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4 years ago

If ABCD is a parallelogram, what can we say about the diagonals BD and AC?

1 answer:

5 0

A parallelogram is a quadrilateral with two pair of parallel sides. The opposite sides of parallelogram are in equal length and opposite angles are of equal measure.

ABCD is a parallelogram with sides as AB, BC, CD and AD. BD and AC are the diagonals of the given parallelogram.

In parallelogram opposite sides are equal that is AB=CD, AD=BC

opposite angles are equal $\angle A = \angle C$ , $\angle B = \angle D$

Diagonals of parallelogram bisect each other.

Diagonals of parallelogram BD and AC are not congruent to the sides AB , CD and AD , BC.

Diagonals are not congruent.

Diagonals always bisect each other.

Option C is correct.

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Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard

Bumek [7]

Answer:

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

<em><u>The question is</u></em>

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

The volume of the open top box is

$V=LWH$

we have

$L=(10-2x)\ cm$

$W=(10-2x)\ cm$

$H=x)\ cm$

substitute

$V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Find the domain for x

we know that

$(10-2x) > 0\\10> 2x\\ 5 > x\\x < 5\ cm$

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

5 0

3 years ago

Spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 62.1

Marta_Voda [28]

Caution: you need to use the same units of measurement throughout. If the spring stretches by 21 cm when a 135 newton object is attached, then you must ask for the mass (in newtons) of a fish that would stretch the spring by 62.1 cm.

We will need to assume that the spring is not stretched at all if and when no object is attached to the spring.

Write the ratio

21.0 cm 135 newtons
------------- = --------------------
62.1 cm x

Solve this for x. This x value represents the mass of a fish that would stretch the spring by 62.1 cm. You can cancel "cm" in the equation above:

21.0 135 newtons
------ = --------------------
62.1 x

Then 21.0x = (62.1)(135 newtons). Divide both sides of this equation by 21.0 to solve it for x.

7 0

3 years ago

Read 2 more answers

Find f (0) and find x when f (x) =4

Anuta_ua [19.1K]

At x = 0, y-coordinate is at -4 so that means f(0) = -4

Now for f(x) = 4, we need to find any x-coordinates such that y-coordinates is 4.

There are two possible answer: x = -8 and x = 8

So x = -8, 8

Hope this helps.

4 0

3 years ago

15 POINTS ANSWER ASAP, SHOW WORK

forsale [732]

Answer:

$V=97.6\ in^3$