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Mila [183]
3 years ago
12

Expand and simplify

x-2)^{2} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Rus_ich [418]3 years ago
7 0
You can just 1) multiply the binomial by itself, or you can use 2) the square of a binomial pattern. I'll show it to you both ways.

1) Multiply the binomial by itself.

(3x - 2)^2 = (3x - 2)(3x - 2) =

Multiply every term of the first binomial by every term of the second binomial, then collect like terms. (This is often called using FOIL.)

= 9x^2 - 6x - 6x + 4

= 9x^2 - 12x + 4

2) Use the square of a binomial pattern

The square of a binomial is

(a - b)^2 = a^2 - 2ab - b^2

a^2 is the square of the first term.
b^2 is the square of the second term.
-2ab is the product of the two terms and 2.

You have

(3x - 2)^2,
where the first term is 3x, and the second term is -2

square the first term: 9x^2
square the last term: 4
the product of the terms and 2 is: -12x

Put it all together, and you get

9x^2 - 12x + 4

just like we got above with the other method.
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A piston rises to 5 cm and falls to 3 cm in such a way that it returns to the maximal height three times every two seconds. If w
sveticcg [70]

Answer:

(1 cm)cos3πt

Step-by-step explanation:

Since the piston starts at its maximal height and returns to its maximal height three times evert 2 seconds, it is modelled by a cosine functions, since a cosine function starts at its maximum point. So, its height h = Acos2πft

where A = amplitude of the oscillation and f = frequency of oscillation and t = time of propagation of oscillation.

Now, since the piston rises in such a way that it returns to the maximal height three times every two seconds, its frequency, f = number of oscillations/time taken for oscillation where number of oscillations = 3 and time taken for oscillations  = 2 s

So, f = 3/2 s =1.5 /s = 1.5 Hz

Also, since the the piston moves between 3 cm and 5 cm, the distance between its maximum displacement(crest) of 5 cm and minimum displacement(trough) of 3 cm is H = 5 cm - 3 cm = 2 cm. So its amplitude, A = H/2 = 2 cm/2 = 1 cm

h = Acos2πft

= (1 cm)cos2π(1.5Hz)t

= (1 cm)cos3πt

7 0
3 years ago
I will give you BRAINLIEST for the correct answer
Nadya [2.5K]

Answer:

a or b

Step-by-step explanation:

if I did the math right it's a but I tried another way and got b, so I'm sorry if that was no help at all

6 0
2 years ago
Read 2 more answers
There are 21 bags of pears on a market stall.
geniusboy [140]

Answer:

13 pears in the 21st bag

Step-by-step explanation:

mean = total number of pears/total number of bags

8 = x/21

x = 168

number of pears in 20 bags = (6 x 2) + (7 x 6) + (8 x 9) + (9 x 1) + (10 x 2)

= 155

number of pears in the 21st bag = 168 - 155

= 13

4 0
3 years ago
Plot the point first and then use the slope from that point<br> (-4,3) M=-1/2
Goshia [24]
Plot the point first and then use the slope from that point<span> - 3270801. ... </span>Plot the point first and then use the slope from that point (-4,3<span>) </span>M=-1/2<span>. 0</span>
7 0
3 years ago
Solve B+B=2 B+C=5 B+C*2=
Illusion [34]

B+B=2

assuming that B is 1 I will say that 4 is C.

4+1*2= 10 is your answer.

7 0
2 years ago
Read 2 more answers
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