Prove that for any natural n: a the number 7^(n+4) −7^n is divisible by 30.

The required solution for the inequality a + 5 > -7 is (-12, ∞).

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

a + 5 > -7

To find the solution for the inequality,

Simplify the inequality,

a + 5 > - 7

a > - 7 - 5

a > -12

The value of a is greater than -12, implies that,

The solution for the value of the given inequality is (-12, ∞).

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Answer:

B

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

like you said don't explain

Explanation:

You have a right triangle with legs of 11 and 60. The hypotenuse is unknown.

Use the pythagorean theorem to find the hypotenuse.

[tex]a^2 + b^2 = c^2\\\\11^2 + 60^2 = c^2\\\\121 + 3600 = c^2\\\\3721 = c^2\\\\c^2 = 3721\\\\c = \sqrt{3721}\\\\c = 61\\\\[/tex]

The ramp is exactly 61 inches long.

The three consecutive number are 17 , 18 and 19 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be = x

Let the second number be = ( x + 1 )

Let the third number be = ( x + 2 )

Now ,

A = 4 times the first decreased by the second is 12 more than twice the third

Substituting the values in the equation , we get

4x - ( x + 1 ) = 12 + 2 ( x + 2 )

On simplifying the equation , we get

4x - x - 1 = 12 + 2x + 4

3x - 1 = 16 + 2x

Subtracting 2x on both sides of the equation , we get

x - 1 = 16

Adding 1 on both sides of the equation , we get

x = 17

Therefore , the value of x is 17

Hence , the consecutive numbers are 17 , 18 and 19

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Answer:7 7/8. pounds.

Step-by-step explanation:

The answer is A (x,y) -> (2x, 2y) it is representing the dilation.

Dilation is a medical procedure that involves widening a part of the body, such as the cervix or esophagus, by stretching and enlarging it. This can be done for a variety of reasons, including to allow for the passage of a baby during childbirth or to facilitate the insertion of a medical instrument or device. Dilation is usually done using dilators, which are cylindrical tools with a tapered end that can be inserted into the body and then gradually increased in size.

Dilation is a geometric transformation that enlarges or reduces the size of a shape by a factor. In this case, the shape is enlarged, with the resulting shape being twice the size of the original black figure. This is represented by the equation A (x,y) -> (2x, 2y), where the x and y coordinates of each point in the figure are multiplied by two.

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Answer: 10 sides

Step-by-step explanation:

You can always use the given formula to calculate but I (personally) find it much easier to calculate the number of sides using the exterior angle.

To calculate the exterior angle, it is 180 - the interior angle.

In this example, the exterior angle would be 180-144 = 36°

Because it is a regular polygon, we know that all the angles in the shape are the same.

In all polygons, the exterior angles always add up to 360 degrees.

So divide 360 by 36 (the size of each exterior angle), and you get 10.

360/36 = 10

Answer:

not proportional

Step-by-step explanation:

0.2/2.6 is 1:13

0.3/3.6 is 1:12

The sum of the given equation is 7[tex]\sqrt[5]{x^{2} y}[/tex].

Given data :

4 ([tex]\sqrt[5]{x^{2} y}[/tex].) + 3 ([tex]\sqrt[5]{x^{2} y}[/tex].)

Add similar elements

= 7[tex]\sqrt[5]{x^{2} y}[/tex].

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Answer:

2.5 litres

Step-by-step explanation:

The scale factor of the dilation is 3

From the question, we have the following parameters that can be used in our computation:

Line segment AB = 12 units

After the dilation = 36 units

The scale factor of the dilation is then calculated as

Scale factor of the dilation = After the dilation/Line segment AB

Substitute the known values in the above equation, so, we have the following representation

Scale factor of the dilation = 36/12

Evaluate

Scale factor of the dilation = 3

Hence, the scale factor is 3

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Answer:

Step-by-step explanation:

An explanatory variable is what you manipulate or observe changes in  while a response variable is what changes as a result (e.g., reaction times). The words “explanatory variable” and “response variable” are often interchangeable with other terms used in research.

Answer:

1/a³

Step-by-step explanation:

(1/a)³ = 1³/a³ = 1/a³

Answer:

  c : d : u = 8 : 6 : 27

Step-by-step explanation:

Given c:d = 4:3 and d:u = 2:9, you want c:d:u.

