Which statement is not always true for a parallelogram?

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

3 0

<h3>Answer: B. Diagonals are congruent.</h3>

Explanation:

If the diagonals are congruent, then we'd have a rectangle. Any rectangle is a parallelogram, but not the other way around.

If we had a non-rectangular parallelogram, with none of the angles 90 degrees, then the diagonals will not be the same length.

Choices A, C and D are true for any parallelogram (rectangle or not).

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this is formula manipulation, I'd appreciate if the steps were provided. only respond if you know how to get the answer, thank y

marissa [1.9K]

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."

4 0

3 years ago

A sweater is on sale for 20% off. A jacket is on sale for 15% off. The sale price for each item is $34.00. Which item cost more

SashulF [63]

The sweater cost more originally. It costs $2.50 more from jacket.

Step-by-step explanation:

Given,

Discount rate of sweater = 20%

Sale price of sweater = (100-20)% = 80%

Discount rate of jacket = 15%

Sale price of jacket = (100-15)% = 85%

Sale price of each item = $34.00