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Shkiper50 [21]
3 years ago
6

= (4x3 + 7x2 – 2) (2x2 – 3x + 8) how to simplify this?

Mathematics
1 answer:
valentinak56 [21]3 years ago
3 0

Answer:

24 ( 12 -3x)

Step-by-step explanation:

(4x3 + 7x2 – 2) (2x2 – 3x + 8)

(12 + 14 - 2) (4 - 3x + 8)

(26-2) (12 - 3x)

24 (12 -3x)

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Find the sum of all positive integers less than 100, which:
wlad13 [49]

Answer:

The sum of all positive integers less than 100, which are not divisible by 3 is 3267.

Step-by-step explanation:

The all positive integers less than 100 has sum, given by

S₁ = 1 + 2 + 3 + 4 + ......... + 99

⇒ S₁ = \frac{99 \times (99 + 1)}{2} = 4950

Now, the sum of all positive integers less than 100 which are divisible by 3 is

S₂ = 3 + 6 + 9 + 12 + 15 + ........ + 99

⇒ S₂ = 3(1 + 2 + 3 + ........ + 33)

⇒ S₂ = 3 \times \frac{33 \times (33 + 1)}{2} = 1683

Therefore, the sum of all positive integers less than 100, which are not divisible by 3 is = S₁ - S₂ = 4950 - 1683 = 3267. (Answer)

Note : The sum of n natural numbers S is given by

S = 1 + 2 + 3 + 4 + ....... + n = \frac{n \times (n + 1)}{2} .

3 0
3 years ago
An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. W
IceJOKER [234]
The total cost is given by the equation:
C(t) = 45 + 25(h-1) where h is the number of hours worked.

We can check for each option in turn:

Option A:

Inequality 5 < x ≤ 6 means the hour is between 5 hours (not inclusive) to 6 hours (inclusive)
Let's take the number of hours = 5
C(5) = 45 + (5-1)×25 = 145
Let's take the number of hours = 6
Then substitute into C(6) = 45 + (6-1)×25 = 170
We can't take 145 because the value '5' was not inclusive.


Option B:
The inequality is 6 < x ≤ 7
We take number of hours = 6
C(6) = 25(6-1) + 45 = 170
We take number of hours = 7
Then C(7) = 25(7-1) + 45 = 195

Option C:
The inequality is 5 < x ≤ 6
Take the number of hours = 5
C(5) = 25(5-1) + 45 = 145
Take the number of hours = 6
C(6) = 25(6-1) + 45 = 170
We can't take the value 145 as '5' was not inclusive in the range, but we can take 170

Option D:
6 < x ≤ 7
25(6-1) + 45 < C(t) ≤ 25(7-1) + 45
170 < C(t) ≤ 195

Correct answer: C


7 0
3 years ago
Determine whether theses lines are parallel, perpendicular or neither
belka [17]

Answer:

Lines 2 and 3 are parallel with slope (-2/3) and different y intercepts, and both are perpendicular to line 1              (-1) / (3/2) = (-2/3)

Step-by-step explanation:

Parallel lines have the same slope

Perpendicular lines have negative reciprocal slopes

line 1: 6x - 4y = 2

line 1: 4y =  6x - 2

line 1:   y = (3/2)x - 0.5

line 2:  y = (-2/3)x - 6

line 3:3y = -2x + 4

line 3: y = (-2/3)x + 4/3

8 0
3 years ago
25 less than a number divided by 2<br><br> how would you write this?
malfutka [58]

Answer:

\frac{x-25}{2\\} or x-25/2

Step-by-step explanation:

3 0
3 years ago
find three points that belong to the graph and use them to sketch the graph of the equation: y = 2 + x
iris [78.8K]

Answer:

I only figured out two points which is (0,2) (1,3)

Step-by-step explanation:

8 0
3 years ago
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