To write the desired ratio, we need to convert the others so they have the same number of ratio units representing 'd'. That number can be the least common multiple of 3 and 2, which is 6. Knowing this, we can write ...

  c:d = 4:3 = 8:6

  d:u = 2:9 = 6:27

Then the desired ratio is ...

  c:d:u = 8:6:27

The unit rate for 4543.08 km in 52.4 hours is 86.7 km.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

4543.08 km = 52.4 hours

Divide 52.4 into both sides.

86.7 km = 1 hour

Thus,

The unit rate is 86.7 km.

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Using PEMDAS to resolve the trigonometric identity which involves trigonometric function, the value of tan A + tan B is 416 / 87

A trigonometric identity is an equation that is true for any value of the variables involved. These identities are useful in solving problems involving trigonometric functions. Examples include the Pythagorean identity, the sine and cosine addition formulas, and the double angle formulas.

In the given problem, we have a compound angle problem and we can solve it as;

tan A + tan B = [(tan A + tan B)] / [1 - tan A * tan B]

Substituting the values into the expression and solve;

tan A + tan B = [(7/24 + 15/8)] /[1 - (7/24)(15/8)]

Applying the rules of PEMDAS;

tan A + tan B = (13 / 6) / (29 / 64)

tan A + tan B = 416/87

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Answer:

Step-by-step explanation:

Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Here,

The midline equation is y = M+m /2

when a function has: o a max M AND a min m or o (if it does not have extrema) a bound above M and a bound below m, where M is the minimum bound above and m is the maximum bound below.

When one of the following conditions is true for a function, even though it has a bound below, there is no midline (even if it has a bound above)

It is solely constrained from above (or below)

Any line is midline if a function has the values (-∞, +∞)

Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .

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The number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .

What is area ?

Area can be defined as the total space taken by  a 2-dimensional surface or shape of an object.

Given

Jake has a floor that is 64 square feet.

He wants to tile the entire floor using large tiles that measure 3 feet by 5 feet.

The area of 3 feet by 5 feet could be  = 3 * 5 = 15 square meters.

number of tiles required to fill the space could be  = 64 / 15

that is 4.3 (approx )

Hence , the number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .

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On solving the provided question, we can say that - by formula of simple interest we have SI = [tex]2200 X 2 X 4/100 = > 17600/100 = > 176[/tex]

Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. For instance, he will only pay his portion of the 100% interest if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you lend money, you must charge interest. Most of the time, interest is expressed as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

here,

principal, p = 2200

rate, r = 2%

time, t = 4 rs,

so SI = P X R X T/100

SI -

[tex]2200 X 2 X 4/100\\17600/100\\176[/tex]

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Therefore , the solution of the given problem of ratio comes out to be  15:73 ratio simplified is 15/73.

A ratio or fraction in math displays how many times one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3 or decimal 1.333).

Here,

To simplify the ratio 15:73, we find the greatest common divisor of 15 and 73, and then we divide 15 and 73 by the greatest common divisor.

The greatest common divisor that you can use to simplify 15:73 is 1. Which means the answer to ratio 15:73 simplified is:

Here is the math to illustrate better:

15/1 = 15 and 73/1 = 73

Thus, 15:73 ratio simplified is 15/73

Therefore , the solution of the given problem of ratio comes out to be  15:73 ratio simplified is 15/73.

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Answer:

Step-by-step explanation:

ur STUP1d

The board can be rotated in 4 different ways (0, 90, 180, 270 degrees) and each of the four squares can be painted in 2 different ways (black or white). Since we can rotate the board, the order in which the squares are painted does not matter, so we must divide by the number of ways to rearrange the squares. So, there are (2^4) / 4 = 6 ways the board can be painted when we take rotations into account.

To calculate turnover, it is necessary to consider the departures and additions of people to the company in the period. Calculating turnover is quite simple: you need to add the number of admissions and the number of dismissals, then just divide by 2 and then divide by the total number of employees within your company.

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Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

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Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

Solving the equation the original cost of the shoes before the discount will be obtained as $385.

To find the original cost of the shoes before the discount, you can use the following equation:

original cost = final cost÷ (1 - discount percentage)

In this case:

original cost = $135 ÷  (1 - 0.65)

To find the final cost you need to multiply 135 by 1 - 0.65.

0.65 is the equivalent to 65% when it's represented as a decimal.

0.65 represents the proportion of the original price that was removed (65% or 0.65)

So:

original cost = $135 ÷ (1 - 0.65)

original cost = $135 ÷ (1 - 0.65) = $135 ÷  0.35 = $385

The original cost of the shoes before the discount was $385.

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If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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