Factorise the following.​

Answer:

24 i think

Step-by-step explanation:

I evaluated using he given value

Answer:

150x=y

Step-by-step explanation:

2x150=300

4x150=600

6x150=900

8x150=1200

Answer:

Step-by-step explanation:

From the given information:

[tex]a_n = a_{n-1} + a_{n-2}; \ \ \ n \ge 2 \\ \\ a_o = 1 \\ \\ a_1 =1 \ \ \ \ \ since \ \ a_o = a_1 = 1[/tex]

A)

[tex]a_n - a_{n-1} - a_{n-2} = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2}(a_n -a_{n-1}-a_{n-2} ) x^n = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2} a_nx^n - \sum \limits ^{\infty}_{n=2} a_{n-1}x^n - \sum \limits ^{\infty}_{n=2}a_{n-2} x^n = 0 \\ \\ \implies (a(x) -a_o-a_1x) - (x(a(x) -a_o)) -x^2a(x) = 0 \\ \\ \implies a(x) (1 -x-x^2) -a_o-a_1x+a_ox = 0 \\ \\ \implies a(x)(1-x-x^2)-1-x+x=0 \\ \\ \implies a(x) (1-x-x^2) = 1[/tex]

[tex]\mathbf{Generating \ Function: a(x) = \dfrac{1}{1-x-x^2}=f(x)}[/tex]

B)

[tex]If \ \ 1 -x-x^2 = (1 - \alpha x) ( 1- \beta x) \\ \\ \implies 1 -x - ^2 = 1 + \alpha \beta x^2 - ( \alpha + \beta )x \\ \\ \text{It implies that:} \\ \\ \alpha \beta = -1 \\ \\ \alpha + \beta = 1 \\ \\ \implies \alpha = ( 1-\beta) \\ \\ ( 1- \beta) \beta = -1 \\ \\ \implies \beta - \beta^2 = -1 \implies \beta - \beta^2 -1 = 0\\ \\ \beta = \dfrac{-(-1) \pm \sqrt{(-1)^2 -4(1)(-1)}}{2(1)}[/tex]

[tex]\beta = \dfrac{1\pm \sqrt{5}}{2} \\ \\ \beta = \dfrac{1 + \sqrt{5}}{2} \ \ and \ \ \alpha = \dfrac{1 - \sqrt{5}}{2}[/tex]

C)

[tex]\dfrac{1}{1-x-x^2}= \dfrac{A}{1-\alpha x}+ \dfrac{\beta}{1-\beta x} \\ \\ = \dfrac{A(1-\beta x) + B(1-\alpha x)}{(1-\alpha x) (1 - \beta x)} \\ \\ = \dfrac{(A+B)-(A\beta+B\alpha)x}{(1-\alpha x) (1-\beta x)}[/tex]

[tex]\text{It means:} \\ \\ A+B=1 \\ \\ B = (1-A) \\ \\ A\beta+ B \alpha =0 \\ \\ A\beta ( 1 -A) \alpha = 0 \\ \\ A( \beta - \alpha ) = -\alpha \\ \\ A = \dfrac{\alpha}{\alpha - \beta } \\ \\ \\ \\ B = 1 - \dfrac{\alpha }{\alpha - \beta} \implies \dfrac{\alpha - \beta - \alpha }{\alpha - \beta } \\ \\ =\dfrac{-\beta }{\alpha - \beta} \\ \\ \mathbf{B = \dfrac{\beta }{\beta - \alpha }}[/tex]

D)

[tex]\text{The formula for} a_n: \\ \\ a(x) = \dfrac{\alpha }{\alpha - \beta }\sum \limits ^{\infty}_{n=0} \alpha ^n x^n - \dfrac{\beta}{\beta - \alpha }\sum \limits ^{\infty}_{n=0} \beta x^n \\ \\ \implies \sum \limits ^{\infty}_{n =0} \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta}x^n \\ \\ a_n = \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta } \\ \\ \\ a_n = \dfrac{1}{\sqrt{5}} \Big (\Big( \dfrac{\sqrt{5}+1}{2}\Big)^{n+1}- \Big ( \dfrac{1-\sqrt{5}}{2}\Big) ^{n+1}\Big)[/tex]

Answer:

ix) (2a + 3)² = 4a² +12a + 9

x) a) x² + 7x + 12 = (-3)² + 7(-3) + 12 = 9 -21 + 12 = 0

b) x² - 5x + 6 = (-3)² - 5(-3) + 6 = 9 + 15 + 6  = 30

c) x² + 5x = (-3)² + 5(-3) = 9 -15 =  -6

Answer: $99.99

Step-by-step explanation:

$399.99 * .25 (discount) = $99.99

Answer:

16) 9ft, C

17) 1440 cm^3, D

18) 314 m^2, B

Step-by-step explanation:

16) 18 / 6 = 27 / x

18x = 162

x = 9 (C)

17) 24 / 1,920 = 18 / x

24x = 34,560

x = 1440 (D)

18) Surface Area of a sphere = 4 * pi * radius^2 (4r^2)

SA = 4pi(5)^2

SA = 4pi25

SA = 100pi

SA = 100(~3.14)

SA = 314 (B)

Answer:

13.9

Step-by-step explanation:

Use the distance formula:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\\\d = \sqrt{(7 - (-5))^2 + (-4-3)^2}\\d = \sqrt{(12)^2 + (-7)^2}\\d = \sqrt{144 + 49}\\d = \sqrt{193}\\[/tex]

The square root of 193 rounded to the nearest tenth is 13.9.

