# Posts by Bosnian

Total # Posts: 2,464

**math 1**

Correct answer. But 82=-82 Isn't correct. Least Common Denominator of 6 and 8 is 24, not 48. 6 x + 8 y = 4 Multiply both sides by 4 24 x + 32 y = 16 8 x - 3 y = 19 Multiply both sides by - 3 - 24 x + 9 y = - 57 24 x + 32 y = 16 + - 24 x + 9 y = - 57 ___________________ 41 ...

**math**

a) x = numbers of marbles when the container is filled ( 3 / 5 ) x = 45 Multiply both sides by 5 3 x = 5 * 45 3 x = 225 Divide both sides by 3 x = 225 / 3 x = 75 b ) 2 / 5 marbles are needed to completely fill. ( 2 / 5 ) * 75 = 2 * 75 / 5 = 150 / 5 = 30 OR a) 3 / 5 = 2 * 3 / 2...

**math 1**

Correct answer

**Math**

1. ? 13 ^ 2 = 13 3 ? 13 ^ 2 = 3 * 13 = 39 2. ( 2 / 3 ) ^ 5 = ( 2 / 3 ) ^ 4 * ( 2 / 3 ) = [ ( 2 / 3 ) ^ 2 ] ^ 2 * ( 2 / 3 ) ? ( 2 / 3 ) ^ 5 = ? [ ( 2 / 3 ) ^ 2 ) ^ 2 ] * ? ( 2 / 3 ) = ( 2 / 3 ) ^ 2 * ? ( 2 / 3 ) = ( 4 / 9 ) * ? ( 2 / 3 ) = 4 * ? ( 2 / 3 ) / 9 = 4 * ? 2 / 9 * ? 3

**Math**

A. Flat doesn't change 2 changes with x y = 2 x + 5 B. y-intercept is a point on the graph where x is zero. y = 2 * 0 + 5 = 0 + 5 = 5 x = 0 , y = 5 x-intercept is a point on the graph where y is zero. 2 x + 5 = 0 2 x = - 5 x = - 5 / 2 = - 2 .5 x = - 2.5 , y = 0 Draw ...

**Math**

x = first number x + 1 = second number 1 / x + 1 / ( x + 1 ) = 17 / 72 [ 1 * ( x + 1 ) + 1 * x ] / [ x * ( x + 1 ) ] = 17 / 72 [ ( x + 1 ) + x ] / [ x * x + x * 1 ) ] = 17 / 72 ( 2 x + 1 ) / ( x ^ 2 + x ) = 17 / 72 Multiply both sides by 72 72 * ( 2 x + 1 ) / ( x ^ 2 + x ) = ...

**math**

2 ^ ( - 3 x ) = 1 / 2 ^ ( 3 x ) = 1 / 4 so: 2 ^ ( - 3 x ) = 1 / 4 1 / 2 ^ ( 3 x ) = 1 / 4 Take reciprocials of both sides: 2 ^ ( 3 x ) = 4 2 ^ ( 3 x ) = 2 ^ 2 Take the logarithm base 2 of both sides 3 x = 2 Divide both sides by 3 x = 2 / 3

**Calculus**

A constant factor within an integrand can be separated from the integrand and multiplied by the integral. In this case: integral [ ( 1 / 2 ) * e ^ ( t / 2 ) dt ] = 1 / 2 integral e ^ ( t / 2 ) Substitute: u = t / 2 du = dt / 2 Multiply both sides by 2 2 du = dt dt = 2 du 1 / 2...

**math**

a = first numbner b = second number b = 3 a a + b = 20 a + 3 a = 20 4 a = 20 Divide both sides by 4 a = 5 b = 3 a = 3 * 5 = 15 The two numbers: 5 and 15

**Algebra**

3 n ^ 2 + 21 n = 3 n * n + 3 n * 7 = 3 n ( n + 7 ) 6 n ^ 2 + 18 n = 6 n * n + 6 n * 3 = 6 n ( n + 3 )

**math**

52 % of 825 = ( 52 / 100 ) * 825 = 52 * 825 / 100 = 42900 / 100 = 429 boys When more boys joined the school numbers of boys will be: 429 + x total number of pupils will be 825 + x ( 429 + x ) / ( 825 + x ) = 64 % = 64 / 100 = 0.64 ( 429 + x ) / ( 825 + x ) = 0.64 Multiply both...

