George is painting fences at the zoo. It takes 2 2/3 cans of paint to paint each fence. If George paints 9 fences, how much paint will he use?

Answer:

a) Arithmetic    yₙ = 3*(n - 1) + 13

b) Geometric   yₙ = 2*5⁽ⁿ⁻¹⁾

Step-by-step explanation:

The formula for the nth term e, of that sequence is; yₙ = 3*(n - 1) + 13 and yₙ = 2*5⁽ⁿ⁻¹⁾

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

(a) 13, 16, 19

Here,  yₙ = 3*(n - 1) + 13

This is an Arithmetic.

b) 2, 10, 50

Here, yₙ = 2*5⁽ⁿ⁻¹⁾

This is Geometric .  

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Answer:

a. You can find the value of 4w by using inverse operations. Subtract 8 from both sides in the equation 4w+8=32. You will get 4w=24. Now, you divide 4 by both sides to get w by itself. You will soon get 6. Now multiply 6 and 4, coming to the conclusion that 4w=24.

b. To find the value of w using the value of 4w, which is 24, simply use inverse operations once more. Using the equation 4w=24, we can use division and divide 4 by both sides, leaving us with w by itself. We end up with w=6. The value of w is 6.

c. You can check if the value of w is correct by plugging in your number back into the equation. Our equation is 4w+8=32, so we replace w with 6, the value for w that we found. We end up with 4(6)+8=32. Multiply 4 by 6, ending up with 24, then add it to 8, coming up with 32. 4(6)+8=32, which shows us that 6 is the correct value for w.

[tex] \large\color{lime}\boxed{\colorbox{black}{Answer : - }}[/tex]

We know that, in ∆ABC,

∠A+∠B+∠C = 180°

But the triangle is right angled at C

ie., ∠C = 90°

Therefore, ∠A+∠B+ 90° = 180°

⇒ ∠A + ∠B = 90°

Therefore, cos(A + B) = cos 90º = 0

Answer:

Solution given:

f(x)=2x²-5

g(x)=3x+3

now

(f-g) (x)=?

we have

(f-g)(x)=f(x)-g(x)

Answer:

[tex]2x^{2} - 3x - 8[/tex]

Step-by-step explanation:

Step 1:  Define what (f-g)(x) means

(f-g)(x) means that we have two different functions, f(x) and g(x).  (f-g)(x) is a shorter way of writing f(x) - g(x).  Therefore you just plug in the equations and combine like terms.

Step 2:  Find (f-g)(x)

[tex]f(x) = 2x^{2} - 5[/tex]

[tex]g(x) = 3x + 3[/tex]

[tex](f-g)(x) = 2x^{2} - 5 - (3x + 3)[/tex]

[tex](f-g)(x) = 2x^{2} - 5 - 3x - 3[/tex]

[tex](f-g)(x) = 2x^{2} - 3x - 8[/tex]

Answer:  [tex]2x^{2} - 3x - 8[/tex]

Answer:

360 in.

Step-by-step explanation:

In order to get this answer, you have to multiply 5 and 8 by 3 because the drawing is 1/3 of the actual flag.

5 x 3 = 15

8 x 3 = 24

So, 24 x 15 = 360 in.

Hope this helps! :)

Mark Brainliest if correct:

x = -2, 9

Step-by-step explanation:

x2: x + 2 = 0

x = -2

x1: x - 9 = 0

x = 9

x = -2, 9

Step-by-step explanation:

please check the attachment for solutions

Step-by-step explanation:

a is the answer if is wrong I'm sorry

A=(–2,–4) , B=(0,4)

m=(y2-y1)/(x2-x1)= (4-(-4)) / (0-(-2))=8/2=4

(x+2)(x+4)=x²+4x+2x+8=x²+6x+8

I hope I helped you^_^

Answer:

E, D and E

Step-by-step explanation:

(28)

The equation of a line passing through the origin is

y = mx ( m is the slope )

Calculate the slope using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (- 2, 3) and (x₂, y₂ ) = B (2, - 3) ← 2 points on the line

m = [tex]\frac{-3-3}{2-(-2)}[/tex] = [tex]\frac{-6}{2+2}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]

y = - [tex]\frac{3}{2}[/tex] x → E

(29)

Using the slope formula

with (x₁, y₁ ) = A (- 2, -4) and (x₂, y₂ ) = B (0, 4) ← 2 points on the line

m = [tex]\frac{4-(-4)}{0-(-2)}[/tex] = [tex]\frac{4+4}{0+2}[/tex] = [tex]\frac{8}{2}[/tex] = 4 → D

(30)

(x + 2)(x + 4)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 2(x + 4) ← distribute both parenthesis

= x² + 4x + 2x + 8 ← collect like terms

= x² + 6x + 8 → E

Answer:

7a²b²(a - 2b)

Step-by-step explanation:

Given

7a³b² - 14a²b³ ← factor out 7a²b² from each term

= 7a²b²(a - 2b)

Answer:

100

Step-by-step explanation:

2h (l+b)​

Let l=6  b=4 and h = 5

2*5( 6+4)

Parentheses first

2*5(10)

Multiply

10*10

100

Answer:

given values are:

1200 = 20×30 + 1/2 × 30²a

1200= 600 + 1/2 × 900a

600 = 450a

a = 600 / 450

a = 1.33 m/s²

v² = 20² +2 × 1.33 × 1200

v²= 400 + 3192

v = √3592

v = 59.9 ≈ 60 m/s

Option B is 1/3 + 1/4.

