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sveticcg [70]
3 years ago
7

"Find the length of AC for which ABCD is a parallelogram.

Mathematics
2 answers:
tresset_1 [31]3 years ago
7 0
AC is the diagonal of parallelogram ABCD.

AE = 4x
EC = x + 3

AE = EC
4x = x + 3
4x - x = 3
3x = 3
3x/3 = 3/3
x = 1

AE + EC = AC
4x + x + 3 = AC
4(1) + 1 + 3 = AC
4 + 1 + 3 = AC
8 = AC

Choice D. 8.


schepotkina [342]3 years ago
7 0

Answer:

D. 8 is the length of AC.

Step-by-step explanation:

We are given,

The parallelogram ABCD with BE = ED.

So, by bisection property, we have that AE = EC.

Then, AE = EC implies,

4x=x+3\\\\4x-x=3\\\\3x=3\\\\x=1

That is, the value of x = 1.

So, length of AE = 4x=4\times 1=4

And, length of EC = x+3=1+3=4

<em>Thus, the length of AC = length of AE + length of EC</em>

<h3>That is, the length of AC = 4 + 4 = 8.</h3>

Hence, option D is correct.

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<img src="https://tex.z-dn.net/?f=%20%7C3%20-%20x%7C%20%20-%20%28x%20-%201%29%20%3D%204" id="TexFormula1" title=" |3 - x| - (x
aleksley [76]

Answer:

x=0

Step-by-step explanation:

Evaluate all the arithmetic first, and then remember absolute value equations have two possible ways to go (+ and -).

You can see how I split them on the 3rd line, later demonstrating how the 2nd one is invalid.

|3-x|-x+1=4\\\\|3-x|-x=3\\\\3-x-x=3\\-(3-x)-x=3\\\\3-2x=3\\-3+x-x=3\\\\-2x=0\\-3\neq 3\\\\x=0\\-3\neq 3\\

Therefore, the solution is x=0

4 0
3 years ago
Please someone help me solve this question
miv72 [106K]

Answer:

  D.  right 4, down 8

Step-by-step explanation:

The usual transformations applied to functions are ...

  f(x) ⇒ f(x -h) . . . . translation right h units

  f(x) ⇒ f(x) +k . . . . translation up k units

  f(x) ⇒ k·f(x) . . . . . vertical scaling by a factor of k; reflection over x-axis when k < 0

  f(x) ⇒ f(x/k) . . . . . horizontal scaling by a factor of k; reflection over y-axis when k < 0

In the above, "scaling" will be expansion when |k| > 1, compression when |k| < 1.

__

Your transformation is ...

  x^2 ⇒ (x -4)^2 -8

  f(x) ⇒ f(x -4) -8

This is translation with h=4 and k=-8. That is, it is translation right 4 units and down 8 units.

_____

<em>Additional comment</em>

Like much of math, it is all about matching patterns.

4 0
2 years ago
Jane paid $35 for her meal. If the cost of the meal was $30 , what was the tax rate.
marta [7]
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6 0
3 years ago
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Mariana [72]
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BBQ BURGER W/ CHEESE   :    9.99
CHICKEN FINGER BASKET  :    8.99
MUSHROOM BURGER         :   10.99
CHILI CHEESE FRIES          : <u>    8.99</u>
TOTAL:                                      38.96
SALES TAX 8.75%                <u>      3.41 </u> (38.96 * 8.75% = 3.409)
TOTAL:                                     42.37
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Total amount paid by Kacey and friends  : $48.73
Total tip paid by Kacey and friends          :   $6.36
Total sales tax paid by Kacey and friends:   $3.41
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The answer would be 64
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