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nevsk [136]
3 years ago
13

30 POINTS!!! PLZ HELP The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congrue

nt:
Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD.

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct a diagonal from A to C with a straightedge. ________________. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the Alternate Interior Angles Theorem. Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.

Which sentence accurately completes the proof?

A. Angles BAC and DCA are congruent by the Same-Side Interior Angles Theorem.

B. Diagonal BD is congruent to itself by the Reflexive Property of Equality

C. Diagonal AC is congruent to itself by the Reflexive Property of Equality.

D. Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent).
Mathematics
1 answer:
sweet [91]3 years ago
7 0

Answer:

C.) It is congruent to itself by the Reflexive Property of Equality.

Step-by-step explanation:

Sorry I actually read it this time and I'm in Honors Geometry and this is 100% right.

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If g is a differentiable function such that g(x)<0 for all real numbers x and if f'(x) = (x2 - 4)g(x), which of the following
galina1969 [7]

We want to see what can we say about f(x) extremes for the given information. We will see that the correct option is:

V: f has a relative minimum at x=-2 and a relative maximum at x=2.

<h3>Maximums and minimums.</h3>

A given function f(x) will have a maximum/minimum at x₀ if:

f'(x₀) = 0

  • It will be a maximum if f''(x₀) < 0
  • It will be a minimum if f''(x₀) > 0.

Here we do know that:

  • f'(x) = (x^2 - 4)*g(x)
  • g(x) < 0 for all numbers x.

Then the only zeros of f'(x) are when (x^2 - 4) = 0.

And this happens for x = 2 and x  = -2

Now let's see if these are minimums or maximums, we have:

f''(x) = 2*x*g(x) + (x^2 - 4)*g'(x)

If we evaluate this in x = 2, we get:

f''(2) = 2*2*g(2) + (2^2 - 4)*g'(2)

       = 4*g(2) + 0*g'(2) = 4*g(2)

And g(x) is always negative, then 4*g(2) < 0, then:

f''(2) < 0

Meaning that in x = 2 we have a relative maximum.

For x = -2 we have:

f''(-2) = 2*-2*g(-2) + ((-2)^2 - 4)*g'(-2)

       = -4*g(2) > 0

Then f''(-2) > 0, meaning that in x = -2 we have a relative minimum.

Then the correct option is:

V:  f has a relative minimum at x=-2 and a relative maximum at x=2.

If you want to learn more about maximums and minimums, you can read:

brainly.com/question/1938915

6 0
3 years ago
What is the approximate volume of a cylinder with a height of 2 ft and a radius of 6 ft?
patriot [66]
We know, Volume of a Cylinder = πr²h
Here, r= 6 & h = 2

Substitute their values into the expression:
V = 3.14 * (6)² * 2
V = 3.14 * 36 * 2
V = 3.14 * 72
V = 226.08

In short, Your Answer would be 226.08 Ft³

Hope this helps!
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3 years ago
How do u know haw many palces are in 50million without writing it in standerd form
TEA [102]
Write it out

50,000,000
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3 years ago
What’s the gcf (greatest common factor) of this expression
love history [14]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
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The difference between a number and 8 is 11
quester [9]

Answer:

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Step-by-step explanation:

Given:

The difference between a number and 8 is 11

Find the number.

Solution:

Let the unknown number be =x

The difference between the unknown number can be written as:

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We are given that the difference =11

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Using additive property to solve for x

Adding 8 to both sides to isolate x on one side.

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∴ x=19

∴ The unknown number = 19

6 0
4 years ago
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