Mathematics: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. Consider the given table. The “?” in the table represents the number (blank) because the average rate of change on every interval of the function is (blank).

Type the correct answer in each box. Use numerals

Ответ:

shanicet047ox9ff6

28.01.2022

The answers to the blanks are:

381/3

The “?” in the table represents the number 38 because the average rate of change on every interval of the function is 1/3.

Step-by-step explanation:

How you can see in the table, after the first values [x=-2, f(x)=5], each time that x add 1, f(x) add 3, (that is the reason why the average rate is 1/3), how you can see below:

2. x = 2 (were added 4 to the first number -2)

f(x) = 17 (were added 12 to the first number 5)

3. x = 5 (were added 3 to the second number 2)

f(x) = 26 (were added 9 to the second number 17)

4. x = 9 (were added 4 to the third number 5)

How in the last column were added 4, you must multiply this value by 3 (remember the average rate), so 4*3 = 12, now:

f(x) = 38 (were added 12 to the third number 26)

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Ответ:

robloxlover1987

30.01.2022

Mathematics

1) The conjugate for $6-7\cdot \sqrt{3}$ is $6+7\cdot \sqrt{3}$ .

2) -111

3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.

Step-by-step explanation:

1) A radical number of the form $r = a + b\sqrt{c}$ , $\forall \,a,b,c\in \mathbb{R}$ , where the first component is a non-radical real number which acts as a "pivot" and the second component is the radical component, which generates a "displacement" from pivot.

The conjugate of is a real number $s = a - b\sqrt{c}$ , $\forall \,a,b,c\in \mathbb{R}$ , which that is "pivot" plus "displacement" in the direction opposite to that of . We proceed to complement this explanation with the image attached below.

Then, the conjugate for $6-7\cdot \sqrt{3}$ is $6+7\cdot \sqrt{3}$ .

2) We proceed to performed all the need algebraic operation until result is found:

1) $(6+7\sqrt{3})\cdot (6-7\sqrt{3})$ Given

2) $6\cdot (6-7\sqrt{3})+7\sqrt{3}\cdot (6-7\sqrt{3})$ Distributive property

3) $6\cdot [6+(-7)\cdot \sqrt{3}]+7\cdot \sqrt{3}\cdot [6+(-7)\cdot \sqrt{3}]$ Definition of subtraction/ $-a\cdot b = (-a)\cdot b$

4) $6\cdot 6 +[6\cdot (-7)]\cdot \sqrt{3}+(6\cdot 7)\cdot \sqrt{3}+[7\cdot (-7)]\cdot (\sqrt{3}\cdot \sqrt{3})$ Distributive, associative and commutative properties

5) $36 +(-42)\cdot \sqrt{3}+42\cdot \sqrt{3}+(-49)\cdot 3$ Definition of multiplication/ $-a\cdot b = (-a)\cdot b$ /Definition of square root

6) $[36 +(-147)]+\sqrt{3}\cdot [42+(-42)]$ Commutative, associative and distributive properties/ $-a\cdot b = (-a)\cdot b$

7) $-111+\sqrt{3}\cdot 0$ Definition of subtraction/Existence of additive inverse

8) -111+0 $a\cdot 0 = 0$

9) Modulative property/Result

3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.

1)Identify the conjugate for 6 – 7√3 and explain your reasoning.

2)Multiply the radical expression

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. Consider the given table. The “?” in the table represents the number (blank) because the average rate of change on every interval of the function is (blank).

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