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Darya [45]
3 years ago
7

Lim (x+1) (3x^2-9) X2

Mathematics
1 answer:
mafiozo [28]3 years ago
5 0

Answer:

\lim_{x \to 2} (x+1)(3x^2-9) = 9

Step-by-step explanation:

Step 1: Write out limit

\lim_{x \to 2} (x+1)(3x^2-9)

Step 2: Evaluate

(2 + 1)(3(2)² - 9)

3(3(4) - 9)

3(12 - 9)

3(3)

9

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Learning Task 3
ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. Distance = 3682km

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. L < 38m

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

Perimeter = 160

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

Perimeter = x + x + 1 + x + 2 + x + 3

This gives:

160 = x + x + 1 + x + 2 + x + 3

Collect Like Terms

160 -1-2-3= x+x+x+x

154= 4x

Divide both sides by 4

38.5 = x

x =38.5

<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>

<em></em>

Solving (b):

Given

Presently: Inzo = 10 + Miz

Five years ago: Miz - 5= \frac{1}{3} * (Inzo-5) --- (Missing from the question)

Required: Determine their present ages

Substitute 10 + Miz for Inzo in the second equation

Miz - 5 = \frac{1}{3} * (10 + Miz - 5)

Miz - 5 = \frac{1}{3} * (Miz + 5)

Multiply both sides by 3

3Miz - 15 = Miz + 5

Collect Like Terms

3Miz -Miz = 15  + 5

2Miz= 20

Divide both sides by 2

Miz = 10

Substitute 10 for Miz in Inzo = 10 + Miz

Inzo = 10 + 5

Inzo = 15

<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>

Solving (3):

Given

Express Train:

Speed = 100kph

Time = t

Local Train:

Speed = 45kph

Time = t + 45

Required: Determine the distance between A and B

Distance is calculated as:

Distance = Speed * Time

For the express train:

Distance = 100 * t

For the local train

Distance = 45 * (45 + t)

Distance between both stations are equal; So,

100 * t = 45 * (45 + t)

100 t = 2025 + 45t

Collect Like Terms

100 t -45t= 2025

55t= 2025

Divide by 55

t = 36.82

Substitute 36.82 for t in Distance = 100 * t

Distance = 100 * 36.82

Distance = 3682km

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: n + n + 2 > 24

Sum less than 60: n + n + 2 < 60

So, we have:

n + n + 2 > 24

2n + 2 > 24

Collect Like Terms

2n > 24-2

2n > 22

n > 11

n + n + 2 < 60

2n + 2< 60

Collect Like Terms

2n < 60-2

2n < 58

Divide by 2

n

So, we have:

n > 11 and n < 29

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

Solving (5):

Given

Perimeter < 152m

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

Perimeter =4 * L

Perimeter =4  L

So, we have:

4L < 152m

Divide through by 4

L < 38m

Hence, length is less than 38m (e.g. 37m)

5 0
2 years ago
HELLO PLEASE HELP!! HAVE A GOOD DAY/NIGHT!!
aliina [53]

So, XZ= 7x+1 and PZ= 4x-1. To figure out XP we have to subtract those two.

(7x+1)-(4x-1)

3x-2

3(8)-2

24-2

22

XP=22

6 0
3 years ago
Read 2 more answers
Allen drove 90 miles in 2 and 1/4 hours at a constand speed, how many miles did he drive in one hour.
Bumek [7]
Use property of proportion:

miles           time (hs)
   90              2.25
    x                   1

x = 90 ÷ 2.25
x = 40 miles


8 0
2 years ago
Can somebody please help me out ?
Sever21 [200]

Answer:

30

Step-by-step explanation:

238,900/7,917=30.1755

7 0
2 years ago
Read 2 more answers
Which angles are adjacent to each other? Question is located in the attached file (image)​
daser333 [38]

Answer:

∠ 1 and ∠2

Step-by-step explanation:

Adjacent angles share a common ray or side between them, and have the same vertex.  

Therefore, the adjacent angles from the given image are: ∠ 1 and ∠2.

The other given options are not adjacent angles because they do not have the same common vertex and ray.  

8 0
2 years ago
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