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RideAnS [48]
2 years ago
11

What is the "least common denominator" of the following two fractions: 1/6 and 1/2

Mathematics
2 answers:
astra-53 [7]2 years ago
8 0

Answer:

it is 6

Step-by-step explanation:

2 and 6 are the denominators and the least common denominator is the number in which 2 & 6 can go in without leaving a remender and 6 is that number

Brut [27]2 years ago
5 0

Answer:

The LCD of the fractions 1/6 and 1/2 is 6

Step-by-step explanation:

The LCD of 2 or more fractions is the least common multiple of the denominators.

The given fractions are 1/2 and 1/6. The denominators are 2 and 6

List the multiples of each denominator:

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ..

The least common multiple that the two share is 6.

So the LCD of 1/2 and 1/6 is 6.

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Resolve into partial fractions<br><br>​
lisabon 2012 [21]

Answer:

See below

Step-by-step explanation:

1)

\frac{11 + x}{(2 - x)(x - 3)}  =  \frac{A}{2 - x}  +  \frac{B}{x - 3}  \\  \\  \therefore \:  \frac{11 + x}{(2 - x)(x - 3)}  =  \frac{A(x - 3) +B(2 - x) }{(2 - x)(x - 3)}   \\  \\ \therefore \:  11 + x = Ax - 3A + 2B - Bx \\  \\  \therefore \: 11 + x = - 3A  + 2B  + Ax -  Bx\\  \\  \therefore \: 11 + x = - 3A  + 2B  + (A - B)x \\  \\ equating \: the \: like \: terms \: on \: both \: sides \\ A - B = 1 \\  \therefore \: A  =  B  +  1.....(1) \\  \\  -  3A  + 2B = 11....(2) \\  from \: eq \: (1) \: and \: (2) \\  - 3(B  +  1) + + 2B = 11 \\  \\ - 3B   - 3  + 2B = 11 \\  \\  - B = 11 + 3 \\  \\ B =  - 14  \\ A  =   - 14 +  1 =  - 13 \\  \\  \frac{11 + x}{(2 - x)(x - 3)}  =  \frac{ - 13}{2 - x}  +  \frac{ - 14}{x - 3} \\  \\ \frac{11 + x}{(2 - x)(x - 3)}  = -   \frac{ 13}{2 - x}   -  \frac{ 14}{x - 3}

2)

\frac{12x + 11}{x^2 +x - 6}

=\frac{12x + 11}{x^2 +3x-2x - 6}

=\frac{12x + 11}{x(x +3) -2(x +3)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{12x + 11}{(x +3) (x - 2)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A}{(x +3)}+\frac{B}{(x - 2)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A(x-2)+B(x+3)}{(x-2)(x+3)}

\therefore 12x + 11 = A(x-2)+B(x+3)

\therefore 12x + 11 = Ax-2A+Bx+3B

\therefore 12x + 11 = Ax+Bx-2A+3B

\therefore 12x + 11 = (A+B) x-2A+3B

Equating like terms on both sides:

A + B = 12\implies A = 12-B... (1)

- 2A + 3B = 11... (2)

Solving equations (1) & (2), we find:

A = 5, B = 7

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{5}{(x +3)}+\frac{7}{(x - 2)}

3 0
3 years ago
I WILL GIVE BRAINLIEST The area of the surface of the trampoline (square) is equal to twice its perimeter. Find the dimensions.
Brums [2.3K]
Given that the area is equal to twice the perimeter and the dimensions are:
length=4x ft, width=(x+6) ft
the perimeter will be:
P=2(L+W)
P=2(4x+(x+6))
P=2(4x+x+6)
P=2(5x+6)
P=(10x+12)

Area of the rectangle is:
A=4x(x+6)
A=4x²+24x
but:
2P=A
thus
2(10x+12)=4x²+24x
20x+24=4x²+24x
thus
4x²+4x-24=0
x²+x-6=0
x²-2x+3x-6=0
x(x-2)+3(x-2)=0
(x-2)(x+3)=0
thus the answer is:
x=-3 or x=2
thus
length=4x=4*2=8 ft
width=(x+6)=(2+6)=8 ft

4 0
3 years ago
As part of quality control, a pharmaceutical company tests a sample of manufacturer pills to see the amount of active drug they
ryzh [129]

Answer:

The z statistic is 0.23.

Step-by-step explanation:

Test statistic (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 104 mg

population mean (mu) = 100 mg

sd = 55 mg

n = 10

z = (104 - 100) ÷ 55/√10 = 4 ÷ 17.393 = 0.23

8 0
3 years ago
Kay and Allen sell cell phones. Kay sold 17 more cell phones than Allen. Together they sold 117. How many did they sell individu
denis-greek [22]

Answer:

Kay sold 67 cell phones and Allen sold 50 cell phones.

Step-by-step explanation:

Let k = # cell phones Kay sold and a = # cell phones Allen sold.

k + a = 117

k = 17 + a

So:

(17 + a) + a = 117

2a = 100

a = 50

Plug this back into 2nd equation:

k = 17 + a

k = 17 + 50

k = 67

Kay sold 67 cell phones and Allen sold 50 cell phones.

5 0
3 years ago
Find the value of y so that the line passing through the two points have the given slope (2,3) (7,y) m=-2/5
Liono4ka [1.6K]

Answer:

y = 1

Step-by-step explanation:

Find the slope of the line passing through the points (2,3) and (7,y):

m=\dfrac{y-3}{7-2}=\dfrac{y-3}{5}

The slope of the line is equal to

m=-\dfrac{2}{5},

then

\dfrac{y-3}{5}=-\dfrac{2}{5}\\ \\y-3=-2\\ \\y=-2+3\\ \\y=1

8 0
3 years ago
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