# Posts by Bosnian

Total # Posts: 2,507

Maths
l = length w = width P = 2 ( w + l ) If each side is a whole number, then: 1. w = 1 , l = 7 P = 2 ( w + l ) P = 2 ( 1 + 7 ) = 2 * 8 = 16 1 x 7 2. w = 2 , l = 6 P = 2 ( w + l ) P = 2 ( 2 + 6 ) = 2 * 8 = 16 2 x 6 3. w = 3 , l = 5 P = 2 ( w + l ) P = 2 ( 3 + 5 ) = 2 * 8 = 16 3 x ...

algebra
x ^ 2 - 3 x = 4 The x-term coefficient = ? 3 The half of the x-term coefficient = ? 3 / 2 After squaring you have ( ? 3 / 2 ) ^ 2= 9 / 4 x ^ 2 - 3 x = 4 Add 9 / 4 to both sides x ^ 2 - 3 x + 9 / 4 = 4 + 9 / 4 x ^ 2 - 3 x + 9 / 4 = 16 / 4 + 9 / 4 x ^ 2 - 3 x + 9 / 4 = 25 / 4 ...

math
P = x + 2 x - 1 + 2 x + 1 = 40 5 x = 40 Divide both sides by 5 x = 8 cm 2 x - 1 = 2 * 8 - 1 = 16 - 1 = 15 cm 2 x + 1 = 2 * 8 + 1 = 16 + 1 = 17 cm Largest angle = 90° becouse your triangle is right triangle. Use the Pythagorean theorem. The square of the hypotenuse is equal...

Algebra
x ^ 2 * y ^ 2 + x ^ 3 * y ^ 4 = ( 3 x y ) ^ 2 x ^ 2 * y ^ 2 + x ^ 2 * y ^ 2 ( x * y ^ 2 ) = 9 x ^ 2 * y ^ 2 x ^ 2 * y ^ 2 * ( 1 + x * y ^ 2 ) = 9 * x ^ 2 * y ^ 2 Divide both sides by x ^ 2 * y ^ 2 1 + x * y ^ 2 = 9 Subtract 1 to both sides 1 + x * y ^ 2 - 1 = 9 - 1 x * y ^ 2...

integral calculus
My typo. Integrate sin ^ 2 (x) dx = x / 2 - sin (2x) / 4 + C

integral calculus
If (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x)) mean: cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x) then: cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x) = sin (x) * { cos ^ 2 (x) / [ 1 - sin(x) ] - 1 } = sin (x) * { [ 1 - sin ^ 2 (x) ] / [ 1 - sin(x) ] - 1 } = sin (x) * { [ 1...

math
3 x + 2 y = 4 Multiply both sides by 2 6 x + 4 y = 8 2 x - 3 y = 7 Multiply both sides by 3 6 x - 9 y = 21 6 x + 4 y = 8 - 6 x - 9 y = 21 ______________ 6 x - 6 x + 4 y - ( - 9 y ) = 8 - 21 4 y + 9 y = 13 13 y = - 13 Divide both sides by 13 y = - 13 / 13 = - 1 Replace this ...

Linear Algebra
Replace F(x)with y y = 3 x Interchange the variables x = 3 y Divide both sides by 3 x / 3 = y y = x / 3 Replace y with F(x) F(x)= x / 3

math
Where is your list of a points?

math
4:8= 1 / 2 b = boys g = girls g = 24 b = g / 2 b = 24 / 2 b = 12

math connections
Correction. I forget - sign. - 4 n + 7 + 2 n = 1 - 4 n + 2 n + 7 = 1 - 2 n + 7 = 1 Subtract 7 to both sides - 2 n + 7 - 7 = 1 - 7 - 2 n = - 6 Divide both sides by - 2 n = - 6 / - 2 n = 3

math connections
1. x / 4 + 1 = - 5 Subtract 1 to both sides x / 4 + 1 - 1 = - 5 - 1 x / 4 = - 6 Multiply both sides by 5 x = - 6 * 4 x = - 24 2. 6 x + 29 = 5 Subtract 29 to both sides 6 x + 29 - 29 = 5 - 29 6 x = - 24 Divide both sides by 6 x = - 24 / 6 x = - 4 3. - 21 a + 16a = - 5 a 4. 9 a...

