Find the middle term of ([tex]( x^{2}+2) ^{20}
[/tex]

Answer:Sample answer: Using a multiplication table, you would see that 6 and 15 are multiples of 3 by factors 2 and 5. You would also see that 14 and 35 are multiples of 7 by factors 2 and 5.

The required equivalency of the ratios 6:14 and 15:35 is 3 / 7 = 3 / 7.

Given that,
To determine that 6:14 is equivalent to 15:35 using a multiplication table.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
the given ratios are,
1) 6 : 4 = 6/4 = 2* 3/ 2 *7
2) 15:35= 15 / 35 = 5 * 3 / 5 *  7

Implies both the ratios are equivalent, by
6 : 14 = 15 : 35
2[ 3 : 7] = 5 [ 3 : 7 ]

Thus, the required equivalency of the ratios 6:14 and 15:35 is  3 / 7 = 3 / 7.

Learn more about ratio here:

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In the number 474, the 4 in the ones place is less than the value of the 4 in the hundreds place by a factor of 100 because each position to the left in the place value system is worth ten times more than the one to its right.

The question deals with the concept of place value in mathematics. Specifically, it requires understanding how the value of a digit changes based on its position within a number. In the number 474, the 4 in the ones place has a value of 4, whereas the 4 in the hundreds place has a value that is 100 times greater, since each move to the left in place value represents a multiplication by 10. Therefore, the 4 in the ones place is less than the value of the 4 in the hundreds place. Here's a simple breakdown of the place values in the given number 474:

Since 1 is less than 100, the 4 in the ones place is worth less than the 4 in the hundreds place by a factor of 100.

The value of the 4 in the ones place is 10 times the value of the 4 in the hundreds place.

The 4 in the ones place is 10 times the value of the 4 in the hundreds place.

Answer is C but if its on grad point your answer is 0.5(2)^x

Final answer:

To find the side lengths of the right triangle, we let the shorter leg be x cm, resulting in the longer leg and hypotenuse being (x + 4) cm and (x + 8) cm, respectively. Using the Pythagorean theorem, we establish the equation x² + (x + 4)² = (x + 8)², then solve for x to determine the side lengths.

Explanation:

The problem involves solving for the lengths of the sides of a right triangle using the Pythagorean theorem. Let the shorter leg of the triangle be x cm. According to the problem statement, the longer leg would then be x + 4 cm, and the hypotenuse would be x + 8 cm. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Using the theorem we can set up the equation:

x² + (x + 4)² = (x + 8)²

Solving for x will give us the lengths of the sides of the triangle:

Answer:

Option A - [tex]W=\frac{P}{2}-L[/tex]

Step-by-step explanation:

Given : The formula for the perimeter of a rectangle is P=2(L+W).

To find : Solve for W ?

Solution :

The formula for the perimeter of a rectangle is

[tex]P=2(L+W)[/tex]

Multiply,

[tex]P=2L+2W[/tex]

Subtract 2L both side,

[tex]P-2L=2W[/tex]

Divide by 2 both side,

[tex]W=\frac{P-2L}{2}[/tex]

or [tex]W=\frac{P}{2}-L[/tex]

Therefore, Option A is correct.

The correct answer is: c. 4. In some cases, a fourth-degree polynomial with five terms could have at most 4 different linear factors.

To understand how many different linear factors a fourth-degree polynomial with five terms could have at most, let's consider the Fundamental Theorem of Algebra, which states that a polynomial of degree (n) has exactly (n) complex roots, counting multiplicity. For a fourth-degree polynomial, this means it can have at most 4 linear factors, as each linear factor corresponds to a root.

However, the polynomial could have repeated roots, reducing the number of distinct linear factors. If all four roots are distinct, then there will be 4 different linear factors. But if one or more roots are repeated, the number of different linear factors will decrease. The polynomial could have fewer than 4 distinct linear factors if it has repeated roots.

Complete Question:

A fourth degree polynomial with five terms could have, at most, how many different linear factors?

a. 3

b. 2

c. 4

d. 5

Answer: The measure of angle a is 90-25=65° and the measure of angle be is 25°.

Step-by-step explanation:

Let the two complementary angles be 'a' and 'b'.

So, the sum of two complementary angles is 90°.

So, it becomes,

[tex]a+b=90^\circ---------------(1)[/tex]

First angle is 15 less than twice the measure of the second angle.

So, it becomes,

[tex]a=2b-15-------------(2)[/tex]

Put the equation (2) in equation (1), we get

[tex]a+b=90^\circ\\\\2b-15+b=90^\circ\\\\3b+15=90^\circ\\\\b=90-15\\\\3b=75^\circ\\\\b=\dfrac{75}{3}\\\\b=25^\circ[/tex]

Hence, the measure of angle a is 90-25=65° and the measure of angle be is 25°

x = 35/sin(40) = 54.4503

 round answer as needed.

Answer:

3/14

Step-by-step explanation: