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2 years ago

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In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram? AB ≅

CD AC ≅ BD AB ⊥ BD CD ⊥ BD

1 answer:

torisob [31]2 years ago

6 0

Answer:

Step-by-step explanation:

For any quadrilateral to be a parallelogram

i) either both the pairs of opposite sides must be equal

ii) Both the pairs of opposite sides must be parallel

iii) Opposite pairs of angles must be equal

iv) Diagonals must bisect each other.

v) A pair of opposite sides must be parallel and equal

Here we are already given that AB || CD

So either we should be given that AD || BC

or we must be given that AB = CD

Here it is given AB = CD as an option.

So Option A) or the first option is the right answer that AB ≅CD is needed to prove ABCD is a parallelogram.

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Express the product in simplest form.

Dmitry [639]

The product in simplest form is (x - 4)

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

$\frac{8}{2x+8} \times \frac{x^2-16}{4}$

We have to find the product in simplest form

In the given expression,

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2 years ago

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alukav5142 [94]

In this problem, we need to plug in the given x values for $f(x)=0$ and find a and b.

When we plug in 1, we get: $2 \times {1}^{4} - 5 \times {1}^{3} - 14 \times {1}^{2} + a \times 1 + b = 0$

Simplify:
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We got our first statement about the values of the variables. If we find one more we can find those 2 variables.

We have another given root: 4.

Plug it in:
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Now we have our second one. We can combine them:
$a + b = 17 \\ 4a + b = 32$

I use elimination method which is easier here.

Multiply the top equation by -1: $- a - b = - 17 \\ 4a + b = 32$

Add them up:
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Simplify:
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So, the answers are $a=5$ and $b=12$ .

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I believe it’s your first choice .

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The solution and explanation is attached.

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