elementary school
( 15 / 4 ) / ( 9 / 1 ) = 15 * 1 / ( 4 * 9 ) = 15 / 36 = 3 * 5 / ( 3 * 12 ) = 5 / 12 15 / 4 divided by 9 / 1 = 5 / 12

help with math plz
Suppose your function y is a linear function. Linear equation in slope-intercept form: y = m x + b m = the slope of a linear function = rise / run = change in y / change in x b = y ? intercept = the point where the graph of a linear equation intersect the y-axis y ? intercept ...

HELP ME PLZ MATH
Yes, you are right.

Math
| x - 2 | + 1 = x - 2 + 1 = x - 1 OR | x - 2 | + 1 = - ( x - 2 ) + 1 = - x + 2 + 1 = - x + 3 For vertex you must find point where: x - 1 = - x + 3 x - 1 = - x + 3 Add x to both sides x - 1 + x = - x + 3 + x 2 x - 1 = 3 Add 1 to both sides 2 x - 1 + 1 = 3 + 1 2 x = 4 Divide ...

Math
The total number of football (x) and basketball (y) is 180 mean: x + y = 180 There are 30 more football than basketball mean: x = y + 30 Replace this value in equation x + y = 180 x + y = 180 y + 30 + y = 180 2 y + 30 = 180 Subtract 30 to toth sides 2 y + 30 - 30 = 180 - 30 2 ...

Algebra
1. 4 ( ax + 3 )-3 ax = 25 + 3a 4 * ax + 4 * 3 - 3 ax = 25 + 3a 4 ax + 12 - 3 ax = 25 + 3a 4 ax - 3 ax + 12 = 25 + 3a ax + 12 = 25 + 3a Subtract 12 to both sides ax + 12 - 12 = 25 + 3a - 12 ax = 25 - 12 + 3a ax = 13 + 3a Subtract 3a to both sides ax - 3a = 13 + 3a - 3a ax - 3a...

math
Full circle = 360° For 1 hour small hands move 360° / 12 = 30° 1h to 4h = 3h 3 * 30 ° = 90 °

Calculus
1. f ( x ) = x ^ - 2 = 1 / x ^ 2 f'(x) = lim ? f ( x ) / ?x ?x ->0 ? f ( x ) = 1 / ( x + ?x ) ^ 2 - 1 / x ^ 2 = [ x ^ 2 - ( x + ?x ) ^ 2 ] / [ ( x + ?x ) ^ 2 * x ^ 2 ] = [ x ^ 2 - ( x ^ 2 + 2 x * ?x + ?x ^ 2 ) ] / [ ( x + ?x ) ^ 2 * x ^ 2 ] = ( x ^ 2 - x ^ 2 - 2 x * ?x...

Maths
Your question does not make sense. If the ratio of numerator and denominator is 5:2 = 2.5 is impossible increase the numerator and decrease the denominator and get the ratio 1:4

Algebra
Rewrite your equations: 11 + x = - 15 y Subtract 11 to both sides 11 + x - 11 = - 15 y - 11 x = - 15 y - 11 Add 15 y to both sides x + 15 y = - 15y - 11 + 15 y x + 15 y = - 11 2 x - 5 y = 48 Multiply both sides by 3 2 x * 3 - 5 y * 3 = 48 * 3 6 x - 15 y = 144 Now your system ...

Math fractions
4 + 22 / 15 = 4 + ( 15 + 7 ) / 15 = 4 + 15 / 15 + 7 / 15 = 4 + 1 + 7 / 15 = 5 + 7 / 15 = 5 7/15

Algebra
x ^ 2 - 12 x = - 36 Add 36 to both sides x ^ 2 - 12 x + 36 = - 36 + 36 x ^ 2 - 12 x + 36 = 0 a = 1 , b = - 12 , c = 36 Quadratic Formula : x1/2 = [ - b ± sqroot ( b ^ 2 - 4 a c ) ] / 2 a x1/2 = [ - ( - 12 ) ± sqroot ( ( - 12 ) ^ 2 - 4 * 1 * 36 ) ] / 2 * 1 x1/2...

math
Let 3x be the smallest angle; this will make other angles 5x and 7x. There are 180° in a triangle, so: 3 x + 5 x + 7 x = 180 ° 15 x =180° Divide both sides by 15 x = 180° / 15 x = 12 ° Angles: 3 x = 3 * 12 = 36° 5 x = 5 * 12 = 60° 7 x = 7 * 12 = 84&...

