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3 years ago

4/5 divided by 16/15 to lowest terms

Mathematics

2 answers:

liraira [26]3 years ago

7 0

Answer:

3/4

Step-by-step explanation:

4/5 ÷ 16/15

To divide by a fraction, multiply by the reciprocal.

4/5 × 15/16

Switch the numerators.

15/5 × 4/16

Reduce each fraction.

3/1 × 1/4

Multiply.

3/4

Ludmilka [50]3 years ago

6 0

Answer:

3/4

Step-by-step explanation:

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3 years ago

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bija089 [108]

Answer:

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Step-by-step explanation:

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3 0

3 years ago

Consider this equation:

aleksandrvk [35]

Answer:

Plan: separate the variable term from the constant term; divide by the coefficient of the variable.
Steps: add 4 to both sides; collect terms; divide both sides by 3.

Step-by-step explanation:

The first step is to look a the equation to see where the variable is in relation to the equal sign, and whether there are any constants on that same side of the equal sign.

Here, the variable terms are on the left, and there is a constant there, as well. The plan for solving the equation is to eliminate the constant that is on the same side of the equation as the variable, then divide by the coefficient of the variable. To find that coefficient, we need to collect terms. In summary, the plan is to ...

add 4 to both sides of the equation
collect terms
divide by the coefficient of the variable (3)

Executing that plan, the steps are ...

-2x -4 +5x +4 = 8 +4 . . . . add 4

3x = 12 . . . . . . . . . . . . . . . collect terms

x = 4 . . . . . . . . . divide by 3

4 0

3 years ago

(6x-5y+4)dy+(y-2x-1)dx=0

Len [333]

(6x - 5y + 4) dy + (y - 2x - 1) dx = 0

(6x - 5y + 4) dy = (2x - y + 1) dx

dy/dx = (2x - y + 1) / (6x - 5y + 4)

Let X = x - a and Y = y - b. We want to find constants a and b such that

dY/dX = (a rational function)

where the numerator and denominator on the right side are free of constant terms. Substituting x and y in the equation, we have

dY/dX = (2 (X + a) - (Y + b) + 1) / (6 (X + a) - 5 (Y + b) + 4)

dY/dX = (2X - Y + 2a - b + 1) / (6X - 5Y + 6a - 5b + 4)

Then we solve for a and b in the system,

2a - b + 1 = 0

6a - 5b + 4 = 0

==> a = -1/4 and b = 1/2

With these constants, the equation reduces to

dY/dX = (2X - Y) / (6X - 5Y)

Now substitute Y = VX and dY/dX = X dV/dX + V :

X dV/dX + V = (2X - VX) / (6X - 5VX)

The equation becomes separable after some simplification:

X dV/dX + V = (2 - V) / (6 - 5V)

X dV/dX = (2 - V) / (6 - 5V) - V

X dV/dX = (2 - V - (6 - 5V)) / (6 - 5V)

X dV/dX = (4V - 4) / (6 - 5V)

- (5V - 6) / (4V - 4) dV = 1/X dX

Integrate both sides:

-5/4 V + 1/4 ln|4V - 4| = ln|X| + C

Extract a constant from the logarithm on the left:

-5/4 V + 1/4 (ln(4) + ln|V - 1|) = ln|X| + C

-5/4 V + 1/4 ln|V - 1| = ln|X| + C

-5V + ln|V - 1| = 4 ln|X| + C

Get this back in terms of Y :

-5Y/X + ln|Y/X - 1| = 4 ln|X| + C

Now get the solution in terms of y and x :

-5 (y - 1/2)/(x + 1/4) + ln|(y - 1/2)/(x + 1/4) - 1| = 4 ln|x + 1/4| + C

With some manipulation of constants and logarithms, and a bit of algebra, we can rewrite this solution as

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|x + 1/4| + 4 ln(4) + C

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| - ln|4x + 1| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| = 5 ln|4x + 1| + C

8 0

3 years ago

Heather was asked to graph 3x - y = -4 by using slope and y-intercept. Her graph is shown.

irakobra [83]

Hello! The y-intercept is (0, 4), because the line crosses 0 in the x-axis at that point. We can cross out C and D, because those don't show that. The slope is rise/run. You would go up 3, and go to the right once. If you need to, solve for slope by doing y2 - y1/ x2 - x1. Let's use the point (0, 4) and (1, 7) as an example. We would set it up like this: 7 - 4 / 1 - 0. Solving that would give us 3/1 or just simply three. The slope is positive 3 and the y-intercept is (0, 4). The answer is A.

7 0

3 years ago