Multiply: (3x + 2)(4x + 2)

Margaret can invite up to 102 guests and still stay within her budget for the wedding reception. This constraint is illustrated on a number line with a break at 103.

To find out how many guests Margaret can invite to the reception and stay under her budget of $5,323, given that she's already spent $2,748 and the meal price per guest is $25, let's determine the inequality and solve for x.

Formulate the Inequality

Margaret's remaining budget after her initial spending is:

[tex]\[ 5,323 - 2,748 = 2,575.[/tex]

If she wants to stay within this budget, and the meal price per guest is $25, the total cost for (x ) guests is:

[tex]\[ 25 \times x. \][/tex]

Margaret wants to spend less than her remaining budget, so the inequality is:

[tex]\[ 25 \times x < 2,575. \][/tex]

Solve for x :

To find x, divide by 25:

[tex]\[ x < \frac{2,575}{25}, \][/tex]

x < 103.

Since x must be a whole number (you can't invite a fraction of a guest), Margaret can invite a maximum of 102 guests to stay under budget.

Graph on a Number Line

On a number line, draw an open circle at 103, indicating that 103 is not included in the set of possible guest counts.

Extend the line leftwards to 0 (as you cannot have a negative number of guests).

|------|------|------|------|------|

0      25     50     75     100    125

The asterisk represents the open circle, indicating that the maximum number of guests is strictly less than 103.

Margaret can invite 103 guests to the reception and stay under budget. Number line A includes the largest number of guests.

In order to write a linear inequality to describe this situation, we would assign a variable to the number of guests can Margaret invite while staying within her budget, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the number of guests.

Since Margaret wants to spend less than her budget of $5,323, and she has already spent $2,748, and the meal price per guest is $25, a linear inequality that models this situation is given by;

2748 + 25x < 5323

25x < 5323 - 2748

25x < 2575

x < 2575/25

x < 103

In this context, we can logically deduce that the largest number of guests Margaret can invite without exceeding her budget is correctly represented by number line A, with a hollow dot located at 104.

Complete Question;

Margaret is planning a wedding reception. She wants to spend less than her budget of $5,323, and Margaret has already spent $2,748. The meal price per guest is $25. How many guests, x, can Margaret invite to the reception and stay under budget?

Select the number line that includes the largest number of guests Margaret can invite without exceeding her budget.

Answer:

Step-by-step explanation:

C,D and E

Pairs of triangles appear to be congruent are :

" Congruent triangles are defined as the pairs of triangles with same measurement."

According to the question,

Given pairs of triangles,

A. Triangles [tex]1[/tex] and [tex]4[/tex] :

After observing triangles  [tex]1[/tex] and [tex]4[/tex]   it appears that triangle [tex]1[/tex] is smaller than triangle [tex]4[/tex] .

Option A is not the correct answer.

B. Triangles [tex]1[/tex] and [tex]3[/tex] :

After observing triangles  [tex]1[/tex] and [tex]3[/tex]   it appears that triangle [tex]1[/tex] is smaller than triangle [tex]3[/tex] .

Option B is not the correct answer.

C. Triangles [tex]2[/tex] and [tex]3[/tex] :

After observing triangles  [tex]2[/tex] and [tex]3[/tex]   it appears that triangle [tex]2[/tex] is congruent to triangle [tex]3[/tex] .

Option C is the correct answer.

D. Triangles [tex]2[/tex] and [tex]4[/tex] :

After observing triangles  [tex]2[/tex] and [tex]4[/tex]   it appears that triangle [tex]2[/tex] is congruent to triangle [tex]4[/tex] .

Option D is the correct answer.

E. Triangles [tex]3[/tex] and [tex]4[/tex] :

After observing triangles  [tex]3[/tex] and [tex]4[/tex]   it appears that triangle [tex]3[/tex] is congruent to triangle [tex]4[/tex] .

Option E is  the correct answer.

F. Triangles [tex]1[/tex] and [tex]2[/tex] :

After observing triangles  [tex]1[/tex] and [tex]2[/tex]   it appears that triangle [tex]1[/tex] is smaller than triangle [tex]2[/tex] .

Option F is not the correct answer.

Hence, Option(C), (D), and (E) are correct answer.