Math
10 / 5 = 2 10 / 5 - ?5 = 2 - ?5

math
- 4 - ( - 15 ) = - 4 + 15 = 11 7 - ( - 4 ) = 7 + 4 = 11 18 - 7 = 11 29 - 18 = 11 d = 11

Math
A = greatest angle B = smaller angle A = B + 18° The sum of the angles in a triangle is 180° 2 A + B = 180° 2 ( B + 18° ) + B = 180° 2 B + 2 * 18° + B = 180° 3 B + 36° = 180° Subtract 36° to both sides 3 B + 36° = 180° 3 B + 36&...

Maths
You must find the least common multiple (LCM) of the positive integers 2 to 10 One way to find LCM's is to use prime factorization: 2 is prime 3 is prime 4 = 2 * 2 = 2 ^ 2 5 is prime 6 = 2 * 3 7 is prime 8 = 2 * 2 * 2 = 2 ^ 3 9 = 3 * 3 = 3 ^ 2 10 = 2 * 5 The LCM of all of ...

Maths
a5 = 3 a2 a12 = 2 a6 + 1 For AP: an = a1 + ( n - 1 ) d a1 = initial term of an arithmetic progression d = common difference of successive members a2 = a1 + ( 2 - 1 ) d a2 = a1 + 1 * d a2 = a1 + d a5 = a1 + ( 5 - 1 ) d a5 = a1 + 4 d a6 = a1 + ( 6 - 1 ) d a6 = a1 + 5 d a12 = a1...

Math
LCM ( Least Common Multiple ) for 8 and 20 = 40 a. 4 / 20 = 4 * 2 / 20 * 2 = 8 / 40 7 / 8 = 7 * 5 / 8 * 5 = 35 /40 Abigail collected more aluminum. b. 8 / 40 + 35 / 40 = 43 / 40 = ( 40 + 3 ) / 40 = 40 / 40 + 3 / 40 = 1 + 3 / 40 = 1.075lb

Algebra 2
A quadratic equation have the standrad form: a x ^ 2 + b x + c R = 290 x ? 0.2 x ^ 2 is quadratic equation: R = ? 0.2 x ^ 2 + 290 x + 0 The vertex of a quadratic parabola is the highest or lowest point, the maximum or minimum. When a < 0 a quadratic parabola has a maximum. ...

Math
n = 1 Denominator = 2 = 2 * 1 n = 2 Denominator = 4 = 2 * 2 n = 3 Denominator = 6 = 2 * 3 n = 4 Denominator = 8 = 2 * 4 n = 5 Denominator = 10 = 2 * 5 Expression for the n-th term: 1 / 2n

Math
The product of two prime numbers is NEVER a prime number becouse that it is a product and therefore has factors.

mathematics
315° = 360° - 45° cos 315° = cos ( 360° - 45° ) cos ( A - B ) = sin A * sin B + cos A * cos B In this case: A = 360° , B = 45° sin A = sin 360° = 0 cos A = 1 sin B = sin 45° = sqroot ( 2 ) / 2 cos B = cos 45° = sqroot ( 2 ) / 2 cos...

Algebra
x = Your number The difference between 5 times a number and 20 equals the sum of the number and 40 mean: 5 x - 20 = x + 40 5 x - 20 = x + 40 Subtract x to both sides 5x - 20 - x = x + 40 - x 4 x - 20 = 40 Add 20 to both sides 4 x - 20 + 20 = 40 + 20 4 x = 60 Divide both sides ...

