Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.Cooper is starting a business selling handmade necklaces. He has decided to invest an initialamount of $24 for advertising, and materials cost $8 for each necklace he makes. Cooper cansell his creations for $14 per necklace. Once he makes and sells a certain number ofnecklaces, he will break even, with identical expenses and sales. What would the totalexpenses and sales be then? How many necklaces would that take?

To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.

Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.

First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.

Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.

Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.

Answer:

Step-by-step explanation:

h and c are the numbers of hamburgers and cheeseburgers, respectively.

“a combined total of 486 hamburgers and cheeseburgers”

h + c = 486

“64 fewer cheeseburgers sold than hamburgers”

c = h - 64

Substitution:

h + (h-64) = 486

2h = 550

h = 275

275 hamburgers were sold

On solving the provided question, we can say that  on matching the expressions are 100X 14 = 1400 and 14(10) = 140 and 361 . 100 = 36100 and 100(361) = 36100

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

so, on matching the expressions are

100X 14 = 1400

14(10) = 140

361 . 100 = 36100

100(361) = 36100

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The total amount Derek repaid after 5 years of quarterly payments at 10% per annum is $12,829.40.

The quarterly payments represent periodic payments made every three months to offset the credit.

The periodic payments can be computed using an online finance calculator.

Where the periodic payment is given, the total payment made can be determined as the product of the periodic payments and the number of periods involved.

N (# of periods) = 20 quarters (5 years x 4)

I/Y (Interest per year) = 10%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $-641.47

Results:

FV = $-0.03

Sum of all periodic payments = $-12,829.40

Total Interest = $2,829.43

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Derek borrowed $10,000 at 10% per annum compounded quarterly and repays $641.47 quarterly.  How much money did he repay after 5 years?

Answer:

B. (x³ - 10)(x⁶ + 10x² + 100)

Answer:

B

Step-by-step explanation:

(x³ - 10)(x^6 + 10x³+ 100)

x^9 + 10x^6 + 100x³ - 10x^6 - 100x³ - 1000

x^9 - 1000

d. both a relation and a function:

Given:

Mark records his science scores in each monthly assessment over a period of 5 months. In the first assessment he scores 76%. In the second assessment he scores 73%. After that, his scores keep increasing by 2% in every assessment.

x represents the number of assessments since he starts recording and y represents the scores in each assessment.

In order for a relation to be a function the association has to be unambiguous that means that for a given input only one output can exist.If an input can have two or more outputs then you cannot determine which is the correct output for that input.

In the given situation:

x is the input that is number of assessments since mark starts recording the scores so there is only one assessment no repeating.so there is only one output.

Hence the relation is a function.

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If the sum of the squares on its other two sides equals the square of its greatest side.

Given:

AB = 9 cm CB = 40 cm AC = 41 cm

The Pythagorean Theorem states that

If the largest side's square is equal to the sum of the squares on the other two sides, the triangle will have a right angle.

AB = 9 cm CB = 40 cm AC = 41 cm

The Pythagorean Theorem states that

AC 2 =BC² +AB ²

41²=40²+9²

41 ²=40 ² +9 ²

1681 = 1600 + 81

1681 = 1681

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The question is incomplete

Show that the triangle ABC is a right-angled triangle; if:

AB = 9 cm, BC = 40 cm, and AC = 41 cm.

Answer:

yes  

Step by-step explanation:

it will take up 8 12/16 space and the wall has 8 15/16

Therefore , the solution of the given problem of unitary method comes out to be the letters A, B, A, and B can thus be arranged in six distinct ways.

Using what was learned, utilising this varied approach, and combining all crucial factors from prior researchers who employed a certain methodology can enable completion of the assignment. The entity indicated in the proposition can then either also be discovered or both crucial processes will definitely miss the expression if the desired claim outcome occurs. A refundable prepayment of Rupees ($1.21) may be needed for fifty pens.

Here,

The following formula can be used to create permutations of n objects with repeats of k1, k2,..., kr objects of each type:

=> n!/(k1! * k2! * ... * kr!)

We have two different object kinds (A and B) here, both of which are repeated twice. As a result, we have:

n = 4 (the total number of things) (the total number of objects)

=>k1 = k2 = 2 (the number of objects of each category) (the number of objects of each type)

The result of the formula is:

=> 4!/(2! * 2!) = 24/(2 * 2) = 6

The letters A, B, A, and B can thus be arranged in six distinct ways.

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Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

THe answer is, \(21/5\)

And in decemal form it will be, \(4.2\)

The matrix products are given as follows:

a. AB = [58 -6 24]

        [18 63 45]

        [-22, -39, -33]

b. BA = [32 -26]

            [10 56]

The addition A + B is not possible to obtain, the matrices have different dimensions.