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Answer:

Step-by-step explanation:

Find the prime factorization of 10

10 = 2 × 5

Find the prime factorization of 24

24 = 2 × 2 × 2 × 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 2 × 2 × 3 × 5

LCM = 120

Answer:

1

Step-by-step explanation:

1 to any power is 1, so you are basically just saying 1*1, and that equals 1

Answer:

7.24/7= 1.03

1.0 is the nearest

Mari has 42 coins consisting of nickels, dimes, and quarters. The total value of the coins is $9.35. The number of dimes is one less than three times the number of nickels. Mari has 17 nickels, 8 dimes, and 17 quarters.

Let's use algebraic equations to solve this problem.

Let "n" be the number of nickels, "d" be the number of dimes, and "q" be the number of quarters.

We have three pieces of information from the problem:

1. The total number of coins: n + d + q = 42

2. The total value of the coins: 0.05n + 0.10d + 0.25q = 9.35

3. The number of dimes is one less than three times the number of nickels: d = 3n - 1

Now, let's substitute the third equation into the first equation to express "d" in terms of "n":

(3n - 1) + n + q = 42

4n + q = 43

q = 43 - 4n

Next, we'll substitute the values of "q" and "d" into the second equation:

0.05n + 0.10(3n - 1) + 0.25(43 - 4n) = 9.35

0.05n + 0.30n - 0.10 + 10.75 - n = 9.35

0.35n + 10.65 = 9.35

0.35n = 9.35 - 10.65

0.35n = -1.30

n = -1.30 / 0.35

n ≈ 3.71

Since the number of coins can't be a fraction, we'll round down to the nearest whole number. Therefore, Mari has 3 nickels.

Now, let's find the number of dimes:

d = 3n - 1

d = 3(3) - 1

d = 9 - 1

d = 8

Finally, we can find the number of quarters using the equation for "q":

q = 43 - 4n

q = 43 - 4(3)

q = 43 - 12

q = 31

In conclusion, Mari has 3 nickels, 8 dimes, and 31 quarters.

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Answer:

In year 2030 the population is predicted to be 71.75 million

Step-by-step explanation:

* Lets explain how to solve the problem

- Using data from 2010 and projected to 2020, the population of

 the United Kingdom (y, in millions) can be approximated by the

 equation  10.0 y − 4.55 x = 581

- x is the number of years after 2000

- We need to know in what year the population is predicted to be

  71.75 million

* Lets substitute the value of y in the equation by 71,75

∵ The equation of the population is 10.0 y - 4.55 x = 581

∵ y = 71.75

∴ 10.0(71.75) - 4.55 x = 581

∴ 717.5 - 4.55 x = 581

- Subtract 717.5 from both sides

∴ - 4.55 x = - 136.5

- Divide both sides by - 4.55

∴ x = 30

∵ x represents the number of years after 2000

∵ 2000 + 30 = 2030

∴ In year 2030 the population is predicted to be 71.75 million

Final answer:

The population of the United Kingdom is predicted to be 71.75 million in the year 2030, calculated by substituting the given population value into the equation and solving for the year.

Explanation:

To find the year in which the population of the United Kingdom is predicted to be 71.75 million, you can use the given equation 10.0y - 4.55x = 581. Here, x is the number of years after 2000, and y is the population in millions.

First, substitute y with 71.75:

Now, add the number of years, x, to the base year, 2000:

Therefore, the population of the United Kingdom is predicted to be 71.75 million in the year 2030.

Answer:

42 that's ur answer u just multiply all the numbers

The multiplication of 3, 7, and 2 (which are all prime numbers) equals to 42. Therefore, 42 is the number which has a prime factorization of 2, 3, and 7.

The product of 3 x 7 x 2 gives us the number for which this is the prime factorization. The prime factorization of a number is the breaking down of that number into its simplest factors that are prime numbers, in this case, it would be 2, 3, and 7. By multiplying these number together: 3 x 7 x 2, we get the number 42, hence, 42 is a number we are looking for.

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Answer:

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

1

2

(8x+20)=18

Simplify: (Show steps)

4x+10=18

Step 2: Subtract 10 from both sides.

4x+10−10=18−10

4x=8

Step 3: Divide both sides by 4.

4x

4

=

8

4

x=2

Answer:

x=2

Answer:

all work is shown and pictured

Answer:25

Step-by-step explanation:Use pemdas first (2x-7y) 2-7=5 next (2x+3) 2+3=5 3•5=15 5•2=10 3•5=15 add 10+15=25

Answer:

A. Translation 5 units up and 4 units to the right

Step-by-step explanation:

A translation is a point-by-point movement by a prescribed number of units up/down and/or left/right.

