please help:) please help:)​

Answer:

-3t+30

Step-by-step explanation:

The equation of remaining chocolate C  in terms of t is C =30 - 3t.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C =30 - 3t.

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Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.

Julio needs to prove that the two triangles have congruent sides in order to use the SAS Triangle Congruence Theorem. This means that he needs to show that one side of one triangle is congruent to a corresponding side of the other triangle and the same applies to the other two sides. This can be done by using methods such as measuring the sides, using algebraic equations, or using geometric constructions.

According to Julio statement, he has already constructed two right triangles to have congruent hypotenuses and one set of congruent legs, which means he has already proved that one side of one triangle is congruent to a corresponding side of the other triangle (hypotenuse) and one set of legs are congruent.

Therefore, Julio need to prove the remaining side of the triangle congruent to the corresponding side of the other triangle. Once he proves this, he can use the SAS Triangle Congruence Theorem to state that the two triangles are congruent.

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(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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Answer:

x = 7 √3 km

Step-by-step explanation:

Here, we want to get the value of x

As we can see, we have a right angled triangle with hypotenuse 14 km

we can use the Pythagoras’ theorem to get the value of x

Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides

Thus,

14^2 = x^2 + 7^2

x^2 = 196-49

x^2 = 147

x = 7 √3 km

The total distance covered during hiking is 15x + 10

Distance is the amount of space between two points.

Given that  Side a is 4x+1 side b:5x+4 side c:6x+5, hence:

Total distance = side a + side b + side c

Total distance = 4x + 1 + 5x + 4 + 6x + 5 = 15x + 10

The factor of the total distance is:

15x + 10 = 0

15x = -10

x = -2/3

The total distance covered during hiking is 15x + 10

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Answer: -53

Step-by-step explanation:

-|10-7•5+8•-4+2•2|=

-|10-7•5+8•(-4)+2•2|=

-|10-35+(-32)+4|=

-|-25-32+4|=

-|-25-28|=

-|-53|=

-(53)=-53

The cost of each cup of coffee at a kiosk is $ 4.

Let the cost of each cup of coffee is $ x.

A person buys 5 cup of coffee at a kiosk in the mall.

This question is related to unitary method problems.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Then, the cost of 5 cup of coffee is 5x.

Given that bill is under $20.

So the cost of 5 cup of coffee will be $20.

5x=20

x=20/5

x=4

Therefore,  the cost of each cup of coffee is $4.

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Answer: Each woman sold her apples at the rate of seven apples for I¢, and 3¢ each for the odd ones which were left over. this made it possible for each to receive the same amount, which is 20¢.

Step-by-step explanation:

given data:

20,

40,

60,

80,

100,

120,

140.

solution.

first woman 20 apples

= 2 + 3 * 6¢.

= 20¢.

second woman 40 apples

= 5 + 5 * 3¢.

= 20¢.

third woman 60 apples

= 8 + 4 * 3¢.

= 20¢.

fourth woman 80 apples

= 11 + 3 * 3¢.

= 20¢.

fifth woman 100 apples

= 14 + 2 * 3¢.

= 20¢.

sixth woman 120 apples

= 17 + 1 * 3¢.

= 20¢.

seventh woman 140 apples

= 20 * 1¢.

= 20¢.

To give your daughter $50,000 towards her college education in 15 years, you must set aside approximately $14,803.42 today.

To calculate the amount of money you need to set aside today, we can use the concept of future value of a lump sum. The future value is the amount of money an investment will grow to in the future, given a certain interest rate and time period.

In this case, we want to determine the present value (the amount you need to set aside today) to achieve a future value of $50,000 in 15 years, assuming an annual interest rate of 9 percent. The formula to calculate present value is:

Present Value = \(Future Value / (1 + Interest Rate)^T^i^m^e\)

Plugging in the values, we have:

Present Value = \($50,000 / (1 + 0.09)^1^5\)

Present Value ≈ $14,803.42

Therefore, you would need to set aside approximately $14,803.42 today in order to accumulate $50,000 for your daughter's college education in 15 years, assuming an annual interest rate of 9 percent.

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To show that the general term of the quadratic number pattern is given by \(tn = n^2 + 4n - 12\) , we need to find a quadratic expression that fits the given pattern.

Let's examine the given sequence: -7, 0, 9, 20. We notice that each term is increasing by a certain amount.

First, let's find the differences between consecutive terms:
0 - (-7) = 7
9 - 0 = 9
20 - 9 = 11

We observe that the differences between consecutive terms are not constant, so this indicates that the sequence is not linear.

To determine if the sequence follows a quadratic pattern, let's find the second differences:
9 - 7 = 2
11 - 9 = 2

The second differences are constant, which suggests a quadratic pattern.

Now, let's find the quadratic expression. We know that the general term of a quadratic sequence can be written as \(tn = an^2 + bn + c\), where a, b, and c are constants to be determined.

Using the given terms, we can form three equations:

1.\(For n = 1: -7 = a(1)^2 + b(1) + c\)
2. \(For n = 2: 0 = a(2)^2 + b(2) + c\)
3.\(For n = 3: 9 = a(3)^2 + b(3) + c\)

Simplifying these equations, we get:
1. a + b + c = -7
2. 4a + 2b + c = 0
3. 9a + 3b + c = 9

Solving this system of equations, we find a = 1, b = 4, and c = -12.