Math
b = number of boys g = number of girls At first the ratio of the number of boys to the number of girls in a Mathematics Club was 1 : 2 b / g = 1 / 2 When 5 more boys joined the club , the ratio became 3 : 4 ( b + 5 ) / g = 3 / 4 b / g = 1 / 2 Multiply both sides by 2 2 b / g...

math
h = the height of the flagpole Proportion of the shadows: 4 / 1.5 = 12 / h 4 / 1.5 = 12 / h Multiply both sides by h 4 h / 1.5 = 12 Multiply both sides by 1.5 4 h = 12 * 1.5 4 h = 18 Divide both sides by 4 h = 18 / 4 h = 2 * 9 / 2 * 2 h = 9 / 2 = 4.5 m

Math
( x - 3.15 ) ^ 2 = x ^ 2 - 2 * x * 3.15 + 3.15 ^ 2 = x ^ 2 - 6.3 x + 9.9225 ( x - 3.15 ) ^ 2 = 4 p ( y - 219.7981936 ) x ^ 2 - 6.3 x + 9.9225 = 4 p ( y - 219.7981936 ) Divide both sides by 4 x ^ 2 / 4 - 6.3 x / 4 + 9.9225 / 4 = p ( y - 219.7981936 ) 0.25 x ^ 2 - 1.575 x + 2,...

Math
8 / 12 = 4 * 2 / 4 * 3 = 2 / 3

Mathematics
For the AP: 2 x = 8 + d 2 y = 2 x + d = 8 + d + d = 8 + 2 d 2 y = 8 + 2 d For the GP: 2 y = 36 / q 2 x = 2 y / q = ( 36 / q ) / q = 36 / q ^ 2 So: 2 x = 2 x 8 + d = 36 / q ^ 2 2 y = 2 y 8 + 2 d = 36 / q Now you must solve system: 8 + d = 36 / q ^ 2 8 + 2 d = 36 / q 8 + 2 d = ...

f math
Correction. On interval 0 ? x ? 270° sin x = 0 only for x = 0 and x = 180°

f math
1 - cos ^ 2 x = sin ^ 2 x 1 - cos ^ 2 x = 0 mean: sin ^ 2 x = 0 take square root of both sides: sin x = 0 On interval 0 ? x ? 270° sin x = 0 only for x = 0

Pre-calculus
Use trigonometric identities: sin ( x + y ) = sin x cos y + cos x sin y sin ( x - y ) = sin x cos y - cos x sin y cos ( x + y ) = cos x cos y - sin x sin y cos ( x - y ) = sin x sin y + cos x cos y sin ( x + y ) + sin ( x - y ) = sin x cos y + cos x sin y + sin x cos y - cos x...

Math
A woman is twice as old as her daughter mean: W = 2 D Five years ago wooman was W - 5 yrs , daughter was D - 5 yrs Five years ago the sum of their age was 62 mean: W - 5 + D - 5 = 62 W - 10 + D = 62 Add 10 to both sides W - 10 + D + 10 = 62 + 10 W + D = 72 Replace : W = 2 D in...

Algebra
Write your equation in explicit form: y = m x + n where: m is the slope of the line n is the y intercept 9 x + 3 y = - 22 Subtract 9 x to both sides 9 x + 3 y - 9 x = - 22 - 9 x 3 y = - 9 x - 22 Divide both sides by 3 y = - 9 x / 3 - 22 / 3 y = - 3 x - 22 / 3 Parallel lines ...

maths
Rearange your equations. 3 x - 2 y = 1 Multiply both sides by 2 6 x - 4 y = 2 2x + y = - 4 Multiply both sides by 3 6 x + 3 y = - 12 6 x - 4 y = 2 - 6 x + 3 y = - 12 ______________ 6 x - 6 x - 4 y - 3 y = 2 - ( - 12 ) 0 - 7 y = 2 + 12 - 7 y = 14 Divide both sides by - 7 y = 14...