**Math**

The ratio: 5 : 3 : 2 5 + 3 + 2 = 10 5 / 10 = 0.5 = 50 % peanuts 3 / 10 = 0.3 = 30 % walnuts 2 / 10 = 0.2 = 20 % cashews 0.3 * 12 = 3.6 Answer c

**calculus**

v = ds / dt = s´(t) = 1/ ( 1 + t ) ^ 2

**math**

12 days / 10 days = 12 / 10 = 1.2 1.2 * 20 men = 24 men

**math**

t1 = 75 = results of the first test t2 = 81 = results of the secondt test t3 = 88 = results of the third test t4 = 92 = results of the fourth test t = results of the fifth test average of 5 test a = ( t1 + t2 + t3 + t4 + t ) / 5 Nick needs a test average of 80 or better mean...

**math**

N = Present Nancy ages C = Present Cathy ages Nancy is 3 times as old as Cathy mean: N = 3 C In seven years Nancy will be N + 7 yrs old , Cathy will be C + 7 yrs old In seven years, she will be ten years older than Cathy Mean: N + 7 = C + 7 + 10 N + 7 = C + 17 Subtract 7 to ...

**Math**

26

**Algebra**

Every odd integer can be written in the form 2 k + 1 So your first integer is a1 = 2 k + 1 Second integer is a2 = first integer + 2 = a1 + 2 = 2 k + 1 + 2 = 2 k + 3 Third integer is a3 = second integer + 2 = a2 + 2 = 2 k + 3 + 2 = 2 k + 5 Product of the first integer and the ...

**algebra**

x = 5 y = - 2 x + 9 = - 2 * 5 + 9 = - 10 + 9 = - 1 x = 5 , y = - 1

**algebra**

2 x + y = 9 Subtract 2x to both sides 2 x + y - 2 x = 9 - 2 x y = 9 - 2 x y = - 2 x + 9 Now put x values in this formula x = - 3 y = - 2 x + 9 = - 2 * ( - 3 ) + 9 = 6 + 9 = 15 x = - 3 , y = 15 x = 1 y = - 2 x + 9 = - 2 * 1 + 9 = - 2 + 9 = 7 x = 1 , y = 7 x = 4 y = - 2 x + 9...

**math**

Correction y > ( 99 / 13 ) / - 15 y > - 99 / 13 * 15 y > - 33 * 3 / 13 * 5 * 3 y > - 33 / 13 * 5 y > - 33 / 65

**math**

If ?15/9y < 11/13 mean: ?( 15 / 9 ) y < 11 / 13 then multiply both sides by 9 - 15 y < 99 / 13 Divide both sides by - 15 When you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality. y > ( 99 / 13...

**math**

J = Justin's age S = Sam's age Justin is 3 years older then Sam mean: J = S + 3 Justin’s age in 2 years will be twice what Sam’s age was 3 years ago mean: J + 2 = 2 ( S - 3 ) Replace J = S + 3 in this equation. S + 3 + 2 = 2 * S - 2 * 3 S + 5 = 2 S - 6 ...

**math**

R = L + 6 R + 5 + L + 5 = 2 ( R - 4 + L - 4 ) R + L + 10 = 2 ( R + L - 8 ) R + L + 10 = 2 * R + 2 * L - 2 * 8 R + L + 10 = 2 R + 2 L - 16 Replace R = L + 6 in this equation L + 6 + L + 10 = 2 ( L + 6 ) + 2 L - 16 2 L + 16 = 2 * L + 2 * 6 + 2 L - 16 2 L + 16 = 2 L + 12 + 2 L - ...

**maths**

25 m

**algebra**

a = first integer a + 1 = second integer a + 2 = third integer first integer + third integer: a + a + 2 = 16 2 a + 2 = 16 Subtract 2 to both sides 2 a + 2 - 2 = 16 - 2 2 a = 14 Divide both sides by 2 a = 14 / 2 = 7 Three consecutive integers are 7, 8 , 9 7 + 9 = 16

**math**

x = present age One half of her age two years from now: ( x + 2 ) / 2 One third of her age three years ago: ( x - 3 ) / 3 ( x + 2 ) / 2 + ( x - 3 ) / 3 = 20 Multiply both sides by 2 2 * ( x + 2 ) / 2 + 2 * ( x - 3 ) / 3 = 20 * 2 ( x + 2 ) + 2 * ( x - 3 ) / 3 = 40 Multiply both...

