Store employees are handing out coupons. Every 5th customer gets a free bagel coupon. Every 9th customer gets a free drink coupon.

Which customer is the first to receive both coupons?

Part (i)

We start with five dots to make the pattern in figure 1.

In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.

In figure 3, there are 9+4 = 13 dots

So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.

The first three terms of this arithmetic sequence are: 5, 9, 13

Your teacher wants to know what the general nth term is

We start with a = 5 and the common difference is d = 4

T(n) = nth term

T(n) = a + d(n-1)

T(n) = 5 + 4(n-1)

T(n) = 5 + 4n - 4

T(n) = 4n + 1

Let's try it out. Say we want to plug in n = 2

T(n) = 4n + 1

T(2) = 4(2) + 1

T(2) = 8 + 1

T(2) = 9

This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.

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Part (ii)

Your teacher wants to know how many dots occur when n = 50

T(n) = 4n + 1

T(50) = 4(50)+1

T(50) = 200 + 1

T(50) = 201

Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.

In this question, we given a piece-wise function, that has different definitions depending on the domain.

Evaluate the function at x = 0.

The exercise asks for us to evaluate the function at [tex]x = 0[/tex]

We have to look at the definition, and see which definition includes [tex]x = 0[/tex]. The equal sign at [tex]x = 0[/tex] is on the second definition, that is:

[tex]f(x) = 1, 0 \leq x < 2[/tex]

Thus, at [tex]x = 0[/tex], the value of the function is 1, and the correct answer is given by option A.

For another example of evaluation of a piece-wise function, you can check https://brainly.com/question/17966003

HOPE ITS HELPFUL ^_^

Answer:

No adda doesnt get free delivery

Step-by-step explanation:

Answer: A) No, the distance from the restaurant to Ada’s house is Square Root of 41 miles, which is greater than the 6-mile maximum radius.

Step-by-step explanation:

Answer:

you have to put them in order

Answer:

A. {x| –4 < x ≤ 4}

Step-by-step explanation:

Answer:

{x| –4 < x ≤ 4}

Step-by-step explanation:

Edge Quiz 2023

Answer:

A) Q(x) = (x + 3)² + 5, and the vertex is (-3, 5)

B) R(x) = (x - 3)² + 2, and the vertex is (3, 2)

C) S(x) = (x - 1)² - 5, and the vertex is (1, -5)

Step-by-step explanation:

The given function is P(x) = (x + 3)² + 2

The given function is a parabolic function in vertex form, f(x) = a·(x - h)² + k, and vertex, (h, k)

By comparison, the vertex of the function P(x) = (x + 3)² + 2 is (-3, 2)

A) A function f(x) translated α units UP gives

f(x) (translated α units UP) → f(x) + α

A translation of the function 3 units UP is given by adding 3 to the given function as follows;

Q(x) = P(x) + 3

∴ Q(x) = (x + 3)² + 2 + 3 = (x + 3)² + 5

Q(x) = (x + 3)² + 5, and the vertex by comparison to f(x) = a·(x - h)² + k, and vertex, (h, k) is (-3, 5)

B) A function f(x) translated b units RIGHT gives;

f(x) translated b units right → f(x - b)

∴ P(x) = (x + 3)² + 2 translated 6 units RIGHT gives;

P(x) = (x + 3)² + 2 (translated 6 units RIGHT) → R(x) = (x + 3 - 6)² + 2 = (x - 3)² + 2

R(x) = (x - 3)² + 2, and the vertex by comparison is (3, 2)

C) A function translated α units DOWN and b units RIGHT is given as follows;

[tex]f(x) \ translated \ by\ \dbinom{b}{a} \rightarrow f(x - b) - a[/tex]

Therefore, the given function, P(x) = (x + 3)² + 2, translated 7 units DOWN and 4 units RIGHT gives;

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow P(x - 4) - 7 = S(x)[/tex]

S(x) = P(x - 4) - 7 = (x + 3 - 4)² + 2 - 7 = (x - 1)² - 5

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow (x - 1)^2 - 5= S(x)[/tex]

S(x) = (x - 1)² - 5, and the vertex by comparison is (1, -5)