Therefore, the general term of the quadratic number pattern is given by\(tn = n^2 + 4n - 12\).

The general term of the quadratic number pattern is \(tn = n^2 + 4n - 12\).

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To determine whether the series k ¡(²-³)* 2√3 2k + 1 converges or diverges, we need to examine the behavior of its terms.

The series can be rewritten as:

∑((-1)^k * (2√3)/(2k + 1)) where k starts from 0

Let's analyze the terms of the series:

Term 0: (-1)^0 * (2√3)/(2(0) + 1) = 2√3/1 = 2√3

Term 1: (-1)^1 * (2√3)/(2(1) + 1) = -2√3/3

Term 2: (-1)^2 * (2√3)/(2(2) + 1) = 2√3/5

Term 3: (-1)^3 * (2√3)/(2(3) + 1) = -2√3/7...

The terms alternate in sign and decrease in magnitude as k increases.

Now, let's estimate the value of the sum of the series by including the first 5 terms:

Sum ≈ 2√3 - 2√3/3 + 2√3/5 - 2√3/7 + 2√3/9

To investigate the magnitude of the error, we can compare the absolute value of the residual term with the absolute value of the first omitted term, as stated in the given theorem.

The absolute value of the residual term can be approximated by the absolute value of the sixth term, |2√3/11|.

The absolute value of the first omitted term is the absolute value of the sixth term, |2√3/11|.

From this comparison, we can observe that the absolute value of the residual term is indeed less than or equal to the absolute value of the first omitted term, satisfying the condition for convergence of an alternating series.

The exact value of the sum of the series is not provided in the given information.

However, based on the terms of the series, it appears that the sum may be related to √3 or a multiple of √3.

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Answer:

According to the pythogorean theorem, this triangle is not a right triangle.

Answer:

steps: divide, multiply, subtract, and bring down.

Step 1. Calculate how many times the number outside the division bar goes into the first number inside the bar. Step 2. Put the answer on top of the bar. Step 3. Multiply the number outside the division bar by the number at the top of the bar.

To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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Answer:

13 and 32

Step-by-step explanation:

let one number be x

Then the other number is x + 19 , then

x + x + 19 = 45

2x + 19 = 45 ( subtract 19 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13

The 2 numbers are 13 and 13 + 19 = 32

Answer:

41.44

the tax is 2.88$

the tip is 5.88$

bill is 32.68

add equals 41.44$

Answer:

0.23076923

Step-by-step explanation:

To express 3/13 as a decimal, we divide the the numerator by the denominator.

This will give us:

3:13

=0.23076923

simplifying the above we get: 0.230769...

Answer:

61 degrees

Step-by-step explanation:

A triangle has a total of 180 degrees. We already know 80 and 39. 80+39 is 119. 180-119+61

Answer:

Step-by-step explanation:

In a triangle, the sides have a ratio of 3:7:10. If the perimeter is 210 feet, what is the length of the longest side in feet? (A) * 10.5 (B) 31.5 (C) (D) 105​

[210 : (3 + 7 + 10)] x 10 = 105 ft (your answer)

Step-by-step explanation:

the ratio tells us into how many units the total amount is split and then distributed among the different parts or members of the ratio.

3:7:10 means there are 3+7+10 = 20 units of length.

210 ft is the total of all lengths.

this is now split into these 20 units.

that means one unit of length for the ratio is

210/20 = 10.5 ft

the longest side is clearly the one with 10 units in the ratio.

so, it has

10×10.5 = 105 ft

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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If Bill does not really know if the concept will be viable, so he develops a limited menu and has friends and family fill out a questionnaire to gather information. Bill is using creation in action.

What is questionnaire?

A questionnaire is a type of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a set of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Although statistical analysis of the replies is frequently the goal of questionnaire design, this is not always the case.

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Answer:

12.5 hours

Step-by-step explanation:

divide 375 by 30 and you get how many hours it would take

12.5

Answer:

\(5x^{2} + 34x - 22\)

Step-by-step explanation:

-5x ( x + 6 ) = 4 ( x - 3 ) - 10

Distribute

\(-5x^{2} - 30x = 4x - 12 - 10\)

Simplify,

\(-5x^{2} -30x = 4x -22\)

Inverse operations;

\(-5x^{2} - 30x = 4x - 22\\ +30x +30x\\\\-5x^{2} = 34x - 22\\+5x^{2} +5x^{2}\\\\5x^{2} + 34x - 22\)

Answer:

5x^2 + 34x - 22 = 0

Step-by-step explanation:

-5x(x+6) = 4(x-3)-10

-5x^2 - 30x = 4x - 12- 10

-5x^2 - 30x - 4x + 22 = 0

-5x^2 - 34x + 22 = 0

5x^2 + 34x - 22 = 0

z + 16.2 ≤ 30

z ≤ 13.8

Answer:

-5

Step-by-step explanation:

\(- k^{2} - (8k - 3n) + 7n\\= -(-3)^{2} - (8(-3)-3(-2)) +7(-2) \\= -9 +18 -14\\=-5\)