(number of hours) x (wage rate) = (gross earnings)
hours x 10.62 = 127.40
hours = 127.40 / 10.62 = 12 hours (approximately)
4x + ay = -8 ---> 4x + ay = -8
2x - 3y = b ---> 4x - 6y = 2b
Choose a = -6 and b = -4
Then, you have two equivalent equations: 4x - 6y = -8
4x - 6y = -8
t1 = 2/3
t9 = t1 + 8d ---> -4/5 = 2/3 + 8d ---> -22/15 = 8d ---> d = -11/60
t5 = t1 + 4d ---> t5 = 2/3 + 4(-11/60) = -1/15
1*2*3*2*3 = 36 posibilities.
But if he gets it right on the first try then he doesn't need to try any more.
Luna used 3/5 of her money to buy 10 earphones.
Rest of the money is (1 - 3/5) = 2/5. Let, Luna buy x earphones with the
rest of her ,only.
So, 10/3/5 = x/2/5
=> 50/3 = 5x/2
=> x = 29/3 = 6
So, Luna can buy almost 6 earphones with the rest of her money.
Find the fraction
Hello Guest!
Why easy when it can be cumber.
\(0.72\overline 6 + 0.02\overline 3=\frac{109}{150}+\frac{7}{300}=\frac{218+7}{300}=\frac{225}{300}=\color{blue}\frac{3}{4}\)
!
So we have that
[Bx - 11 ] / [ x^2 -7x + 10] = A / [ x -2 ] + 3 / [x - 5]
Using partial fractions we can simplify this as
Bx - 11 = A[x - 5] + 3 [ x - 2] simplify more
Bx - 11 = Ax - 5A + 3x - 6
Bx - 11 = [ A + 3 ] x + [ -5A - 6 ] equate coefficients
B = A + 3
-11 = -5A - 6 ⇒ -5 = -5A ⇒ A = 1
So....B = 1 + 3 = 4
So....A + B = 1 + 4 = 5
🎅🎅🎅🎅🎅
🥳🥳🥳🥳🥳
floor (r) + r = 12.2 - r
floor (r) + 2r = 12.2
Note if r = 4.1 we have
floor (4.1) + 2(4.1) =
4 + 8.2 =
12.2
The four angles are a, a + d, a + 2d, a + 3d
---> (a) + (a + d) + (a + 2d) + (a + 3d) = 180
---> 4a + 6d = 360
---> 2a + 3d = 180
Also: a + 3d = 126 ---> 3d = 126 - a
Combining: 2a + 3d = 180 and 3d = 126 - a ---> 2a + (126 - a) = 180
a + 126 = 180
a = 54
The angles are: 54, 78, 102, and 126.
log4a (8b) = x ---> [ 4a ]x = 8b ---> [ (22)a ]x = (23)b ---> 22ax = 23b
---> 2ax = 3b
---> x = (3b) / (2a)
f(x) is a linear equation with slope = -0.5 and y-intercept = 2 ---> f(x) = -0.5x + 2
g(x) is a linear equation with slope = 1 and y-intercept = 0 ---> g(x) = x
g(1) = 1 ---> f( g(1) ) = -0.5(1) + 2 = 1.5
f(1) = -0.5(1) + 2 = 1.5 ---> g( f(1) ) = g(1.5) = 1.5
f( g(1) ) · g( f(1) ) = 1.5 · 1.5 = 2.25
If the function is: f(x) = 1 / (x - 64) + 1 / (x2 - 64) + 1 / (x3 - 64)
The real solution of x - 64 is 64
The real solutions of x2 - 64 are 8 and -8
The real solution of x3 - 64 is 4 (there are also two complex solutions)
Thus, there are 4 real numbers not in the domain of this function.
A + B + C = 180
(x + 2y) + (6x - 5y)+ (8x + 3y) = 180
15x = 180
x = 12o
The answer for x is independent from the value for y; y can have any value ...
x2 - 2x + 5 = 0
Using the quadratic formula:
x1 = [ 2 + sqrt( (-2)2 - 4(1)(5) ) ] / [ (2)(1) ] = [ 2 + sqrt( 4 - 20) ] / 2 = [ 2 + sqrt(-16) ] / 2 = ( 2 + 4i ) / 2 = 1 + 2i
x2 = [ 2 - sqrt( (-2)2 - 4(1)(5) ) ] / [ (2)(1) ] = [ 2 - sqrt( 4 - 20) ] / 2 = [ 2 - sqrt(-16) ] / 2 = ( 2 - 4i ) / 2 = 1 - 2i
a = 1 / ( 1 + 2i )
b = 1 / ( 1 - 2i )
a·b = [ 1 / ( 1 + 2i ) ] · [ 1 / ( 1 - 2i ) ] = 1 / ( 12 - (2i)2 ) = 1 / ( 1 + 4 ) = 1 / 5
2x2 - 5x - 4 = 2x + 3 ---> 2x2 - 7x - 7 = 0
Using the quadratic formula with a = 7 b = -7 and c = -7:
x = [ - -7 +/- sqrt( (-7)2 - 4(2)(-7) ) ] / [ (2)(2)
x = [ 7 +/- sqrt(105) ] / 4
0.7266666666...
+ 0.0233333333...
= 0.7499999999...
= 0.75
= 3/4
I checked with a quick sketch and it is reasonably clear that that is correct.
0.0909090909 ...
100*0.0909090909 ... = 9.09090909 ...
1 *0.0909090909 ... = 0.0909090909 ...
subract
99*0.0909090909 ...=9
0.0909090909 ...=9/99 = 1/11
yes that is right.
So
\(\frac{16}{LN}=\frac{2}{3}\)
Oh, I get it... sinN = 16 / LN
(x - y)^2 = x^2 - 2xy + y^2 => 2xy = x^2 + y^2 - (x - y)^2 => 2xy = 24 - 6^2 = -12 => xy = -6
x^3 - y^3 = (x - y) (x^2 + x y + y^2) = 6( 24 - 6 ) = 108
What is the least possible value of the sum | x - 1 | + | x - 1.5 | + | x - 2 | + | x - 2.5 | + | x - 3 |?
Let x = 0.5 => 0.5 + 1.0 + 1.5 + 2.0 + 2.5 = 7.5
Let x = 1.0 => 0 + 0.5 + 1.0 + 1.5 + 2.0 = 5.0
Let x = 1.5 => 0.5 + 0 + 0.5 + 1.0 + 1.5 = 3.5
Let x = 2.0 => 1.0 + 0.5 + 0 + 0.5 + 1.0 = 3.0 (Least Possible Value)
Let x = 2.5 => 1.5 + 1.0 + 0.5 + 0 + 0.5 = 3.5
Let x = 3.0 => 2.0 + 1.5 + 1.0 + 0.5 + 0 = 5.0
Let x = 3.5 => 2.5 + 2.0 + 1.5 + 1.0 + 0.5 = 7.5
Roll 2 fair dice = 36 outcomes. Outcomes with both dice showing prime number = {(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)}
P(both dice showing a prime number) = 9/36 = 1/4.
Circle centre O with r = 2, angle subtended between A and B, B and C, C and D, D and E, E and A with centre O = 3600 / 5 = 720
Area of triangle ABO = (1/2)(2*2*sin 720) = 1.902 sq units
[ABCDE] = There are 5 triangles of equal area = (1.902 sq units)5 = 9.51 sq units.
I expect this diagram comes with more information.
From what I have read:
This is a skin disease that can be inherited from either parent.
If it comes from both parents it will be more severe.
!