The dimensions of each matrix are given as follows:

Hence the dimensions of each product are given as follows:

To multiply matrices, the rows of the first are multiplied by the columns of the second, hence matrix AB is obtained as follows:

Hence the matrix AB is given as follows:

AB = [58 -6 24]

        [18 63 45]

        [-22, -39, -33]

Matrix BA is obtained as follows:

Hence the matrix BA is given as follows:

BA = [32 -26]

        [10 56]

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Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Answer:

first graph

Step-by-step explanation:

x > n

the graph will have an open circle at the value n , indicating that x cannot equal n ( note solid circle if x ≥ n )

the arrow from n will point in the right direction, indicating values of x greater than n.

the graph representing x > n is the first graph

To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The required composite value f(g(-8) is 28

A composite function is a function inside another function. Given the following functions

f(x) = x² - 3x - 12

g(x) = -x - 12

Required composite function is f(g(-8))

First we need to get f(g(x))

f(g(x)) = f(-x-12)

f(-x-12) =  (-x-12)² - 3x - 12

Expand

f(-x-12) = x² +24x + 144 - 3x - 12

f(-x-12) = x² +21x + 132

f(g(x)) = x² +21x + 132

Substitute x = -8 into the result

f(g(-8)) = (-8)² +21(-8) + 132

f(g(-8)) = 64 - 168 + 132

f(g(-8)) = 28

Hence the required composite value f(g(-8) is 28

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The piecewise function for this problem is defined as follows:

B.

The function is a piecewise function, as the function has different definitions based on the input of the function.

The different definitions for the graph are given as follows:

To the left of x = 0, we have a linear function with intercept of 2 and slope of 2, hence it is given as follows:

y = 2x + 2, x ≤ 0.

To the right of x = 0, we have a linear function with intercept of 4 and slope of -4/3, hence it is given as follows:

y = -4/3x + 4, x > 0.

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Answer:

3/2

Step-by-step explanation:

\(f(-2)=\frac{-5(-2)+8}{-9(-2)-6} \\ \\ =\frac{18}{12}=\frac{3}{2}\)

Answer:

Step-by-step explanation:

1000m = 1km

So 3000m = 3km

The value of a for the given expression will be -3.31.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 3.6= − a/0.8 − 1.6 − 0.8 a ​ −1.6. The value of a will be calculated as below,

3.6 = − a/0.8 − 1.6 − 0.8 a ​ −1.6

3.6 + 1.6 + 1.6 = -a / 0.8  - 0.8a

6.8 = ( -a - 0.64a ) / 0.8

5.44 = -1.64a

a = -3.31

Therefore, the value of a will be -3.31.

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The value of the expression a(b + c) when a = 2, b = 3, and c = 4 is 14.

Given the expression in the question:

a( b + c )

Also, a = 2, b = 3, and c = 4

To evaluate the expression a( b + c ) when a = 2, b = 3, and c = 4, we substitute these values into the expression:

Hence:

a( b + c )

Plug in a = 2, b = 3, and c = 4

2( 3 + 4 )

First, we simplify the parentheses by adding 3 and 4:

2( 7 )

Next, we multiply 2 and 7:

14

Therefore, the value of a(b + c) is 14 .

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The surface area of each box is 0.52 square meters.

To calculate the surface area of ​​an orthohedron with 6 rectangular faces, add the areas of the 6 faces together. You can also identify the length (c), width (l) and height (a) of the orthohedron and use the formula: surface area (AS)=2cl+2ca+2al.

Knowing that:

\(2 * (L * H) + 2 * (W * H)\)

Substituting the values:

\(2 * (0.2 * 0.3) + 2 * (0.5 * 0.3) = 0.12 + 0.3 = 0.42\)

Now, the surface area of the base:

\(L * W\\0.2 * 0.5 = 0.1\)

The total surface will be:

\(0.42 + 0.1 = 0.52\)

Therefore, the surface area of each planter box is 0.52 square meters.

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Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

We are given the following information

Toby eats tacos every 5 days.

Toby also drinks horchata every 6 days.

If Toby has horchata and tacos today how many days will he have to wait to enjoy his favorite treats on the same day again?

We need to find the least common multiple (LCM) of 5 and 6 days.

Multiples of 5 = 5, 10, 15, 20, 25, 30

Multiples of 6 = 6, 12, 18, 24, 30

As you can see, the least common multiple (LCM) of 5 and 6 is 30

Therefore, Toby has to wait for 30 days to enjoy his favorite treats on the same day again.

Answer:

50%

Step-by-step explanation:

Girls                                            Boys

total:                 59                     total:                              41

- Chemistry       35                   - Physics                           2

                       = 24                                    =                     39

                                                 - Chemistry ( 30 - 6 )      24

                                                                   =                     15

Total boys and girls for Biology = 35 + 15 = 50

% = 50/100*100

   = 50%

Answer:

B

Step-by-step explanation:

x + 3y = 2 → (1)

4x - 3y = 23 → (2)

adding (1) and (2) term by term will eliminate y

(x + 4x) + (3y - 3y) = 2 +  23

5x + 0 = 25

5x = 25 ( divide both sides by 5 )

x = 5

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)