Factorise the following expressions.
a² + 8a + 16​​

Answer:

Option D

Step-by-step explanation:

Use Factoring Methods

[tex]4x^3-8x^2-9x+18\\[/tex]

put bracket around each 2 terms as such [tex](4x^3-8x^2)+(-9x+18)[/tex]

And then factor each respective bracket. We'll start with the first one

[tex](4x^3-8x^2) = 4x^2(x-2)[/tex]

Then do the other, and try to get similar brackets as the first

[tex](-9x+18)=-9(x-2)[/tex]

Since they are both simiar, the equation is now: [tex](4x^2-9)(x-2)[/tex]

Now factor the first bracket again for final result

[tex]4x^2-9=(2x-3)(2x+3)[/tex]

Ans when you put it all together, you get: [tex](2x-3)(2x+3)(x-2)[/tex]

Correct answer is option D

The approximate population in 2016 is 91, 604 population

The exponential equation representing the statement is [tex]P=P_0e^t[/tex]

Substituting into the formula will give:

If by 2012 the population had increased to 81,000, then:

81000 =  56000e^12k

81000/56000 = e^12k

1.4464 = e^12k

ln1.4464 = 12k

0.3691 = 12k

k = 0.3690/12

k = 0.03076

Get the prediction of the population in 2016.

[tex]P = 56000e^{16(0.03076)}\\P=56000e^{0.49213}\\P = 56000(1.6357)\\P = 91,603.70[/tex]

Hence the approximate population in 2016 is 91, 604 population

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Answer:

30 are present 10 are absent

Step-by-step explanation:

75%=3/4

so 3/4 of them are absent

3/4(40)=30

and 40-30=10 are absent

Answer:

Y intercept is (0,3)

Step-by-step explanation:

Check out the image

Using the least common factor, it is found that it will take 120 days until all four buses return to the terminal on the same day.

To find their least common factor, we factor each number by prime numbers, hence:

6 - 8 - 10 - 15|2

3 - 4 - 5 - 15|2

3 - 2 - 5 - 15|2

3 - 1 - 5 - 15|3

1 - 1 - 5 - 5|5

1 - 1 - 1 - 1

Hence, lcm(6, 8, 10, 15) = 2³ x 3 x 5 = 8 x 15 = 120.

It will take 120 days until all four buses return to the terminal on the same day.

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Answer:

The answer is 9

Explanation:

0.5a+8.75=13.25

We simplify the equation to the form, which is simple to understand

0.5a+8.75=13.25

We move all terms containing a to the left and all other terms to the right.

+ 0.5a=+13.25-8.75

We simplify left and right side of the equation.

+ 0.5a=+4.5

We divide both sides of the equation by 0.5 to get a.

a=9

Answer:

x=8

Step-by-step explanation:

5x+10+130=180

5x+140=180

5x=40

x=8

Answer:

540 last week

52X540.=$28,080 a year

Step-by-step explanation:

Answer:

-1, 3, 7, 11

Step-by-step explanation:

First, let's find term 1. To find this term, we need to replace n with 1 - what is 4(1) - 5? Well, that's just 4 - 5, or -1. So, our first term is -1. Next, we'll find our second term. To do this, we'll replace n with 2. 4(2) = 8, and then 8 - 5 is equal to 3, so our second term is 3. Let's now find the third term by replacing n with the number 3. 4(3) - 5 is equal to 12 - 5, or 7. So, 7 is our third term. Finally, we'll find the fourth term. 4(4) is equal to 16, and 16 - 5 is equal to 11. So, the fourth and final term is equal to 11.

Hopefully that's helpful! :)

Step-by-step explanation:

Term 1: - 1

Term 2: 3

Term 3: 7

Term 4: 11

The rule is, where you see n, substitute with the position/term requested

First 4 terms are: - 1,3,7, 11

Answer:

x =-27

Step-by-step explanation:

X/3= -9

or,X=-9×3(cross multiplication)

or, X=-27

A good option available to you as a financial expert is to request a part payment from the customer while the remaining part is to be made on the next pay day.

For a good financial management, the best decision to make profit or avoid loss is paramount.

The most difficult challenge faced today by loan companies is the non complaisance of the customers to pay back when the period given expires.

The best option that may be available for the loan manager must be a request  for the customer to pay part of the loan and complete the payment in the next  pay day.

Thus, a good option available to you as a financial expert is to request a part payment from the customer while the remaining part is to be made on the next pay day.

Learn more about options for loan payment here: https://brainly.com/question/12233464

Answer:

D <----last option  Domain is set of real numbers or (-∞,+∞)

The rate at which the water was drained from the tank is 6 gallons of water per minute (option A)

To know the speed at which the tank was drained, we must carry out the following operations:

Taking into account the information provided by the table we establish how much water has been drained from the tank in 20 minutes.

450 gallons - 330 gallons = 120 gallons.

Subsequently, we must divide the amount of water (120 gallons) that was drained by the time it was drained (20 minutes).

