help me pls i need it fastest for my math project !!!!!! please help

For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.

An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.

Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.

Let, n = 0.

Therefore,

7⁴ - 7⁰.

= 2401 - 1.

= 2400.

= 30×80, Divisible by 30.

Similarly for n = 1 we have,

7⁵ - 7¹.

= 16807 - 7.

= 16800.

= 30×560.

Hence by induction, the cycle will continue.

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Answer: To model the problem with a division equation, we can write 46 ÷ 7 = x, where x represents the number of swimmers that each lane will have.

To solve the equation using repeated subtraction, we can subtract 7 from 46 several times until we reach a number that is less than 7. The number of times we subtract 7 will give us the number of swimmers each lane will have. Here's one way to do it:

46 - 7 = 39

39 - 7 = 32

32 - 7 = 25

25 - 7 = 18

18 - 7 = 11

11 - 7 = 4

As you can see, we are able to subtract 7 from 46 a total of 6 times before we get a number less than 7. This means that each lane will have 6 swimmers, and the remaining 4 swimmers will practice diving. So each lane will have 6 swimmers.

So the equation 46 ÷ 7 = 6, and also by repeated subtraction method it shows the same result of 6 swimmers each lane.

Step-by-step explanation:

The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over the x-axis, (x, -y).

Given, A function f(x) = x².

Now, p(x) = f(x + 3).

p(x) = (x + 3)² and it is a transformed function to the parent function f(x).

Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.

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a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.

b) Based on the above, the best interest rate the borrower could get is 8%.

Many factors are considered in determining the interest rate for a loan.

Some of the factors include:

We know that the longer the term of a loan, the higher the interest rate charged.  This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.

Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.

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Answer:

Step-by-step explanation:

As she is baking cookies = 3/20

she egave it to her neigbour = 7/20

Remaining = ?

R = 3/20 -7/20 = -1/5

Answer:

37.04%

Step-by-step explanation:

To find the percentage increase in the value of Tessa's stock, we need to calculate the difference between the original price and the current price, and then divide that difference by the original price, and multiply by 100 to express the result as a percentage.

Here is the calculation:

percentage increase = ((284.96 - 208.00) / 208.00) * 100

= (76.96 / 208.00) * 100

= 37.04 * 100

= 37.04%

So Tessa's stock has increased in value by 37.04%.

Answer:

37 % increase

Step-by-step explanation:

To find the percentage increase, take the new amount and subtract the original amount

284.96 -208 =76.96

Divide this by the original amount

76.96/208=.37

Change the decimal form to a percent

.37 * 100% = 37 %

On solving the provided question we can say that - The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.

The order of rotational symmetry is the maximum number of rotations that a geometry may fit in. 360°A°, where A° is the smallest angle by which a figure may be rotated from its rotated shape to match its original shape, represents the degree of rotational symmetry. (180 degrees) A shape's degree of rotational symmetry is determined by how many times a perfect circle may be turned while maintaining its appearance. Only when a triangle is back in its original beginning position will a full 360° revolution appear the same.

If a geometric figure maps onto itself when rotated around an angle at its center, it possesses rotational symmetry.The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.

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Answer:

Step-by-step explanation:

Given

[tex]x=1-sin(a)\\y=1+cos(a)[/tex]

Solve for [tex]a[/tex] in the second equation.

[tex]y=1+cos(a)[/tex]

[tex]y-1=cos(a)[/tex]

[tex]a=cos^{-1}( y-1)[/tex]

Insert our answer for [tex]a[/tex] into the first equation.

[tex]x=1-sin(a)[/tex]

[tex]x=1-sin(cos^{-1}( y-1))[/tex]

[tex]cos^{-1}=arccos[/tex]

[tex]x=1-sin(arccos( y-1))[/tex]

Lets simplify [tex]1-sin(arccos( y-1))[/tex]

A piece of graph paper would be helpful in my opinion.

Here is how I would go about doing so

Draw a triangle in the plane with vertices [tex](y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)[/tex] and the origin.

