Find the measure of each interior angle and each exterior angle of the following regular polygons. Show your work

Answer:

2.[tex]16a^2-4a+4a-1[/tex]

Step-by-step explanation:

We have to find the polynomial can be simplified to a difference of squares.

1.[tex]10a^2+3a-3a-16[/tex]

Combine like terms

[tex]10a^2-16[/tex]

10 in [tex]10a^2[/tex] is not a perfect square number  because when a number end with one zero then the number is not perfect square number.

Therefore, it can not be simplified to a difference of squares.

2.[tex]16a^2-4a+4a-1[/tex]

[tex]16a^2-1[/tex]

Combine like terms

[tex](4a)^2-(1)^2[/tex]

Hence, the polynomial can be simplified as difference of squares.

3.[tex]25a^2+6a-6a+36[/tex]

Combine like terms

[tex]25a^2+36[/tex]

[tex](5a)^2+(6)^2[/tex]

Hence, the polynomial can not be simplified as  difference of squares because the polynomial can be  simplified as sum of squares.

4.[tex]24a^2-9a+9a+4[/tex]

Combine like terms

[tex]24a^2+4[/tex]

[tex]24a^2+(2)^2[/tex]

[tex]24=2\times 2\times 3\times 2[/tex]

24 is not  a perfect square number because  when factorize 24 then 2 and 3 are not paired.

Hence, the polynomial can not be simplified as difference of squares.

The true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Let's analyze each statement:

1. The graph of [tex]\(y - \log(x-4)\)[/tex] is the graph of [tex]\(y - \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y - \log(x-4)\)[/tex] is the result of shifting the graph of [tex]\(y = \log(x)\) 4[/tex] units to the right, not down.

2. The graph of [tex]\(y = \log(x) - 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y = \log(x) - 4\)[/tex] represents a vertical translation of 4 units down from the graph of [tex]\(y = \log(x)\)[/tex], not left.

3. The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units up.

  This statement is true. Adding a constant term to a function vertically shifts the graph of the function by that amount. So, adding 4 to [tex]\(y = \log(x)\)[/tex] shifts it 4 units up.

4. The graph of [tex]\(y = \log(x+4)\)[/tex] is the graph of [tex]\(y = \log_2(x)\)[/tex] translated 4 units right.

  This statement is incorrect. The function [tex]\(y = \log(x+4)\)[/tex] represents a horizontal translation of 4 units to the left from the graph of [tex]\(y = \log(x)\).[/tex]

Therefore, the true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Question

Which statement is true?

The graph of Y - log(x-4) is the graph of y-log,(x) translated 4 units down.

The graph of Y = log: (x)-4 is the graph of y = log. (x) translated 4 units left.

The graph of y = log,(x)+4 is the graph of Y=log.(x) translated 4 units up.

The graph of y = log. (x+4) is the graph of y = log2 (x) translated 4 units right.

the first line in the chart has x as 0 and Y as 25

 this means the fixed amount would be $25

Answer:

$25

Step-by-step explanation:

because the first number in the chart is $25

hope this helps!

The surface area of the earth using the given formula is 51471.85 m².

The surface area of a solid can be defined as the area covered by its surface. There are two types of area for a solid exact and lateral.

The lateral area represents only the visible portion of the surface area while the exact area is the area of the total surface of the solid.

Given that,

The radius of earth r = 6.4 × 10⁶ m.

The area of a sphere is given as S = 4π × r².

Substitute the value of r to obtain,

S = 4π × (6.4 × 10⁶)²

  = 51471.85

Hence, the surface area of Earth is approximated as 51471.85 m².

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Let the length of the rectangle = x

since the perimeter is 24m then the width of rectangle is (12-x)m.

the area of rectangle is:
 A=x*(12-x)

A=-x^2+12x

x=-12/-2 =6:

Since the length is 6m the width will be: 12-6=6m

We conclude that this rectangle has the maximum area when its shape is square of side 6m.
We find the value of area for x=6m :

Area = 6^2 =36M^2

The term that you want is 5C2*p^2*q^3 representing 2 successes and 3 failures.  This term's value is

(5C2)(0.5^5) = 10*0.03125 = 0.3125 = P(2 successes in 5 trials) =31.3%

Answer:

d. Carrying a notebook and immediately recording all of her transactions in it.