Answer:

2. the interquartile range is 20

3. 80 is the median.

Step-by-step explanation:

have a nice day.

Answer:

im confused please explain better

Step-by-step explanation:

Answer:

25%

hope this helps

Answer:

a) -2 < 3

b) |-12| < |15| (the absolute value of -12 is 12 so that's comparing 12 to 15)

c) 3 > -4

d) |15| > |-12|

e) 7 > -11

Answer:

92 feet.

Step-by-step explanation:

Answer:

3 times 4 = 12 BIG BRAIN!!!

Answer:

12/4 =c

Step-by-step explanation:

Answer:

[tex]169cm^2[/tex]

Step-by-step explanation:

The perimeter is the sum of the side lengths of the shape. Since a square has equal side lengths, each side must be the same. Divide 52/4=13cm. 13cm is the length of 1 side. Area is length times width, and since each side is 13, multiply 13cm*13cm to get the area, which is [tex]169cm^2[/tex],

If this helped, brainliest answer would be greatly appreciated!

Answer:

169cm^2

Step-by-step explanation:

Since it's a square both of the lengths of the different sides are the same. (A square has 4 sides, therefore we can form an equation : 4x=52)

When you solve for x which determined the length of one single side (x=52/4) and you get 13.

Using the formula for the area of a square a^2

with a being 13, this means the area is 13^2= 169

Answer:-257.8

Step-by-step explanation:

Answer:

i think it might be 15... im not sure, im not good at math but im good with finding the answers to these type of problems

Step-by-step explanation:

hope this helps

Minimum means smallest, so what is the smallest number possible for this set?

-8

---

hope it helps

Answer:

-2

Step-by-step explanation:

Answer: The answer would be y=1/3x-3

Answer: r = 2/7 -t

Step-by-step explanation: solve r from equation

7r = 2-7t l:7. r = 2/7 - t

The relationship as a function r=f(t) is [tex]\rm f(t)=\dfrac{7-2t}{7}\\\\[/tex].

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Consider the relationship;

7r+2t=7

Substitute r = f(t) in the equation

[tex]\rm 7r+2t=7\\\\7f(t)+2t=7\\\\ 7f(t)=7-2t\\\\f(t)=\dfrac{7-2t}{7}\\\\[/tex]

Hence, the relationship as a function r=f(t) is [tex]\rm f(t)=\dfrac{7-2t}{7}\\\\[/tex].

Learn more about equation here;

https://brainly.com/question/9699841

#SPJ2

Answer:

A graph is a chart or drawing that shows the relationship between changing things.

- They are a diagram displaying the relationship between numbers or amounts.

- A graph is one of the easiest ways to compare numbers.

- A graph or chart is used to present facts in visual form.

- They are a drawing that displays the relative sizes of numerical quantities.

- Graphs can be used to illustrate many types of data.

- They should be used to make facts clearer and more understandable.

- it shows trends over time.

- Forceful -- Emphasizes main point

- Convincing -- proves a point, see and hear

- Compact way to convey information

- More interesting than just talk or print

- Quick way for the audience to visualize what you are saying -- numbers trends up or down

- To bring facts to life

- To show and compare relationships

- To show and compare changes

- They are much easier to understand then a large

table of numbers

- without

the need to understand what each and every number in a table means.

They help you visually see the difference between two or more values.

Hope this helps!

Answer: 1= 41

2= 3 hours biking at the other speed.

3= We began to drive at 75 mph at 1:00 p.m

Step-by-step explanation:

3= x/55 + (630 - x)/75 = 10

75x + 55 * (630 - x) = 41,250 (4,125 as Lowest common multiple)

75x + 34,650 - 55x = 41,250

20x = 41,250 - 34,650 (Subtracting 34,650 at both sides)

20x = 6,600

x = 6,600/20

x = 330 ⇒ 630 - x = 300

Time we drove at 55 mph = 330/55 = 6 hours

Time we drove at 75 mph = 300/75 = 4 hours

We began to drive at 75 mph at 1:00 p.m. (7 am + 6 hours)

hope this helps :)

Answer:

1. 3/2

2. 4

Step-by-step explanation:

Answer:

1. Yes

2. Distributive property

3. 2x+8y

4. I'm assuming its supposed to say 5(4x+3)-2x otherwise none of the options work, so the answer for that would be A

5. C