[tex]arccos(y-1)[/tex] is is the angle between the positive x-axis and the ray beginning at the origin and passing through [tex](y-1,\sqrt{1^2-(y-1)^2})[/tex]. Therefore [tex]sin(arccos(y-1))[/tex] is [tex]\sqrt{1-(y-1)^2}[/tex]

Now we have

[tex]x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)[/tex]

We can write [tex]1[/tex] as [tex]1^2[/tex]. Since both terms are now perfect squares, we can factor using the difference of squares formula.

[tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=1[/tex] and [tex]b=y-1[/tex]

[tex]x=1-\sqrt{(1+y-1)(1-(y-1))}[/tex]

After simplifying we get

[tex]x=-\sqrt{y(-y+2)}+1[/tex]

[tex]x=-\sqrt{y(-y+2)}+1[/tex]

[tex]a=arccos(y-1)[/tex]

I think this is what your question was. If not let me know.

So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

A. 2+3 × 4 = 22 +12 is not a true statement, because the order of operations is not followed, multiplication should be done before addition.

B. z+zx9 = 9z is not a true statement, because it is not clear what the operation is between z and x, and what the operation is between x and 9

C. -8y + 4.3y + 3.7 = 0 is a true statement because it is a linear equation with one variable y, it represents a straight line.

D. 12-1.8b+ 1.8b = 1.8b is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.

E. m8+7(8) = m is not a true statement, as it seems to be a mathematical manipulation of one side of the equation to the other, but it doesn't seem to make sense mathematically.

So the only true statement among the options is C. -8y + 4.3y + 3.7 = 0

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By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

What is the value of 1meter in terms of centimeter ?

1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .

Given,

1 meter= 3.28 feet

1 Liter= 0.26 gallons

1 kilogram = 2.20 pounds

we know that ,

1yard = 0.0009144 km

so ,

26.794 yard = 26.794*0.0009144 km

= 0.024500

Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .

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Answer:

Step-by-step explanation:

20)63(3

    -60

   -------

        3

so every children gets 3 toys but 3 toys are left which can be distributed among 3 children.

so 3 children get 1 toy more.

Hence 3 children get 3+1=4 toys (each)

Answer: 240 Calories are from Carbohydrates

Step-by-step explanation:

First, we will convert 80% into the decimal 0.8, then we will multiply this by the amount of total calories in the drink to create the following equation:

300 * 0.8 = 240 Calories.

Work Shown:

[tex]\text{y} = \frac{1}{4}\text{x}+3\\\\\text{y}-3 = \frac{1}{4}\text{x}\\\\\frac{1}{4}\text{x}=\text{y}-3\\\\\text{x}=4(\text{y}-3)\\\\\text{x}=4\text{y}-12\\\\[/tex]

Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.

Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either contingent equations or identities are categories for equations. An identity holds true for whatever value of the variables.

given

x+y=7

2x-y=-1

8x=20

x= 5/2

-4y = -8

y = 2

Combination of variables x+y=7. 2x-y=-1 has (5/2, 2) as its solution. For each value of the variables, an identity is true.

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Answer:

5

Step-by-step explanation:

Answer:I believe it would be 5

Step-by-step explanation:

because if you do it on a table chart you reach five first as the same number

The value of x is 18.

An equation is an expression that shows the relationship between two or more numbers and variables.

First, both angles shown are equal to each other.

5x + 5 = 95

Next, the opposite side of the equation to isolate x value (5x).

5x + 5 (-5) = 95 (-5)

5x = 90

Finally, we need to divide both sides of the equation by 5.

5x / 5 = 90 / 5

x = 18

The final answer: x = 18

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Answer:

The length of the diagonal is 12.53

Step-by-step explanation:

Since we have a rectangle, the diagonal is the hypotenuse of a right triangle. So we can use Pythagorean Theorem.

a^2 + b^2 = c^2

We know the two legs are 6 and 11, so we can find the hypotenuse (which is the diagonal) see image.

See image.

Answer:

a. Their down payment is 25% of the purchase price.

Calculation:

Down payment ÷ Purchase price = Percentage

$35,000 ÷ $140,000 = 0.25 = 25%

b. A $7,000 down payment would be 5% of the purchase price.