Math
So what?

math
1. 2 / 5 = 2 * 2 / ( 5 * 2 ) = 4 / 10 4 2/5 = 4 + 2 / 5 = 4 + 4 / 10 = 4 * 10 / 10 + 4 / 10 = 40 / 10 + 4 / 10 = 44 / 10 1 7/10 = 1 + 7 / 10 = 10 / 10 + 7 / 10 = 17 / 10 4 2/5 - 1 7/10 = 44 / 10 - 17 / 10 = 27 /10 = 20 / 10 + 7 / 10 = 2 7/10 2. 5 2/3 = 5 + 2 / 3 = 5 * 3 / 3 + ...

math
( m n ) ^ 5 = m ^ 5 * n ^ 5

math
A student has passed 60 percent of the 20 quizzes he has written so far successfully mean: successfully quizzes = 60 % of 20 quizzes = ( 60 / 100 ) * 20 = 60 * 20 / 100 = 1200 / 100 = 12 The remaining quizzes = 50 - 20 = 30 quizzes 80 percent of the remaining quizzes ...

math
M = Mimi’s cd’s R = Rita’s cd’s The ratio of the number of Mimi’s Eminem cd’s to the number of Rita’s Eminem cd’s is 5:8 mean: M / R = 5 / 8 Rita has 18 more Eminem cd’s than Mimi mean: R = M + 18 Now you have system of 2 equations ...

math
You can represent your number like: x = 10 * a + b where: a = tens digit b = ones digit Two of my divisor are 8 and 12 mean you must find least common multiple of 8 and 12 Least Common Multiple ( 8 , 12 )= 24 This mean x = 24 b = 2 , a = 4 Proof: x = 10 b + a = 24 x = 10 b + a...

Calculus
f(x) is concave up on an interval if f"(x) > 0 In this case f"(x)= 2 So x^2-3 is concave up for all vales of x, including interval ( -1, 1 )

Maths
Length of the diagonal of a square: d = sqroot ( a^ 2 + a ^ 2 ) = sqroot ( 2 a ^ 2 ) = sqroot ( 2 ) * a The area of a square is A = a ^ 2 So a = sqroot ( A ) 1 hectare = 10,000 m ^ 2 0.5 hectare = 5,000 m ^ 2 a = sqroot ( A ) = sqroot ( 5,000 ) = sqroot ( 50 * 100 ) = sqroot...

mth/208
d = a b c Divide both sides with b c d / b c = a a = d / b c Your answer is correct.

Geometrical progration
a1 = initial value r = common ratio = 10 The n-th term of a geometric sequence: an = a1 * r ^ ( n - 1 ) In this case: a6 = a1 * r ^ 5 2,000 = a1 * 10 ^ 5 2,000 = 100,000 a1 Divide both sides by 100,000 2,000 / 100,000 = a1 0.02 = a1 a1 = 0.02

Math
5 1/2 = 5 + 1 / 2 = 10 / 2 + 1 / 2 = 11 / 2 2 1/3 = 2 + 1 / 3 = 6 / 3 + 1 / 3 = 7 / 3 5 1/2 /2 1/3 = ( 11 / 2 ) / ( 7 / 3 ) = 11 * 3 / 2 * 7 = 33 / 14 33 / 14 = 28 / 14 + 5 / 14 = 2 + 5 / 14 = 2 5/14 Average number of pages = 33 / 14 = 2 5/14

Algebra
You're welcome

Algebra
- 2 / 5 x - 9 < 9 / 10 Add 9 to both sides - 2 / 5 x - 9 + 9 < 9 / 10 + 9 - 2 / 5 x < 9 / 10 + 90 / 10 - 2 / 5 x < 99 / 10 Multiply both sides by 5 - 2 x < 99 * 5 / 10 - 2 x < 99 * 5 / 2 * 5 - 2 x < 99 / 2 Divide both sides by - 2 When we multiply or ...

algebra
Put x coordinate into equation: 3 x - 2 y = 12 and check y coordinate 1. For x = 2 3 x - 2 y = 3 * 2 - 2 y = 12 6 - 2 y = 12 Subtact 6 to both sides 6 - 2 y - 6 = 12 - 6 - 2 y = 6 Divide both sides by - 2 y = 6 / - 2 y = - 3 x = 2 , y = - 3 True 2. For x = 4 3 x - 2 y = 3 * 4...

