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postnew [5]
3 years ago
7

Complete the square to transform the expression x2 + 4x + 2 into the form a(x − h)2 + k.

Mathematics
1 answer:
Nina [5.8K]3 years ago
3 0

Answer:

Step-by-step explanation:

y = (x^2 + 4x)      + 2

Take 1/2 of the linear term 4/2 = 2 and square that result. 2^2 = 4.

Put it after 4x

y = (x^2 + 4x + 4)   +2  Subtract what you put inside the brackets on the outside.

y = (x^2 + 4x + 4) + 2 - 4      Combine the right.

y = (x^2 + 4x + 4) - 2            Express the brackets as a square.

y = (x + 2)^2 - 2

That's your answer

a = 1

h = 2

k = -2

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It took Shane 2 hours to drive 120 miles. If she continues at this rate, how far will she travel in 4 hours and 30 minutes?
vodomira [7]

Answer:

270 miles

Step-by-step explanation:

If she drove 120 miles in 2 hours, that means she drives at 60 miles per hour. 4 hours and 30 minutes can be seen as 4.5, since 30 minutes is half an hour. So then you multiply 60 by 4.5 and get 270.

6 0
2 years ago
Dave is comparing the circumferences of several trees in his yard. The oak tree is 0.539 meters in circumference, the ash tree h
stepan [7]

Answer:   c. elm

Step-by-step explanation:

Given : The circumference of the oak tree= 0.539 meters

=0.539\times100=53.9\text{ cm}   [∵ 1 m = 100 cm]             (1)

The circumference of the ash tree= 0.509 yards

=0.509\times3\text{ feet}   [∵ 1 yard = 3 feet]

=0.509\times3\times 30.48\text{ cm}  [∵ 1 foot = 30.48 cm]

=46.54296\approx46.54\text{ cm}        (2)

The circumference of the elm tree = 6281.70 millimeters

=\dfrac{6281.70}{10}=628.17\text{ cm}          (3)

The circumference of the poplar tree = 0.000385 miles

=0.000385 \times5280\text{ feet}   [∵ 1 mile = 5280 feet]

=0.000385 \times5280\times30.48\text{ feet}  [∵ 1 foot = 30.48 cm]

=61.959744\approx61.96\ \text{ cm}              (4)

From (1) , (2) , (3 ) and (4) it is clear that

46.54< 53.9 < 61.96 < 628.17

Hence, the elm tree has the greatest circumference.

5 0
3 years ago
What's the answer? Serious answers only please, :/.
mr Goodwill [35]

Answer:

2.5 cm

Step-by-step explanation:

Rectangle A    L x W = 40

                   

Rectangle B     L * W   = 1/2 (40)

                        8 * W = 20

                              W = 2.5 cm

5 0
2 years ago
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What is the value of 4 to the 3 power divided by 2 to the third power?
Sholpan [36]

Answer:

8

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7 0
2 years ago
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To better understand the financial burden students are faced with each term, the statistics department would like to know how mu
Semmy [17]

Answer:

Answer:

a).

The amount spent on school materials for each term of all ST201students

b).

a).

It is not a random sample. This looks like a convenience sampling and there is sampling bias. This sample is not representative of the entire population. Since it is not a random sample it is not appropriate to generalize the results to all students.

b).

The sample size is 80 which is greater than 30. It is large enough to assume normal distribution according to central limit theorem.

c).

mean: $617

z critical value at 95%: 1.96

standard error = σ/sqrt(n) =500/sqrt(80) = 55.9017

lower limit= mean-1.96*se = 617-1.96*55.9017=507.43

upper limit= mean+1.96*se = 617+1.96*55.9017=726.57

d).

The amount spent on school materials for each term for the 80 ST201students is $617. We are 95% confident that amount spent on school materials for each term of all ST201students falls in the interval ($507.43, $726.57).

Step-by-step explanation:

3 0
3 years ago
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