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Oksana_A [137]
3 years ago
15

Which property justifies this statement if x=3, then x-3=0

Mathematics
1 answer:
PolarNik [594]3 years ago
5 0

You would subtract 3 from 0 and then the 3's would cancel out and it would be X=3

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Work out the formula of the nth term in the following quadratic sequence:<br> 19, 15, 9, 1...
Butoxors [25]

In a quadratic sequence we'll get a linear first difference and a constant second difference.  Let's verify that.

n          1   2   3   4

f(n)       19  15  9   1

1st diff   -4  -6  -8

2nd diff     2   2

We see that we got a constant second difference.  We could just extend that and work back up to get more values.

n          1   2   3   4       5    6      7

f(n)       19  15  9   1      -9   -21   -35

1st diff   -4  -6  -8   -10  -12   -14

2nd diff     2   2    2     2    2

That's just an aside; we're after the general formula.  We have

f(1)=19, f(2)=15, f(3)=9

In general we can assume

f(n) = an²  + bn + c

We get three equations in three unknowns,

19 = a(1²)+b(1)+c = a+b+c

15 = a(2²) + b(2) + c = 4a + 2b + c

9 = a(3²) + b(3) + c =  9a + 3b + c

That's a 3x3 linear system; it's easy to solve directly.  Subtracting pairs,

4 = -3a - b

6 = -5a - b

Subtracting those,

-2 = 2a

a = -1

b = -3a -4 = -1

c = 19-a-b = 21

Answer: f(n) = -n² - n + 21

Check:

f(1) = -1 - 1 + 21 = 19, good

f(2) = -4 - 2 + 21 = 15, good

f(3) = -9 - 3 + 21 = 9, good

f(4) = -16 - 4 + 21 = 1, good

Let's check our extended table, how about

f(7)= -49 - 7 + 21 = -35, good

6 0
3 years ago
Candice bought 6 dozen eggs and broke 9 eggs how many eggs did she have left
Nadya [2.5K]

Answer:

63

Step-by-step explanation:

12x6=72

72-9=63

the answer is 63

3 0
2 years ago
Read 2 more answers
The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers.
guajiro [1.7K]

Answer: the player answered 30 questions correctly.

Step-by-step explanation:

Let x represent the number of questions that the player answered correctly.

Let y represent the number of questions that the player answered incorrectly.

The number of questions that the player answered is 40. It means that

x + y = 40- - - - - - - - - - -1

The score on the trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If the player obtained a score of 50, It means that

2x - y = 50

y = 2x - 50

Substituting y = 2x - 50 into equation 1, it becomes

x + 2x - 50 = 40

3x - 50 = 40

3x = 40 + 50 = 90

x = 90/3

x = 30

5 0
3 years ago
Can someone solve this
77julia77 [94]

Answer:

A ≈ 269.81 cm²

Step-by-step explanation:

This shape is a hexagon (it has 6 sides) so let's use the formula for the area of a hexagon.

A = \frac{3\sqrt{3} }{2} s^{2}

Where s is the length of the sides

Substitute:

A = \frac{3\sqrt{3} }{2} s^{2}

A = \frac{3\sqrt{3} }{2} 10^{2}

Solve:

A = \frac{3\sqrt{3} }{2} 10^{2}

A = \frac{3\sqrt{3} }{2} 100

Multiply the numerator:

A = \frac{3\sqrt{3} }{2} 100

A ≈ \frac{5.12 }{2} 100

(The numerator reflects a rounded number, but the actual calculations are exact)

Divide the fraction:

A ≈ \frac{5.12 }{2} 100

A ≈ 2.6(100)

Multiply:

A ≈ 2.6(100)

A ≈ 269.81 cm²

Therefore, the area is approximately 269.82 cubic centimeters.

6 0
3 years ago
Write an expression equivalent to the expression -1/2(-3/2x+6x+1)-3x
stiv31 [10]

Answer:

-21/4x-1/2

Step-by-step explanation:

-1/2(-3/2x+6x+1)-3x

3/4x-3x-1/2-3x

3/4x-3x-3x-1/2

3/4x-6x-1/2

3/4x-24/4x-1/2

-21/4x-1/2

4 0
3 years ago
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