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Natalka [10]
2 years ago
10

Select the polynomial that is a perfect square trinomial.

Mathematics
1 answer:
Alina [70]2 years ago
6 0

Answer:

  16x^2 -8x +1

Step-by-step explanation:

The square of a binomial expands as ...

  (a +b)^2 = a^2 +2ab +b^2

So, you need to look for a trinomial with first and last terms that are perfect squares and a middle term that is double the product of the roots of those terms.

This pattern matches ...

  16x^2 -8x +1 = (4x -1)^2

You might be interested in
Given: ∠AOC, ∠BOC - complementary angles
34kurt

Answer:

  • 30
  • COB . . . . or . . . . BOC

Step-by-step explanation:

The reason given on the line of interest is "substitution," so the problem boils down to determining what was substituted for what. The previous statement says ...

  AOC + COB = 90

and the first part of the statement we're to complete has BOC + ___.

We see from the given statements that m∠AOC = m∠BOC + 30°, so it appears that is the substitution that has been made: AOC has been replaced by BOC + 30.

This means the first blank is filled with 30.

__

The second part of the previous statement is ...

  AOC + COB = 90

so we believe this (COB) should go in the second blank.

__

Then the line of interest would read ...

  BOC + 30 + COB = 90

_____

<em>Comment on the problem</em>

There is a curious mix of notations here. Usually, (as in the beginning of this problem) we refer to the measure of an angle using "m∠" in front of the angle designator, and we use a degree symbol to indicate the units of that measure. Part-way through the problem statement written here, those notations were dropped, and we're to assume they are intended. IMO, this is a poor way to demonstrate careful problem solving.

The substitution given for AOC is BOC+30, but the line into which that is substituted has AOC +COB = 90. This means the equation after substitution is ...

  BOC +30 +COB = 90

Since BOC and COB are the same angle, we can sort of fudge the "algebra" to get to  BOC=30, but if the problem were more carefully written, the angle would be referred to by consistent nomenclature:

  m∠AOC + m∠BOC = 90° . . . . . . . . . preferred angle designations

  (m∠BOC + 30°) + m∠BOC = 90° . . . . substitution for m∠AOC

  2(m∠BOC) = 60° . . . . . . algebra (subtract 30°, collect terms)

  m∠BOC = 30° . . . . . . . . algebra (divide by 2)

3 0
2 years ago
I think of a number and add 6. The result is equal to twice the first number
brilliants [131]

Answer:

A. X+6=6x

X+6=6(x)

Step-by-step explanation:

B. 3+6=3×6

9=18

5 0
3 years ago
Marsha earn $25 per hour up to 36 hours; after this,she is paid double time. In one particular week she earned $1550.00 .how man
mel-nik [20]

Answer: Marta worked 13 hours overtime.

Step-by-step explanation:

1): You do 25 x 36 to get the amount of money she can make before she starts to make double.

36 x 25 = 900

2): Minus $900 from $1550

$1550 - $900 = $650

3): Divide $650 by $50

$650 / $50 = 13 hours worked overtime

7 0
2 years ago
Serena paid $194.99 for a game system and then bought two equally-priced games. If she spent a total of $284.97, what is the pri
Nataly_w [17]
$284.99 - 4194.99 = $89.98
$89.98 ÷ 2 = $ 44.99

p = $44.99 for each game.
3 0
3 years ago
In a collection of nickels, dimes, and quarters worth $6.90, the ratio of the number of nickels to dimes is 3:8. The ratio of th
dimulka [17.4K]
N=number of nickels
d=number of dimes
q=number of quarters

example
if n:d=3:8
lets say n=3 and d=8
3*8=8*3
so
8n=3d
slightly confusing but go with it, it migh make sense or it might not


n:d=3:8
8n=3d

d:q=4:5
5d=4q

solve for one of them
solve for nickels in first and quarters in second

8n=3d, n=(3/8)d
5d=4q, (4/5)d=q

5n+10d+25q=690
divide by 5 to make it easeir
n+2d+4q=138
sub (3/8)d for n
sub (4/5)d for q
(3/8)d+2d+5(5/4)d=138
(3/8)d+2d+25/4d=138

3/8+2+25/4=
3/8+16/2+50/8=
69/8

(69/8)d=138
times both sides by 8
69d=1104
divide both sides by 69
d=16

16 dimes
sub back

(5/4)d=q
(5/4)16=q
80/4=q
20=q

(3/8)d=n
(3/8)16=n
48/8=n
6=n



6 nickles
16 dimes
20 quarters
yah
8 0
3 years ago
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