1/3 + 1/4 is equal to 7/12.

Here, we have,

To find the sum of 1/3 and 1/4, you need to have a common denominator.

The common denominator of 3 and 4 is 12.

To make the fractions have the same denominator, you can convert them as follows:

1/3 = (1/3) * (4/4) = 4/12

1/4 = (1/4) * (3/3) = 3/12

Now that both fractions have a denominator of 12, you can add them together:

1/3 + 1/4 = 4/12 + 3/12 = (4+3)/12 = 7/12

Therefore, 1/3 + 1/4 is equal to 7/12.

now, from the given options, we have,

in option B. it is indicating that,

2/6 + 1/4

=> 1/3 + 1/4.

Hence, Option B is 1/3 + 1/4.

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Answer:

158cm

Step-by-step explanation:

Martine had the height of 50cm when born.

Every year she grows at an average rate of 6cm

So the the first 18 years will be 6cm × 18 = 108cm

She will be 108cm + 50cm = 158cm tall by the time she turns 18 years

50cm + (6 × 18)cm

50cm + (6 × 18)cm50cm + 108cm

50cm + (6 × 18)cm50cm + 108cm158cm

============================================================

Explanation:

We'll use the distance formula here. Rather than compute the distance d based on two points given, we'll go in reverse to use the given distance d to find what the coordinate must be to satisfy the conditions.

We're given that d = 5

The first point is [tex](x_1,y_1) = (5,2)[/tex] and the second point has coordinates of [tex](x_2,y_2) = (x,5)[/tex] where x is some real number.

We'll plug all this into the distance formula and solve for x.

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\5 = \sqrt{(5-x)^2+(2-5)^2}\\\\5 = \sqrt{(5-x)^2+(-3)^2}\\\\5 = \sqrt{(5-x)^2+9}\\\\\sqrt{(5-x)^2+9} = 5\\\\(5-x)^2+9 = 5^2\\\\(5-x)^2+9 = 25\\\\(5-x)^2 = 25-9\\\\(5-x)^2 = 16\\\\5-x = \pm\sqrt{16}\\\\5-x = 4 \ \text{ or } \ 5-x = -4\\\\-x = 4-5 \ \text{ or } \ -x = -4-5\\\\-x = -1 \ \text{ or } \ -x = -9\\\\x = 1 \ \text{ or } \ x = 9\\\\[/tex]

This means that if we had these three points

Then segments AB and AC are each 5 units long.

Answer:

The answer is -51146

Step-by-step explanation:

Just substract simple

Answer:

Step-by-step explanation:

[tex]\displaystyle \Large \boldsymbol{} \tt a) \ 3-2x=3(x+4)-x-1\\\\3-2x=3x+12-x-1 \\\\3-12+1=3x+2x-x \\\\4x=-8 \\\\\boxed{ \tt x=-2} \\\\\\b) \ 5x\underline{(x-1)}-4\underline{(x-1)}=0 \\\\\\(5x-4)(x-1)=0 \Longrightarrow \boxed{ \tt x_1=0.8 \ \ ; \ \ x_2=1}[/tex]

Answer:

it's the 3rd option

Step-by-step explanation:

f(x) 0 over the intervals (–∞ –3)

Hope it's right

Answer:

300 raisins

Step-by-step explanation:

sum the parts of the ratio, 3 + 27 = 30 parts

Divide the total by 30 for the value of one part of the ratio.

3000 ÷ 30 = 100 ← value of 1 part of the ratio , then

3 parts = 3 × 100 = 300 ← number of raisins in a box

the first one is, yes by AA

the second is no you cannot

Answer:

13/9

Step-by-step explanation:

Given

5/9 + 8/9

Both fractions have the same denominator.

Therefore, pick one of the denominator and add the numerators

5/9 + 8/9

= (5+8) / 9

= 13/9

5/9 + 8/9 = 13/9

Answer:

Step-by-step explanation:

r = d/2

r = 2.4 m/2 = 1.2

h = 1.8

pi = 3.14

Volume = pi * r^2 * h

Volume = 3.14 * 1.2^2 * 1.8

Volume = 8.139

Volume = 8 to the nearest m^3

Given height and surface-area-to-volume ratio: r = 2 * h / (h * SA:V - 2) , Given volume and lateral area: r = 2 * V / A_l , Given base area: r = √(A_b / (2 * π)) , Given lateral area and total area: r = √((A - A_l) / (2 * π)) .

Answer:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangle

Answer:

See below.

Step-by-step explanation:

Call the sum of the first n terms S.

S = a + ar + ar^2 + ar^3 + ... + ar^(n -1)

Multiply both sides by r.

Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^n

No subtract S - Sr.

      S =  a + ar + ar^2 + ar^3 + ar^4 + ... + ar^(n -1)

(-)    Sr =       ar + ar^2 + ar^3 + ar^4 + ... + ar^(n - 1) + ar^n

-------------------------------------------------------------------

  S - Sr = a - ar^n

S(1 - r) = a(1 - r^n)

S = a(1 - r^n)/(1 - r)

S = a(r^n - 1)/(r - 1)

a + ar + ar^2 + ar^3 + ... + ar^(n -1) = a(r^n - 1)/(r - 1)

Answer:

35

Step-by-step explanation:

48-15÷(3×5)+12

48-15÷15+12

48-1+12

59