Algebra
Remark: 1 1/4 = 1 2/8 ___________ 1, 1 1/8, 1 1/4, 1 3/8 1 1/8 - 1 = 1/8 1 1/4 - 1 1/8 = 1 2/8 - 1 1/8 = 1/8 1 3/8 - 1 1/4 = 1 3/8 - 1 2/8 = 1/8 Common difference = 1/8 Answer C

Calculus
Using the chain rule: u = 3 x du = 3 dx Divide both sides by 3 du / 3 = dx dx = du / 3 d cosh ( 3 x ) / dx = d cosh ( u ) / ( du / 3 ) = 3 d cosh ( u ) / du d cosh ( u ) / du = sinh u so d cosh ( 3 x ) / dx = 3 d cosh ( u ) / du = 3 sinh u = 3 sinh ( 3 x )

Math
n = the numerator d = the denomenator the fraction = n / d If one be added to the numerator of a fraction it reduces to 1 / 5 mean: ( n + 1 ) / d = 1 / 5 If one be taken from the denomenator it reduces to 1 / 7 mean: n / ( d - 1 ) = 1 / 7 Now: ( n + 1 ) / d = 1 / 5 Multiply ...

MATHS URGENT
ln ( x ^ 4) = 4 ln x 9 / ln x + ln ( x ^ 4 ) = - 12 9 / u + 4 u = - 12 Multiply both sides by u 9 u / u + 4 u * u = ( - 12 ) * u 9 + 4 u ^ 2 = - 12 u Add 12 u to both sides 9 + 4 u ^ 2 + 12 u = - 12 u + 12 u 4 u ^ 2 + 12 u + 9 = 0 Now, find discriminant using formula D = b ^ 2...

MATHS URGENT
7 ^ ( 2 x - 1 ) = 7 ^ ( 2 x ) / 7 ^ 1 = ( 7 ^ x ) ^ 2 / 7 7 ^ ( x - 1 ) = 7 ^ x / 7 ^ 1 = 7 ^ x / 7 7 ^ ( 2 x -1 ) + 4 * 7 ^ ( x - 1 ) - 1 / 14 = 0 ( 7 ^ x ) ^ 2 / 7 + 4 * 7 ^ x / 7 - 1 / 14 = 0 Make the substitution u = 7 ^ x u ^ 2 / 7 + 4 u / 7 - 1 / 14 = 0 Multiply both ...

Math (Derivative)
In your homework you can replace ∆h with h Is all the same.

Math (Derivative)
f´(x)= lim [ f ( x + ∆h ) - f ( x ) ] / ∆h ∆h-> 0 In this case : f ( x ) = 1 + 1 / x ^ 2 f ( x + ∆h ) = 1 + 1 / ( x + ∆h ) ^ 2 f ( x + ∆h ) - f ( x ) = 1 + 1 / ( x + ∆h ) ^ 2 - ( 1 + 1 / x ^ 2 ) = 1 + 1 / ( x + ∆h ) ^ 2...

Maths
a ^ ( n - m ) = a ^ n / a ^ m 7 ^ ( x - 1 ) = 7 ^ x / 7 ^ 1 = 7 ^ x / 7 7 ^ x = u so 7 ^ x / 7 = u / 7 ( a ^ m ) ^ n = a ^ ( m * n ) 7 ^ 2 x = ( 7 ^ x ) ^ 2 Again: a ^ ( n - m ) = a ^ n / a ^ m so 7 ^ ( 2 x - 1 ) = 7 ^ 2 x / 7 ^ 1 = 7 ^ 2 x / 7 = ( 7 ^ x ) ^ 2 / 7 = u ^ 2 / 7

math
Factor 8454 8454 = 2 * 3 * 1409 8454 = 6 * 1409 8454 / 6 = 1409 Remark: 2 , 3 , 1409 is prime mumbers

Math
( 5 x - 1 ) / ( 2 x + 3 ) = 4 / 5 Multiply both sides by 5 5 ( 5 x - 1 ) / ( 2 x + 3 ) = 4 Multiply both sides by ( 2 x + 3 ) 5 ( 5 x - 1 ) = 4 ( 2 x + 3 ) 5 x * 5 - 1 * 5 ) = 2 x * 4 + 3 * 4 25 x - 5 = 8 x + 12 Add 5 to both sides 25 x - 5 + 5 = 8 x + 12 + 5 25 x = 8 x + 17 ...

