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kupik [55]
3 years ago
8

Factor -5a^2b + 10ab^2 - 20b + 25a^3b

Mathematics
2 answers:
Daniel [21]3 years ago
6 0
For this case we have the following expression:
 -5a ^ 2b + 10ab ^ 2 - 20b + 25a ^ 3b
 We observe that the term 5b is repeated throughout the expression,
 therefore it is a common factor.
 So, factoring we have:
 5b (-a ^ 2 + 2ab - 4 + 5a ^ 3)
 Then, rewriting we have:
 5b (a ^ 2 (5a-1) + 2ab-4)
 Answer:
 
The factored expression is given by:
 
5b (a ^ 2 (5a-1) + 2ab-4)
marysya [2.9K]3 years ago
4 0
Factor out the GCF, which is 5b, and you get: 5b(5a^3-a^2+2ab-4)
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Complete this proof.<br><br> Given: EC AC, DB AC, ∠A = ∠F<br> Prove: ΔMDF ∼ ΔNCA
Gelneren [198K]

Answer:

Proved

Step-by-step explanation:

Given: EC || AC, DB || AC, ∠A = ∠F

Prove: ΔMDF ∼ ΔNCA

Solution

See diagram attached to the solution to better understand the following workings.

Redrawing ΔMDF or rotating to be facing the same direction.

EC is parallel to AC

DB parallel to AC

Using similar triangle theorem:

If ΔMDF ∼ ΔNCA

Ratio of Corresponding sides would be equal

(adjacent of ΔMDF)/(adjacent of ΔNCA) = (Opposite of ΔMDF)/(opposite of ΔNCA) = (hypotenuse of ΔMDF)/(hypotenuse of ΔNCA)

DF/ CA = MD/NC = FM/AN

∠A = ∠F

∠M = ∠N

∠D = ∠C

Since the ratio of Corresponding sides and angle are equal, ΔMDF is similar to ΔNCA.

ΔMDF ∼ ΔNCA

6 0
3 years ago
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ANSWER FOR BRAINLIEST
tester [92]

The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:

16 chairs; 24 tables

Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552

Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608  

15 chairs; 18 tables

Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450

Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480  

12 chairs; 28 tables

Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564

Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636  

18 chairs; 20 tables

Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516

Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544

Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:

15 x 65 + 18 x 90 = X

975 + 1,620 = X

2,595 = X

Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

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2 years ago
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a right triangle has legs measuring 4.5 meters and 1.5 meters the lengths of the legs of a second triangle are proportional to t
MrRa [10]

One approach that might be a great help would be if you would look
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3 years ago
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X= 75-53.86<span>
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3 years ago
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Svetach [21]

9514 1404 393

Answer:

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