Calculation:

Down payment ÷ Purchase price = Percentage

$7,000 ÷ $140,000 = 0.05 = 5%

Answer:

Step-by-step explanation:

Answer:

x

)

=

2

x

4

−

3

x

+

3

f(x)=2x

4

−3x+3, then what is the remainder when

f

(

x

)

f(x) is divided by

x

−

1

x−1?

Therefore , the solution of the given problem of triangle comes out to be the distance of  the drone from the start point is  13feet.

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Height of drone  = 5 feet

and  distance of drone covered is 12 feet

Thus ,

to calculate the distance of  the drone from the start point

distance can be represented as H

Since it forms right triangle.

By using pythagoras theorem,

=> 5² + 12² = H²

=> H² = 169

=> H = √169

=> H = 13

Therefore , the solution of the given problem comes out to be the distance of  the drone from the start point is  13feet.

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Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given  :

=> -x-y=-2

=>  5x + 7y= 28

So ,

=>x = 2-y

thus,

=> 5(2-y) + 7y =28

=> 10 -5y + 7y =28

=> 10 -2y = 28

=> -2y = 18

=> y =-9

and

=> x  = 2 - (-9)

=> x  = 11

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

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If you have $82 in your bank account and you write checks for $54, $35, and $15, then the total amount you have written in checks is $54 + $35 + $15 = $104.

So the remaining balance is $82 - $104 = -$22, which means you are now overdrawn.

After you deposit $35 and $42, the new balance will be $82 - $22 + $35 + $42 = $155

So after the deposit, the account balance is $155

It is important to keep track of your bank account balance, if you do not have enough funds in the account and the check you wrote is cashed the bank will bounce the check and incur additional fees.

Answer: 7x+10

Step-by-step explanation:

combine like terms

x+3x+x+2x+2+5+3

7x+10

Answer:

Step-by-step explanation:

Simplification of : x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10

First: find the (x) and collect them, put them in the bracket (to ensure the + or -)

(x + 3x + x + 2x) + 2 + 5 + 3

=  7x + 2 + 5 + 3

Then we add up the numbers

= 7x + 10

This is the end result.

x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10

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Answer: This system of equations can be represented in matrix form as

| -1 | 650 | 175 |

| 75 | -120 | -25080 |

This matrix is called the augmented matrix of the system of equations. The first and second column of this matrix represent the coefficients of the variables x and y, respectively, in the system of equations. The third column represents the constant terms of the equations.

You can use a method such as Gaussian elimination or Gauss-Jordan elimination to solve the system of equations.

The Gaussian elimination method, you would use elementary row operations to transform the matrix into an echelon form or reduced row echelon form. Then you can back-substitute the variables with their values.

Also, the Gaussian-Jordan elimination is similar to Gaussian elimination, but it keeps continuing the elimination process until the matrix becomes an Identity matrix(A matrix with 1 on diagonal and 0 everywhere else) The values on the diagonal of the matrix will give you the solution of the variables.

Step-by-step explanation:

Answer:

It is the first answer,

Step-by-step explanation:

The hypotenuse is always the longest side and opposite of the right angel.  Side b is the adjacent side to J and c is the opposite side of J.

Answer:

  8.4

Step-by-step explanation:

You want to know the value of x that satisfies 1.2/4 = x/28.

The equation ...

  x/28 = 1.2/4

can be solved in one step by multiplying by 28.

  x = 28(1.2/4) = 8.4

The value of x is 8.4.

__

Additional comment

The fraction involving x can be cleared by multiplying by its denominator, effectively the inverse of the coefficient of x. This is the same way you solve any similar one-step equation.

Often, you are told to "cross-multiply" a proportion. Doing that gives you ...

  4·x = 28·1.2

Then you have to divide by 4 (multiply by the inverse of the coefficient of x) to find the value of x:

  x = 28·1.2/4 . . . . same as above.

That is, there is no need to multiply by 4, and then divide by 4. You can simply multiply by 28 and be done.

Answer:

8.4

Step-by-step explanation:

[tex]\frac{1.2}{4}[/tex] = [tex]\frac{x}{28}[/tex]

cross multiply to solve for x:

(1.2)(28) = 4x

4x = 33.6

x = 33.6/4 = 8.4

Answer:

The missing numbers are 74, 105, and 178.