Algebra
( a ) Put t = 8 in your formula h(8) = − 4.9 * 8 ^ 2 + 70 * 8 + 30 h(8) = − 4.9 * 64 + 560 + 30 h(8) = − 4.9 * 64 + 560 + 30 h(8) = − 313.6 + 590 h(8) = 276.4 ( b ) Put t = 0 in your formula h(0) = − 4.9 * 0 ^ 2 + 70 * 0 + 30 h(0) = − 4.9 * ...

Math
a = first number b = second number The sum of two numbers is 21 mean: a + b = 21 Five times the first number added to 2 times the second number is 66 mean: 5 a + 2 b = 66 a + b = 21 Subtract a to both sides a + b - a = 21 - a b = 21 - a Replace this value in equation: 5 a + 2 ...

math
One third of them were men: 1 / 3 * 450 = 450 / 3 = 150 men Two fifth of them were women: 2 / 5 * 450 = 2 * 450 / 5 = 900 / 5 = 180 women One tenth of them were boys: 1 / 10 = 450 / 10 = 45 boys 150 + 180 + 45 = 375 450 - 375 = 75 girls

Math
1 / 50 = 1 * 2 / 50 * 2 = 2 /100 = 0.02

Differentiation
Use chain rule: dy / dx = ( dy / du ) * ( du / dx ) u = log x y = log ( log x ) = log u dy / du = d ( log u ) / du = 1 / u = 1 / log x ( du / dx ) = d ( log x ) / dx = 1 / x dy / dx = ( dy / du ) * ( du / dx ) = ( 1 / log x ) * ( 1 / x ) = 1 / x log x

Geometric progression
s2 = s1 * q s4 = s1 * q ^ 3 8 = s1 * q 40 = s1 * q ^ 3 s1 * q ^ 3 = s1 * q * q ^ 2 40 = s1 * q ^ 3 = ( s1 * q ) * q ^ 2 = 8 * q ^ 2 40 = 8 * q ^ 2 40 / 8 = q ^ 2 5 = q ^ 2 q = ± sqrt ( 5 ) You can construct two g.p. 1. 8 = s1 * g 8 = s1 / sqrt ( 5 ) s1 = 8 / sqrt ( 5 ) ...

math
x = larger number 45 / x = 3 / 5 Multiply both sides by 5 45 * 5 / x = 3 225 / x = 3 Multiply both sides by x 225 = 3 x Divide both sides by 3 225 / 3 = x 75 = x x = 75 Proof: 45 / 75 = ( 3 * 15 ) / ( 5 * 15 ) = 3 / 5

math
- ( 2x + 7 ) = - 2 x - 7

math
1) 11 x + 2 y - 4 x - y = ( 11 x - 4 x ) + ( 2 y - y ) = 7 x + y 2) 9 x + 2y - 5 x = ( 9 x - 5 x ) + 2 y = 4 x + 2 y

algebra
OR 17, 20, 23, 26 is an arithmetic progression. If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence: an = a1 + ( n - 1 ) * d In this case the initial term a1 = 17, the common difference ...

algebra
n = 1, a1 = 17 = 3 * 1 + 14 = 3 + 14 n = 2, a2 = 20 = 3 * 2 + 14 = 6 + 14 n = 3 , a3 = 23 = 3 * 3 + 14 = 9 + 14 n = 4 , a4 = 26 = 3 * 4 + 14 = 12 + 14 an = 3 n + 14

Algebra
a = first number b = second number The sum of two numbers is 6 mean: a + b = 6 One number is 2 times the other mean: a = 2 b Replace a = 2 b in equation: a + b = 6 2 b + b = 6 3 b = 6 Divide both sides by 3 b = 6 / 3 = 2 a = 2 b = 2 * 2 = 4 a = 4 and b = 2

algebra 1
10 - ( s + 3 ) < 20 10 - s - 3 < 20 7 - s < 20 Subtract 7 to both sides 7 - s - 7 < 20 - 7 - s < 13 Multiply both sides by - 1 If you multiplied or divided both sides of an inequality by the negative number, then you must reverse the inequality sign. s > - 13