Answer:

6ft by 8ft

Step-by-step explanation:

12 / 2 is 6 and 16 / 2 is 8

Let S be the sum of the integers 25-210:

S = 25 + 26 + 27 + … + 208 + 209 + 210

Let S₃, S₄, and S₁₂ denote the sums of the integers in S that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

S₃ = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (62 terms)

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

S₄ = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (46 terms)

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₁₂ = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (15 terms)

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at S₃ :

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

S₃* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

Of course S₃ = S₃*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

S₃ + S₃* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2S₃ = 3 × 62 × 79   ==>   S₃ = 7,347

We can compute the other two sums in the same way.

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₄* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

==>   2S₄ = 4 × 46 × 59  ==>   S₄ = 5,428

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

S₁₂* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

==>   2S₁₂ = 12 × 15 × 20   ==>   S₁₂ = 1,800

Then the sum you want is

S₃ + S₄ - S₁₂ = 10,975

We subtract S₁₂ because each of its terms is counted twice (once in S₃ and again in S₄).

Answer:

hi

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]a = \frac{2b+1}{3b-1}[/tex]

b = 2/3

[tex]2b + 1 = 2*\frac{2}{3}+1\\\\=\frac{4}{3}+1\\\\=\frac{4}{3}+\frac{3}{3}\\\\=\frac{7}{3}\\\\3b-1 = 3*\frac{2}{3}-1\\\\=2- 1 = 1\\\\\\[/tex]

[tex]a = \frac{2b+1}{3b-1}\\\\a=\frac{\frac{7}{3}}{1}\\\\=\frac{7}{3}\\\\[/tex]

a = 7/3

b)

[tex]\frac{2b+1}{3b-1}=a\\\\[/tex]

Cross multiply,

2b + 1 = a*(3b - 1)

2b + 1 = a*3b - 3*a

2b + 1 = 3ab- 3a

2b = 3ab - 3a - 1

2b - 3ab = -3a  - 1

b(2 - 3a) = -3a - 1

[tex]b =\frac{-3a - 1}{2 - 3a}[/tex]

Answer:

1 2x-4,x-42,2-4x I hope it will help you please follow me

Answer:

-1

Step-by-step explanation:

Remember PEMDAS! Start with distributing the parentheses -(3x+6) so you get -8x-3x-6=4-x and simplify. Then you get -11x-6=4-x and combine like terms which equals -10=10x. Simplify and you get -1.

The solution to the equation -8x - (3x + 6) = 4 - x is x = -1.

Given the equation in the question:

-8x - (3x + 6 ) = 4 - x

To solve the equation -8x - (3x + 6) = 4 - x, simplify the equation by isolating all terms with variable x:

-8x - (3x + 6 ) = 4 - x

Distribute the negative sign inside the parentheses:

-8x - 3x - 6 = 4 - x

Combine like terms on both sides of the equation:

-11x - 6 = 4 - x

Add 6 to both sides:

-11x - 6 + 6 = 4 + 6 - x

-11x = 4 + 6 - x

-11x = 10 - x

Next, add x to both sides:

-11x + x = 10 - x + x

-10x = 10

Divide both sides of the equation by -10:

x = -10/10

x = -1

Therefore, the value of x is -1.

Learn more about equations here: brainly.com/question/14686792

#SPJ6

Answer:

a=41  b=-9

Step-by-step explanation:

By expanding the brackets on the left hand side of the equation you get,35x + 40 + 6x + 3b and by simplifying you get 41x + 40 + 3b.by comparing the x and constant terms on either side you find that a = 41, and3b + 40 = 13, rearranging b = -9.

Answer from Gauth math

Answer:

Hello,

Step-by-step explanation:

We are going to use identification of terms.

