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3 years ago

Is 16x2 - 16x + 4 a perfect square?

Mathematics

1 answer:

Andrew [12]3 years ago

5 0

Answer:

Yes

Step-by-step explanation:

Use the completing the square method:

16(x^2-x)+4

=16((x-1/2)^2 - (1/2)^2)+4

=16((x-1/2)^2 - 1/4)+4

=16((x-1/2)^2) - 16/4 + 4

=16(x-1/2)^2

=4^2(x-1/2)^2

The product of two square is itself a square.

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The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the

Otrada [13]

(12, 485)

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6 0

2 years ago

Simplify

denis23 [38]

Hello!

Answer:

1. =-6

2. =39

3. =-603

_________________________________________________

Explanation: This question's it's about the order of operations. It stands for p-parenthesis, e-exponents, m-multiply, d-divide, a-add, and s-subtract. It can also go left to right. (PEMDAS)

1. -4(3-1)+2

Do parenthesis first.

$(3-1)=2$

$-4*2+2$

Then do multiply left to right.

$-4*2=-8$

Add left to right.

$-8+2$

$8-2=6$

*Answer should be have negative sign.*

Answer: → $\boxed{=-6}$

______________________________________________________

2. 3⋅[(30−8)÷2+2]

Do parenthesis first.

$(30-8)=22$

$22/2+2$

Then divide left to right.

$22/2=11$

Add left to right.

$11+2=13$

Multiply left to right.

$3*13=39$

*Answer should be have positive sign.*

Answer: → $\boxed{=39}$

_____________________________________________________

3. 14(1-23)2+13

Do parenthesis first.

$(1-23)=-22$

$14(-22)*2+13$

Then, you multiply left to right.

$14(-22)=-308$

$-308*2=-616$

Add/subtract left to right.

$-616+13$

$616-13=603$

*The answer must be have a negative sign*

Answer: → $\boxed{=-603}$

____________________________________________________________

Hope this helps!

Thank you!

Have a great day!

-Charlie

7 0

3 years ago

Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 270 em

allsm [11]

Answer:

The number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf for the complete question.

The explanation of the answers is now provided as follows:

Let U, A and W represents number of empty seats of United Continental, American, and Southwest respectively. Therefore, we have:

U + A + W = 270 ………………………. (1)

Since United Continental had three times as many empty seats as American, this implies that:

U = 3A ………………………………… (2)

Substituting U = 3A into equation (1), we have:

3A +A + W = 270

4A + W = 270

W = 270 - 4A ………………………….. (3)

For the cost, we have:

3,000[((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100)] = $114,990

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = $114,990 / 3,000

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = 38.33

0.447A + 0.146A + 0124W = 38.33

0.593A + 0.124W = 38.33 ………………… (4)

Substituting W = 270 - 4A from equation (3) into (4) and solve for A, we have:

0.593A + 0.124(270 - 4A) = 38.33

0.593A + 33.48 - 0.496A = 38.33

0.593A - 0.496A = 38.33 - 33.48

0.097A = 4.84

A = 4.84 / 0.097

A = 49.8969072164948

Rounding to a whole number, we have:

A = 50

Substituting A = 50 into each of equations (2) and (3), we have:

U = 3 * 50 = 150

W = 270 - (4 * 50) = 70

Therefore, the number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Download pdf

6 0

3 years ago

Write a two column proof

NISA [10]

We are given intersecting lines. The measures of a pair of angles forming vertex angles, are 2x+6° and 96°.

The measure of 2 vertex angles is equal, so we solve the equation:

2x+6°=96°, subtract 6° from both sides of the equation
2x=90°, divide both sides of the equation by 2
x=45°

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3 years ago

What is the p(3,1,2) on rolls of a die

Anna35 [415]

Number 3 is 1/6 to role a 1 on the second roll is 1/36= 1/6 X 1/6
to get 2 on the third role is 1/216 so the probability is 1/216

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3 years ago