Math
9 / 8.1 = 5 / x Multiply both sides by x 9 x / 8.1 = 5 Multiply both sides by 8.1 9 x = 5 * 8.1 9 x = 40.5 Divide both sides by 9 x = 40.5 / 9 x = 4.5 5 apples cost \$4.5

Math
1 / 2 = 1 * 3 / 2 * 3 = 3 / 6 - 1 / 2 = - 3 / 6 1 / 3 = 1 * 2 / 3 * 2 = 2 / 6 - 1 / 2 + 1 / 3 = - 3 / 6 + 2 / 6 = - 1 / 6 Answer A I don't know what3 5/1 nean. 5 / 8 - ( - 2 / 8 ) = 5 / 8 + 2 / 8 )= 7 / 8 Answer D 2 / 5 = 2 * 2 / 5 * 2 = 4 / 10 - 9 / 10 - 2 / 5 = - 9 / 10...

Algebra
- 2 x + 2 y + 3 z = 0 Multiply both sides by - 1 2 x - 2 y - 3 z = 0 - 2 x + 2 y + 3 z = 0 + 2 x + 3 y + 3 z = 5 _________________ 5 y + 6 z = 5 2 x - 2 y - 3 z = 0 + - 2 x - y + z = - 3 __________________ - 3 y - 2 z = - 3 Multiply both sides by 3 - 9 y - 6 z = - 9 - 9 y - 6 ...

Algebra
2 x + 2 z = 4 Divide both sides by 2 x + z = 2 Subtract z to both sides x + z - z = 2 - z x = 2 - z Replace x = 2 - z in equation - x - y - z = - 8 - x - y - z = - 8 - ( 2 - z ) - y - z = -8 - 2 + z - y - z = - 8 - 2 - y + z - z = - 8 - 2 - y = - 8 Add 2 to both sides - 2 - y...

Plane and solid geometry
2 x ^ 2 + 4 y ^ 2 - 12 x - 64 y - 16 = 0 Add 16 to both sides 2 x ^ 2 + 4 y ^ 2 - 12 x - 64 y - 16 + 16 = 0 + 16 2 x ^ 2 + 4 y ^ 2 - 12 x - 64 y = 16 2 x ^ 2 - 12 x + 4 y ^ 2 - 64 y = 16 2 ( x ^ 2 - 6 x ) + 4 ( y ^ 2 - 16 y ) = 16 Divide both sides by 4 2 ( x ^ 2 - 6 x ) / 4...

maths
Half distance = 50 km The first half: 50 km / 40 km/h = 1.25 h The second half: 50 km / 80 km/h = 0.625 h Total time of the travel = 1.25 h + 0.625 h = 1.875 h average speed = 100 km / 1.875 h = 53.333 km / h

math
But if your question mean: The total number of students in a school is 1650. 70% of the pupils are boys. How many girls are there in the school? Then: 70% of the pupils are boys. 100 % - 70 % = 30 % 30% of the pupils are girls. 30 % = 30 / 100 = 0.3 0.3 * 1650 = 495 The total ...

math
The total number of students in a school can't be 1650.70%.

Math
40 % = 40 / 100 = 0.4 0.4 * 33 = 13.2

Math
30 % = 30 / 100 = 0.3 0.3 * 80 = 24

math
( 4 / 7 ) x = - 16 Multiply both sides by 7 4 x = - 16 * 7 4 x = - 112 Divide both sides by 4 x = - 112 / 4 = - 28 Answer B 4 s + 13 + s = 2 s + 40 - 6 5 s + 13 = 2 s + 34 Subtract 2 s to both sides 5 s + 13 - 2 s = 2 s + 34 - 2 s 3 s + 13 = 34 Subtract 13 to both sides 3 s + ...

Math
0.67 = 67 / 100 0.3 = 3 / 10 0.67 * 0.3 = 67 / 100 * 3 / 10 = 67 * 3 / ( 100 * 10 ) = 201 / 1000 = 0.201