120 gallons ÷ 20 minutes = 6 gallons / minute.

According to the above, we can establish that the bath drain rate is 6 gallons / minute (option A).

Note: This question is incomplete because there is some missing information. Here is the complete information:

What is the rate at which the water was drained from the tank?

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Answer:

See attached files.

The answers are there.

Step-by-step explanation:

along the side with 1 cm we can fit 3 cubes, as 3×1/3 = 1.

along the side with 2 2/3 cm we can fit 8 cubes :

2 2/3 = 6/3 + 2/3 = 8/3.

and 8/3 / 1/3 = 8/3 × 3/1 = 3×8 / 3×1 = 8

and the height is 2/3 cm, so we can put 2 layers of cubes on top of each other.

so, we have

3 × 8 × 2 = 48

48 cubes are needed to fill the prism.

I can’t help because I can’t see the coordinate plane.

Step-by-step explanation:

don't panic. just breathe and think logically.

why would these angles be different ? how could they be different ?

right : they cannot be different. otherwise the 2 horizontal lines would not be parallel.

so, yes, indeed, these 2 angles are identical.

3x + 2 = 2x + 6

x = 4

that's it.

True or false, depending on the specifics. True, because the gravity makes it go to the ground. False, because gravity is always working, so you don't need to throw the ball. However since it doesn't say that it only happens when you throw it. The answer should be true.

Answer:

1 [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

the denominators must be the same so, since 4 goes evenly into 24 we can create an equivalent fraction from 3/4 to 18/24 (multiply numerator and denominator by 6)

now you can add:

[tex]\frac{15}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{(15+18)}{24}[/tex] = [tex]\frac{33}{24}[/tex]

since the numerator is larger than the denominator this is called an improper fraction and can be changed into a mixed number by dividing 24 into 33

24 goes into 33 one time with a remainder of 9

so 33/24 = 1 [tex]\frac{9}{24}[/tex] wherein 9 and 24 can each have a 3 factored out to make it fully simplified

9÷3 = 3

24÷3 = 8

final answer is 1 [tex]\frac{3}{8}[/tex]

Answer:

11/8 is the correct answer

Step-by-step explanation:

15/24 + 3/4

Reduce the fraction   15/24 ​   to lowest terms by extracting and canceling out 3.

=5/8 +3/4

Least common multiple of 8 and 4 is 8. Convert 5/8 and 3/4 to fractions with denominator 8.

= 5/8 + 6/8

since 5/8 and 6/8 have the same denominator, add them by adding their numerators.

= 5 + 6/8

Add 5 and 6 to get 11.

=11/8

here is why 9/14 is wrong

Answer:

Your anwser would be A mark brainliest please and thank you

Step-by-step explanation:

Answer:

• As x approaches -∞, g(x) approaches -∞; and as x approaches ∞, g(x) approaches ∞.

Step-by-step explanation:

[tex]{ \tt{g(x) = \frac{ {x}^{2} + 5x}{3x} }} \\ [/tex]

If x approaches -∞;

[tex]{ \tt{g( {}^{ - } \infin}) = \frac{ {( {}^{ - } \infin)}^{2} + {}^{ - } \infin}{ {}^{ - } \infin} } \\ \\ { \boxed{ \tt{g( {}^{ - } \infin) = {}^{ - } \infin }}}[/tex]

If x approaches +∞;

[tex]{ \tt{g( {}^{ + } \infin) = \frac{ {( \infin)}^{2} + \infin}{ \infin} }} \\ \\ { \boxed{ \tt{ g( {}^{ + } \infin) = {}^{ + } \infin }}}[/tex]

Note: I'm taking my infinite value to be 1,000

Answer:

C. [tex] \frac{ {m}^{2} - m - 2}{ {m}^{2} - 1} [/tex]

Explanation:

[tex] \frac{ {m}^{2} - m - 2}{ {m}^{2} - 1} \\ = \frac{ {m}^{2} - 2m + m - 2 }{ {(m)}^{2} - {(1)}^{2} } \\ = \frac{ m(m - 2) + 1(m - 2)}{(m - 1)(m + 1)} \\ = \frac{(m + 1)(m - 2)}{(m - 1)(m +1) } \\ = \frac{(m - 2)}{(m - 1)} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer

To make 15 pies, it will take Alex 20 hours

Step-by-step explanation:

3 x 5 = 15 pies

4 x 5 = 20 hours

Answer:2(4t-9-10t+7) is answer and for the next it 2(-6t-2)

Answer:

5 x + 25 ≤ 20

Step-by-step explanation:

Simplify 5  +  5  (  x  +  4  ) .

5  + 5 x  +  20  ≤  20

Add  5  and 20 .

Answer:

40% of airline A's flights were on time

Step-by-step explanation:

0.4=40% .the top row indicates that it was airline A. the left column indicates that it was on time.

Answer:

B

Step-by-step explanation:

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