**Math**

V = L * W * D V = 25 * 10 * 2 = 500 m ^ 3

**Ordinary Differential Equation**

Straight line in slope intercept form: y = m x + b Differentiate: dy = m dx + 0 dy = m dx dy / dx = m

**algebra**

1) b = ? ( c ^ 2 - a ^ 2 ) b = ? ( 20 ^ 2 - 15 ^ 2 ) b = ? ( 400 - 225 ) b = ? ( 175 ) b = ? ( 7 * 25 ) b = ? 7 * ? ( 25 ) b = ? 7 * 5 2) c = ? ( a ^ 2 + b ^ 2 ) c = ? ( 9 ^ 2 + 12 ^ 2 ) c = ? ( 81 + 144 ) c = ? ( 225 ) c = 25

**math**

L1 = Length of 1st piece L2 = Length of 2st piece L3 = Length of 3st piece The 1st piece is 4.25 feet longer than the second piece mean: L1 = L2 + 4.25 The 3rd piece is 2.24 feet longer than the second mea. L3 = L2 + 2.24 L1 + L2 + L3 = 10 ft L2 + 4.25 + L2 + L2 + 2.24 = 10 3 ...

**math**

Aare you kidding? 78 + 99 = 177 100 - 98 = 2 ( 78 + 99 ) + ( 100 - 98 ) = 177 + 2 = 179

**math**

13 x ? 6 y = 2 Multiply both sides by 4 52 x - 24 y = 8 3 x ? 4 y = ? 10 Multiply both sides by - 6 - 18 x + 24 y = 60 Now solve system: 52 x - 24 y = 8 - 18 x + 24 y = 60 52 x - 24 y = 8 + - 18 x + 24 y = 60 __________________ 34 x + 0 = 68 34 x = 68 Divide both sides by 34 x...

**Math**

7 / 10 = 7 * 4 / 10 * 4 = 28 / 40 11 / 20 = 11 * 2 / 20 * 2 = 22 / 40 4 / 5 = 4 * 8 / 5 * 8 = 32 / 40 Smallest to largest: 22 / 40 , 28 / 40 , 32 / 40 11 / 20 , 7 / 10 , 4 / 5

**slope intercept, math**

The two-point form of a line passing through the points (x1 , y1 ) and ( x2 , y2 ) is given by: y - y1 = [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 ) In this case: x1 = 4 , y1 = 7 x2 = - 5 , y2 = - 5 y - y1 = [ ( y2 - y1 ) / ( x2 - x1 ) ] * ( x - x1 ) y - 7 = [ ( - 5 - 7...

**math**

n = numerator d = denominator A fraction reduces to 2 / 3 when 3 is adding to both its numerator mean: ( n + 3 ) / ( d + 3 ) = 2 / 3 Reduces to 3 / 5 when 1 is added to both its numreator and denominator mean: ( n + 1 ) / ( d + 1 ) = 3 / 5 Now: ( n + 3 ) / ( d + 3 ) = 2 / 3 ...

**maths**

Replace n = 19 in formula 4 n + 3 4 * 19 + 3 = 76 + 3 = 79

**Math (calc)**

In an open box you have square base with area a ^ 2 and 4 rectangle with area a * h where: a = length of base h = height of box Volume of box: V = a ^ 2 * h = 12 ft ^ 3 a ^ 2 * h = 12 Divide both sides by a ^ 2 h = 12 / a ^ 2 Area of an open box: A = a ^ 2 + 4 a * h A = a ^ 2...

**Math**

3 / 4

**Algebra**

0.54 is a rational number = 54 / 100 = 2 * 27 / 2 * 50 = 27 / 50 But if 0.54 mean 0.5454545454 then: 100 * 0.5454545454 = 54.54545454 100 * 0.5454545454 - 0.5454545454 = 99 * 0.5454545454 = 54.54545454 - 0.54545454 = 54 99 * 0.5454545454 = 54 Divide both sides by 99 0....

**math**

18 / ( 2 / 3 ) = 3 * 18 / 2 = 54 / 2 = $27

**Algebra**

1 m = 100 cm 1 cm = 1 m / 100 60.5 / 100 = 0.605 m

**College Algebra**

x + 2 y = 0 Subtract 2 y to both sides x + 2 y - 2 y = 0 - 2 y x = - 2 y x + 2 y = 0 + x + 3 y + z = 1 + - 4 x - y - z = 23 ___________________ - 2 x + 4 y = 24 - 2 * ( - 2 y ) + 4 y = 24 4 y + 4 y = - 24 8 y = 24 Divide both sides by 8 y = 24 / 8 = 3 x = - 2 y = - 2 * 3 = - 6...