[tex]5(7x+8)+3(2x+b)=ax+13\\\\35x+40+6x+3b=ax+13\\\\41x+40+3b=ax+13\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\3b+40&=&13\\\end{array}\right.\\\\\\\Longrightarrow \left\{\begin{array}{ccc}a&=&41\\b&=&-9\\\end{array}\right.\\\\[/tex]

Produced by myself

Answer:

Step-by-step explanation:

By applying tangent rule in the given right triangle AOB,

tan(30°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{BO}{OA}[/tex]

[tex]OA=BO(\sqrt{3})[/tex]

By applying tangent rule in the given right triangle BOC,

tan(60°) = [tex]\frac{OC}{BO}[/tex]

OC = BO(√3)

OA + OC = AC

[tex]BO(\sqrt{3})+BO(\sqrt{3}) =60[/tex]

2√3(BO) = 60

BO = 10√3

OC = BO(√3)

OC = (10√3)(√3)

OC = 30

By applying tangent rule in right triangle DOC,

tan(60°) = [tex]\frac{OD}{OC}[/tex]

OD = OC(√3)

OD = 30√3

Since, BD = BO + OD

BD = 10√3 + 30√3

BD = 40√3

      ≈ 69.3

Answer:

7

Step-by-step explanation:

if the bases of the exponents are the same then we can add the powers. so 2^3 * 2^4 = 2^7 = 128.

Answer:

7

Step-by-step explanation:

2^3⋅2^4= 2^7

2^7=2^x

since it had the same base you wouldn't need to worry about it you can just focus on the exponent.

7=x

swap it over

x=7

Answer:

500*2%=10

500+10=510

Step-by-step explanation:

Answer:

a=6 and b=8

Step-by-step explanation:

a^2=(9/16)b^2. Substitute this in the second equation, you get b^2+b^2*(9/16)=100, b^2=100*16/25=8 and a=6

Answer:

16 degrees

Step-by-step explanation:

Tan(?) = perpendicular/base

Tan(?) = 13/46

?=arctan(13/46)=16

Answer:

y = -3x + 2

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - 8 / 1 - (-2)

-9/3

= -3

y = -3x + b

-1 = -3(1) + b

-1 = -3 + b

2 = b

Answer:

[tex] \sqrt{ - 147} = \sqrt{147} \times \sqrt{ - 1} = 7i \sqrt{3} [/tex]

I hope I helped you ^_^

The answer ; √ –108 = √108 × √–1 = 6i √3

Answer:

x= -2   and x = 6

Step-by-step explanation:

The solutions are where the two graphs intersect

x=6, y= 10  is one point

x=-2 and y = -6 is the other point

The intersection points of both the equations are the solutions

From the graph the points are

Hence

x=-2 and x=6 are the solutions

Option D

Answer:

Looking at the question and goin step by step

we get to know that equation formed wud be ->

product of nine and a number - 9*x = 9x

added to 6 => 9x+6

gives us 24

so

9x + 6 = 24

now 9x = 18 and x = 18/9 = 2

and now keeping x value = 9 *(2)+6 we get 18+6 = 24

so lhs = rhs = 24

9x+6=24 option a

The concept of greatest common factor is used to solve this question. Then, we use it to find the number of crackers and slices of cheese, and the answer is:

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

To find the greatest number of plates, you need to find the greatest common factor between 12 and 18.

Thus, factoring them, always by the same number:

12 - 18|2

6 - 9|3

2 - 3

The greatest common factor is 2x3 = 6, which means that the greatest number of plates you can prepare is 6.

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

18 crackers, so each plate has 18/6 = 3 crackers.

12 slices of cheese, so each plate has 12/6 = 2 slices of cheese.

A similar question is given at https://brainly.com/question/18454593

Answer:

A is the answer to your question

Step-by-step explanation:

To do this, just distribute the 3 to each of the coefficient and see if it would result in the same coefficients in the original expression.

Answer:

The answer is a translation

Step-by-step explanation:

In Math, translation is the displacement of a shape or object from one place to another.

Since the picture shows that the shape moved from one place to the next while remaining the same size, it is translation.

Answer:

2

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

3х - 6 = 6x - 9

Subtract 3x from each side

3х-3x - 6 = 6x-3x - 9

-6 = 3x-9

Add 9 to each side

-6+9 = 3x-9+9

3 =3x

Divide by 3

3/3 = 3x/3

1 =x

Answer:

3x-6=6x-9

3x-6x=-9+6

-3x=-3

-3x÷-3=-3÷-3

x=1