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kolezko [41]
3 years ago
7

Simplify the expression (12x^2y^-2)^5 (4xy^-3)^-7

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0
(12x^2y^−2)^5(4xy^-3)^−7 = (248832x^10y^21)/(16384x^7y^10) = (248832x^3y^11)/(16384) = (243x^3y^11)/16
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ABCD is a rectangle. The measure of angle BCE is 4x-23 and the angle measure of angle DCE is 5+5x. Find the measure of angle BEC
Temka [501]
<h2>Explanation:</h2><h2></h2>

The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:

\angle BCE=\beta \\ \\ \angle DCE=\theta

Every internal angle of any rectangle measures 90 degrees, so:

\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12

So:

\beta=4x-23=4(12)-23=25^{\circ}

So the measure of angle BEC can be found as follows:

We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So

\angle EBC=\beta

The sum of internal angles of any triangle add up to 180 degrees, so:

\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}

7 0
3 years ago
How do I solve 3x+17 greater than or equal to (you can’t do the sign on a phone but it would be _&gt;) 5
Kobotan [32]
<h3><u>The value of x is greater than or equal to -4.</u></h3>

(3x + 17) ≥ 5

Subtract 17 from both sides.

3x ≥ -12

Divide both sides by 3.

x  ≥ -4


5 0
3 years ago
Which is the same as 0.25?
natta225 [31]
1/4 is 0.25 as a fraction
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Answer:

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Step-by-step explanation:

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Any help would be greatly appreciated thanks in advance
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Answer:

i believe its 2

Step-by-step explanation:

7 0
3 years ago
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