Point A is moved from (-3,-1) up 5 and right 4 units to A prime at (1,4)

Point B is moved from (-4,-3) up 5 and right 4 units to B prime at (0,2)

Point C is moved from (-2,-3) up 5 and right 4 units to C prime at (2,2)

Answer:

A. Translation 5 units up and 4 units to the right

Step-by-step explanation:

→ Point C moves up to [-2, 2]

Transition up: → Point B moves up to [-4, 2]

→ Point A moves up to [-3, 4]

→ Point C moves to C'[2, 2]

To the right: → Point B moves up to B'[0, 2]

→ Point A moves up to A'[1, 4]

This is a genuine statement!

I am joyous to assist you anytime.

Answer:

20

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 3x² - 2 + 4x + 2 = 3x² + 4x

Substitute x = 2 into f(x) + g(x)

(f + g)(2) = 3(2)² + 4(2) = (3 × 4) + 8 = 12 + 8 = 20

The provided statement is an example of deductive reasoning, where a specific conclusion is drawn from general observations. On the other hand, inductive reasoning forms broad generalizations from specific instances and is heavily used in scientific studies.

The question relates to the concept of inductive and deductive reasoning in logic and proofs. The given statement “All flying birds and insects have wings. Birds and insects flap their wings as they move through the air. Therefore, wings enable flight.” is an example of deductive reasoning.

Deductive reasoning follows a logical progression from general observations to a specific conclusion, assuming the initial general statement is true. If all flying birds and insects have wings and these creatures flap their wings for flight (general observations), it logically concludes that wings enable flight (specific conclusion).

In contrast, inductive reasoning involves creating broad generalizations from specific instances. Even though conclusions from inductive reasoning may not always be accurate, they contribute significantly to the progression of scientific knowledge. Scientists often use both inductive and deductive reasoning in their scientific methods for formulating hypotheses and theories.

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Answer:$1340

Step-by-step explanation:

Answer:

Second statement 2x2 + 8x – 24 = 0 Is true for the given conditions. When x = -6 2x2 + 8x – 24 = 0 Becomes 2(-6)2 + 8(-6) – 24 = 0 2(36) - 48 - 24 = 0 72 - 48 - 24 = 0 0 = 0 Which is true. When x = 2 2x2 + 8x – 24 = 0 Becomes 2(2)2 + 8(2) – 24 = 0 2(4) + 16 - 24 = 0 8 + 16 - 24 = 0 0 = 0 Which is true. So 2x2 + 8x – 24 = 0 will be answer.

The characteristics of the solutions of the polynomials are listed below:

Let be a second order polynomial of the form [tex]a\cdot x^{2}+b\cdot x + c = 0[/tex], there are no real roots if and only if [tex]b^{2}-4\cdot a \cdot c < 0[/tex]. Now we proceed to determine the nature of the roots of each polynomial:

1) [tex]x^{2} = 49[/tex]

This expression is equivalent to the polynomial [tex]x^{2}-49 = 0[/tex], then the discriminant is:

[tex]d = 0^{2}-4\cdot (1)\cdot (-49)[/tex]

[tex]d = 196[/tex]

The polynomial has two distinct real roots.

2) [tex]2\cdot x^{2} = -128[/tex]

This expression is equivalent to the polynomial [tex]2\cdot x^{2} +128 = 0[/tex], then the discriminant is:

[tex]d = 0^{2} - 4\cdot (2)\cdot (128)[/tex]

[tex]d = -1024[/tex]

The polynomial has two conjugated complex roots.

3) [tex]3\cdot x^{2}-16 = 32[/tex]

This expression is equivalent to the polynomial [tex]3\cdot x^{2}-48 = 0[/tex], then the discriminant is:

[tex]d = 0^{2}-4\cdot (3) \cdot (-48)[/tex]

[tex]d = 576[/tex]

The polynomial has two distinct real roots.

4) [tex]x^{2}+x+1 = 0[/tex]

The discriminant of this expression is:

[tex]d = 1^{2}-4\cdot (1)\cdot (1)[/tex]

[tex]d = -3[/tex]

The polynomial has two conjugated complex roots.