**Algebra**

12 - 3 = 9 21 - 12 = 9 31 - 21 = 9 The common difference of successive members is 9 This is arithmetic progression. In arithmetic progression: an = a1 + ( n - 1 ) * d In this case: a1 = 3 , d = 9 an = a1 + ( n - 1 ) * d an = 3 + ( n - 1 ) * 9 an = 3 + 9 n - 9 an = 9 n - 6 n = ...

**Math**

11

**math**

If the initial term of an arithmetic sequence is a1, and the common difference of successive members is d, then the nth term of the sequence is given by: an = a1 + ( n -1 ) * d In this case: a1 = p , a2 = 2 p + 2 , a3 = 5 p + 3 so a2 = a1 + ( 2 -1 ) * d = p + 1 * d = p + d a2 ...

**Finite math**

a = adults c = childrens s = students With a full audience: a + c + s = 900 There were half as many adults as children and students combined mean: a = ( s + c ) / 2 Replace this in equation: a + c + s = 900 ( s + c ) / 2 + c + s = 900 Multiply both sides by 2 s + c + 2 c + 2 s...

**Basic math**

tan ( A + B ) = ( tan A + tan B ) / ( 1 - tan A * tan B ) In this case: A = 2 alpha , B = beta so tan ( 2 alpha + beta ) = [ tan ( 2 alpha ) + tan ( beta ) ] / [ 1 - tan ( 2 alpha ) * tan ( beta ) ] Since the: tan ( 2 alpha ) = 2 * tan ( alha ) / [ 1 - tan ^ 2 ( alpha ) ] put...

**Algebra 7th grade**

(3,4) m = 2 mean x = 3 , y = 4 , m = 2 slope intercept form: y = m x + b 4 = 2 * 3 + b 4 = 6 + b Subtract 6 to both sides 4 - 6 = 6 + b - 6 - 2 = b b = - 2 Now: y = m x + b y = 2 x + ( - 2 ) y = 2 x - 2

**Algebra**

( x - x1 ) ( x - x2 ) = [ x - ( - 2 ) ] ( x - 3 ) = ( x + 2 ) ( x - 3 ) = 0 Answer c.

**Algebra**

The n-th term of a geometric sequence with initial value a and common ratio r is given by: an = a * r ^ ( n - 1 ) a is the first term r is common ratio In this case: a1 = a * r ^ ( 1 - 1 ) = a * r ^ 0 = a * 1 = a a2 = a * r ^ ( 2 - 1 ) = a * r ^ 1 = a * r a3 = a * r ^ ( 3 - 1...

**Algebra 2**

and yes : (base of logarithm)^ log ( x ) = x log 6 (36) = 2 log base (6) (36) = 2 becouse 6 ^ 2 = 36

**Algebra 2**

log ( x ^ n ) = n * log ( x ) log ( 36 ) = log ( 6 ^ 2 ) = 2 * log ( 6 )

**math**

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 is given by: an = a1 + ( n -1 ) * d a1 = 5 a100 = a1 + ( 100 - 1 ) * d = - 292 a100 = 5 + 99 d = - 292 5 + 99 d = - 292 Subtract 5 ...

**mathematical literacy**

( 6 x 3 ) - 4 + 26 ÷ 2 = 18 - 4 + 13 = 14 + 13 = 27

**Algebra**

2 , 6 , 12 , 20... n = 1 a1 = 2 = 1 + 1 = 1 ^ 2 + 1 = n ^ 2 + n n = 2 a2 = 6 = 4 + 2 = 2 ^ 2 + 2 = n ^ 2 + n n = 3 a3 = 12 = 9 + 3 = 3 ^ 2 + 3 = n ^ 2 + n n = 4 a3 = 20 = 16 + 4 = 4 ^ 2 + 4 = n ^ 2 + n an = n ^ 2 + n

**math**

2 * 48 * 1 + 2 * ( 40 - 2 ) * 1 = 96 + 2 * 38 = 96 + 76 = 172 cm ^ 2 OR 2 * 40 * 1 + 2 * ( 48 - 2 ) * 1 = 80 + 2 * 46 = 80 + 92 = 172 cm ^ 2 OR New dimensions of a picture : 48 - 2 = 46 cm and 40 - 2 = 38 cm 48 * 40 - 46 * 38 = 1920 - 1748 = 172 cm ^ 2

**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