Step-by-step explanation:

The correct answer is option D.

A bank statement is a document that is typically sent by the bank to the account holder every month, summarizing all the transactions of an account during the month.

Bank statements contain bank account information, such as account number and a detailed list of deposits and withdrawals.

Cassandra's best option would probably be carrying a notebook and immediately recording all of her transactions in it.

Since she does not like to do a lot of heavy thinking when she gets home, and tends to lose pieces of paper, this method is ideal because it would allow her to consolidate all her purchase records in one notebook, eliminating the need to carry receipts, and recording them immediately will make it so she can relax when she gets home.

Perhaps once a month, she can compile all of her notebook activity into a computer program and reconcile it to her bank statements. 

Hence, the correct option is D.

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Final answer:

A function is in simplified form when all unnecessary terms have been eliminated, subscripts are used appropriately, and it uses the most compact and standard notation possible. Always verify the reasonableness of the simplified function.

Explanation:

To determine when a function is in simplified form, several steps should be followed:

When you have eliminated all unnecessary terms and used standard conventions for simplification mentioned above, the function is considered to be in its simplest form. It is always good practice to check the answer to see if it is reasonable and does not violate any known principles or constraints.

The consecutive integers are 5 and 6.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

The sum of the reciprocals of two consecutive integers is 11/30.

Let the integers be n and n+1.

Then,

1/n + 1/n+1 = 11/30

{n + 1 + n}/n(n+ 1) = 11/30

30(2n+1 ) = 11(n²+n)

60n + 30 = 11n² + 11n

11n² - 49n - 30 = 0

(11n +6) (n-5) = 0

Only taking,

n = 5.

So, 5 and 6.

Therefore, 5 and 6 are the integers.

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[tex]4(x+2)=2(x+3)+2(x-1)\\\\use\ the\ distributive\ property:\ a(b\pm c)=ab\pm ac\\\\(4)(x)+(4)(2)=(2)(x)+(2)(3)+(2)(x)-(2)(1)\\\\4x+8=2x+6+2x-2\ \ \ \ |simplify\\\\4x+8=(2x+2x)+(6-2)\\\\4x+8=4x+4\ \ \ \ |-4x\\\\8=4\ FALSE!!!\\\\Answer:\ NO\ SOLUTION\ (x\in\O)[/tex]

Answer:

triangle given is not a right triangle

Step-by-step explanation:

Given:-

- The side lengths of a triangle are given as:

                                     24 , 32 , 42

Find:-

is it a right triangle? explain

Solution:-

- Any triangle which conforms to the pythagorean theorem can be classified as a right angle triangle.

- The Pythagorean theorem states that the square of the longest side length known as hypotenuse (H) should be equal to the sum of square of other two side lengths ( Perpendicular / opposite [ P ] and Base / Adjacent [ B] ).

- This can be mathematically expressed as:

                                     H^2 = P^2 + B^2

- From the given side lengths. The largest side length is hypotenuse H = 42. While P and B can be used interchangeably for the other two side lengths. So using the theorem we have:

                                     42^2 = 32^2 + 24^2

                                     1764 : 1024 + 576

                                    1764 ≠ 1600

- We see that the three side lengths of the triangle does not conform to theorem. So we can conclude that the triangle given is not a right triangle.

Since 1764 is not equal to 1600, the triangle is not a right triangle.

To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the sides as follows:

a = 24, b = 32, c = 42

Using the Pythagorean theorem:

c² = a² + b²

Plugging in the values:

42² = 24² + 32²

1764 = 576 + 1024

1764 = 1600

To find the coordinates of the vertices A'B'C' of the new triangle after translation and reflection, subtract 4 from the y-coordinate of each vertex and change the sign of the y-coordinate.

To find the coordinates of the vertices A'B'C' of the new triangle, we first translate the original triangle 4 units down. This means we subtract 4 from the y-coordinate of each vertex. So, the new coordinates of A', B', and C' are: A' (1, -3), B' (2, -1), and C' (5, -4).

Next, we reflect the translated triangle across the x-axis. To do this, we change the sign of the y-coordinate of each vertex. So, the final coordinates of A'B'C' are: A' (-1, 3), B' (-2, 1), and C' (-5, 4).

Answer:

0.039 on gradpoint

Step-by-step explanation:

I got it right on the test