Nota - The original statement reports typing mistakes. Corrected form is presented below:

Select all the equations that do not have a real solution:

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Answer:

The correct answer is 2 1/36.

Answer:

2x-3 = -11

Step-by-step explanation:

|2x-3| = 11

by definition of absolute numbers,

2x-3 = 11 (given)

or

2x-3 = -11 (answer)

Answer:

The missing portion is + 16x + 16.

Step-by-step explanation:

In order to get [tex]f(g(x))[/tex], we put

[tex]g(x)= \dfrac{1}{2x+4}[/tex]  

into

[tex]f(x)= \dfrac{1}{x^2}[/tex],

which gives us

[tex]f(g(x))= \dfrac{1}{(g(x) )^2}[/tex]

[tex]f(g(x))= \dfrac{1}{(\dfrac{1}{2x+4} )^2}[/tex]

[tex]f(g(x))= (2x+4)^2[/tex]

we expand and get:

[tex]f(g(x))= 4x^2+16x+16[/tex].

Thus, we see that the missing portion is [tex]16x+16.[/tex]

Answer:

f(-1)=

[tex] \frac{ - 2}{3} [/tex]

f(2)=

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

Step-by-step explanation:

let f(x)=f(-1)

but f(x) =3x+1

substituting it into the equation

3x+1=-1

3x=-1-1

3x=-2

dividing through by 3

[tex] \frac{3x}{3} = \frac{ - 2}{3} [/tex]

[tex]x = \frac{ - 2}{3} [/tex]

f(-1) =

[tex] \frac{ - 2}{3} [/tex]

f(2)

let f( x )=f(2)

then

3x+1=2

3x=2-1

3x=1

dividing through by 3

[tex] \frac{3x}{3} = \frac{1}{3} [/tex]

[tex] x = \frac{1}{3} [/tex]

f(2)=

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

To find ƒ(2), substitute x = 2 into the Function ƒ(x) = 3x + 1. The answer is 7.

To find ƒ(2), we need to substitute x = 2 into the function ƒ(x) = 3x + 1.

Given: ƒ(x) = 3x + 1

Step 1: Substitute x = 2 into the function:

ƒ(2) = 3(2) + 1

Step 2: Perform the calculations:

ƒ(2) = 6 + 1

Step 3: Simplify the expression:

ƒ(2) = 7

Therefore, ƒ(2) = 7.

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Answer:

[tex]\frac{175}{2x}[/tex]

Step-by-step explanation:

Jon works the same number of hours on Friday and Saturday, therefore x represents the number of hours worked on Friday and also the number of hours worked on Saturday.

So the total hours worked between Friday and Saturday is 2X

If the total for the 2X hours worked is equal to 175 $  

To know how much you earn per hour, we must divide the profit by the total hours worked.

Then we have the following expression

To know how much you earn per hour, we must divide the profit by the total hours worked.

[tex]\frac{175}{2x}[/tex]

Answer:

24

Step-by-step explanation:

- (5*5) +6*5 +19

-25 + 30 + 19 = 24

Answer:

f = -15

Step-by-step explanation:

f/5 - 22 = -25 -------- add -22 to both sides to isolate 'f'

f/5 = -3 ------- multiply 5 to both sides to further isolate 'f'

f = -15

The nature of the graph from point A to B : The graph increases, then decreases.

Given,

Graph is x -y coordinates.

Now,

Graph is concave downwards.

Coordinates of point A : (0,0)

Coordinates of point B : (6,0)

So,

The graph firstly increases from x = 0 to x = 3.

Then,

The graph decreases from x = 3 to x = 6 .

Therefore the graph increases and then decreases.

Thus option D is correct.

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Answer:

168

Step-by-step explanation:

u can eperate the 14 to 10 and 4 then multiple each to 12 then add the two answer so it would be 10×12 and 4×12 then add them so (10×12=120)+(4×12=48)

Answer:

B

Step-by-step explanation:

Answer:

25200

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This curve will only have one maximum point at (-3, 2)

Answer:

- 5

Step-by-step explanation:

Note that - (- 12) = + 12

Thus

- 17 - (- 12) = - 17 + 12 = - 5

It looks like Tom subtracted 12 from - 17, that is - 17 - 12 = - 29

Answer:-17-(-12)=-5

Step-by-step explanation:when there’s a negative number in parenthesis and there’s a minus outside the parenthesis that majestic the number inside the parenthesis a positive