PLEASEE HELP ASAP I REALLY NEED HELP

Mathematics

1 answer:

AURORKA [14]3 years ago

7 0

Answer:

1) y = 115°

2) x = 120°

3) x = 163°

Step-by-step explanation:

the sum of the interior angles of a figure = (number of sides - 2) * 180

the sum of the interior angles of this figure = (5 - 2) * 180 = 540°

the fifth angle = the sum of the interior angles - the sum of the four angles

the fifth angle or y = 540 - (90 + 135 + 112 + 88) = 115

the sum of the interior angles = (6 - 2) * 180 = 720°

x = 720 - (90 + 90 + 140 + 150 + 130) = 120

the sum of the interior angles = (5 - 2) * 180 = 540°

x = 540 - (68 + 121 + 103 + 85) = 163

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Answer:

r = 3V/(2πh²)
h = 3V/b²
r = 25/π cm ≈ 7.9577 cm
w = 15 cm

Step-by-step explanation:

1. Multiply both sides of the equation by the reciprocal of the coefficient of r.

$V\cdot\dfrac{3}{2\pi h^2}=r\\\\r=\dfrac{3V}{2\pi h^2}$

2. Multiply both sides of the equation by the reciprocal of the coefficient of h.

$V\cdot\dfrac{3}{b^2}=h\\\\h=\dfrac{3V}{b^2}$

3. Solve the circumference formula for r, then substitute the given information.

$C=2\pi r\\\\r=\dfrac{C}{2\pi}\qquad\text{divide by the coefficient of r}\\\\r=\dfrac{50\,\text{cm}}{2\pi}=\dfrac{25}{\pi}\,\text{cm}\approx 7.9577\,\text{cm}$

4. Solve the perimeter formula for width, the substitute the given information and do the arithmetic.

$P=2(L+W)\\\\\dfrac{P}{2}=L+W\qquad\text{divide by 2}\\\\\dfrac{P}{2}-L=W\qquad\text{subtract L}\\\\\dfrac{40\,\text{cm}}{2}-5\,\text{cm}=W=15\,\text{cm}$

_____

In general, solving for a particular variable involves "undoing" what has been done to the variable, usually in the reverse order. In part 4, the variable W has L added and the sum is multiplied by 2. We "undo" those operations, last operation first, by dividing by 2 and subtracting L.

The properties of equality say you can do what you like to an equation as long as you do the same thing to both sides of the equation. So, when we say "divide by 2", we mean "divide both sides of the equation by 2." Likewise, "subtract L" means "subtract L from both sides of the equation."

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