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BigorU [14]
3 years ago
15

PLEASEEEE HELPPP!!!!!!WILL GIVE BRAINLIEST!!!!!!!!!!!! In quadrilateral ABCD, we have AB=3, BC=6, CD=4, and DA=4. If the length

of diagonal AC is an integer, what are all the possible values for AC? Explain your answer in complete sentences.
Mathematics
1 answer:
notka56 [123]3 years ago
8 0

Answer:

AC = { 4, 5, 6, 7 }

Step-by-step explanation:

If you see, the diagonal AC forms two triangles, Δ ABC, and Δ ADC. In Δ ABC, AC = 3 units and BC = 6 units, while AC is yet to be known. Respectively in Δ ADC, AD = 4 units and CD = 4 units, while AC is again yet to be known.

In both triangles the triangle inequality can help find the possible value( s ) of AD, as this inequality only restricts some of the possible values with which AC can take. At the same time AC is shared among the two triangles, so if we can apply the Triangle Inequality to both of these triangles, the value of AC can be " further restricted. "

Triangle 1. BC - AB < AC < BC + AB,\\6 - 3 < AC < 6 + 3,\\3 < AC < 9\\\\Triangle2. AD - CD < AC < AD + CD,\\4 - 4 < AC < 4 + 4,\\0 < AC < 8

And there we have two inequalities, 3 < AC < 9, and 0 < AC < 8. Combining both inequalities the only possible integer values for AC would be 4, 5, 6, and 7.

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5.4 puzzle time what has four legs but can't walk answer key
pentagon [3]

Answer:

A table

Step-by-step explanation:

A table has four legs ( supports) but cannot possibly walk because it is not a living thing. For example, see the table in the attachment, it has four legs (supports) but cannot possibly walk.

7 0
3 years ago
Help me plzz help me plzz​
Alik [6]

Answer:

44.1 mm^2

Step-by-step explanation:

The formula for a trapezoid is 1/2(b1 + b2)h

A= 1/2(12.5 + 8.5) 4.2

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4 0
2 years ago
Jim had some dimes, quarters, and nickels. First, he counted only the dimes and quarters and found that he had 9 coins. Then, he
Olegator [25]

Answer:

$1.90

Step-by-step explanation:

Represent the numbers of nickels, dimes and quarters by n, d and q.

Then: d + q = 9, or q = 9 - d.

Also, n + d = 10

Lastly, n + d + q = 15.

Let's substitute 9 - d for q in the equation immediately above:

n + d + (9 - d) = 15, or n + 9 = 15.  Then n must be 6.

In summary, Jim has 6 nickels, (10 - 6) dimes and (9 - 4) quarters, or:

                                    6 nickels, 4 dimes and 5 quarters

Thus, he has 5($0.05) + 4($0.10) + 5($0.25), or

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7 0
3 years ago
Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness, extr
Sunny_sXe [5.5K]

Answer:

f(x) = 3 \cdot 0.2^x

Step-by-step explanation:

f(x) = 3 \cdot 0.2^x


Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is \mathbb{R}

Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore (0, \infty).

Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.

Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.

Symmetry: It is clear to see the graph of f(x) has no symmetry.

Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe f(x-1) > f(x) for all x in the domain.

The function is however bounded below by 0: no value of x in the domain exists which satisfies f(x) < 0.

Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)

Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: y=0.

End behaviour: As x \rightarrow \infty, f(x) \rightarrow 0. As x \rightarrow -\infty, f(x) \rightarrow +\infty

5 0
3 years ago
Cevabını yazarmısınız​
Anit [1.1K]

Answer:

it is side ways

Step-by-step explanation:

6 0
3 years ago
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