# 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

**mystery number math please help**

The digit in the hundreds place is 3 times greater than the digit in the ones place. The digit in the ones place is 6 less than the digit in the hundred thousands place. If you mark digit in the one place with x and digit in the hundreds place with h this mean: h = 3 x and x...

**Math**

a = larger number b = smaller number The difference of two number is seven mean: a - b = 7 a - b = 7 Add b to both sides a - b + b = 7 + b a = 7 + b a = b + 7 When the larger number is decreased by five, then doubled, it is five more than the small number mean: ( a - 5 ) * 2...

**Math**

Your answer is partially correct. 4 ( 9 + 6 ) = 4 * 15 = 60 But also: 36 = 12 * 3 24 = 12 * 2 36 + 24 = 12 * 3 + 12 * 2 = 12 ( 3 + 2 ) 12 * ( 3 + 2 ) = 12 * 5 = 60 Answers b and d

**MATH**

If the initial term of an arithmetic progression is a a1 and the common difference of successive members is d, then the nth term of the AP is given by: an = a1 + ( n - 1 ) d a4 = a1 + ( 4 - 1 ) d a4 = a1 + 3 d = - 3 a9 = a1 + ( 9 - 1 ) d a9 = a1 + 8 d = 12 Now you must solve ...