%
1% = 100%/100 = 5480/100 = 54.8
10% = 1% × 10 = 54.8×10 = 548
and so,
£5480 - 10% = 5480 - 548 = £4932
if course, because of the special number 10% we could have gotten the answer faster, but I wanted to show you the full line of thinking when dealing with %. and needed when the number is not so nice.
Please help me with this math problem
Answer:
Step-by-step explanation:
How to solve your problem
3
+
+
3
3+a+3
3+a+3
Simplify
1
Add the numbers
3
+
+
3
{\color{#c92786}{3}}+a+{\color{#c92786}{3}}
3+a+3
6
+
{\color{#c92786}{6}}+a
6+a
2
Rearrange terms
Solution
+
6
Write the linear equation in slope-intercept form and simplify.
–4x + 13y = 7
[tex]\\ \sf\longmapsto -4x+13y=7[/tex]
[tex]\\ \sf\longmapsto 13y=4x+7[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{4x+7}{13}[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{4}{13}x+\dfrac{7}{13}[/tex]
The width of a rectangle is 3 inches less than its length. The perimeter is equal to 94 inches, what is the length in inches?
Answer:
l=44in
Step-by-step explanation:
Using the formula
P=2(l+w)
Solving forl
l=P
2﹣w=94
2﹣3=44in
How to factor a tri, quad, or polynomial.
Explanation:
Factoring to linear factors generally involves finding the roots of the polynomial.
The two rules that are taught in Algebra courses for finding real roots of polynomials are ...
Descartes' rule of signs: the number of positive real roots is equal to the number of coefficient sign changes when the polynomial is written in standard form.Rational root theorem: possible rational roots will have a numerator magnitude that is a divisor of the constant, and a denominator magnitude that is a divisor of the leading coefficient when the coefficients of the polynomial are rational. (Trial and error will narrow the selection.)In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.
Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)
__
Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.
There are web apps that will find all roots of virtually any polynomial of interest.
_____
Additional comment
Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.
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Which equation represents a line which is parallel to the line 7y - 4x = -14?
Oy= 1x + 2
O y = x - 1
O y = -x + 6
Oy = -x - 3
How do you Form an equation for x and then solve to find the value of x
9514 1404 393
Answer:
x = 38.2
Step-by-step explanation:
Each of the functions of x represents the measure of an angle in the triangle. You write an equation for x by using what you know about the relationships of angles in a triangle: their sum is 180°.
(2x) +(x -18) +(2x +7) = 180
5x -11 = 180 . . . . . . . collect terms
5x = 191 . . . . . . . . . . add 11
x = 38.2 . . . . . . . . . divide by 5
PLS HELP WILL MARK BRAINLIEST!!
Evaluate x - (y - z) and (x- y) - z for y = 3, x = 5, z = 4. Is there any associative property of subtraction
Answer:
There is no associative property of subtraction.
Step-by-step explanation:
Given:
x = 5y = 3z = 4x - (y - z) = 5 - (3 - 4) = 5 - (-1) = 5 + 1 = 6
(x - y) - z = (5 - 3) - 4 = 2 x -4 = -6
Therefore, there is no associative property of subtraction as 6 ≠ -6