Evaluate 15r+6 (60-r)for r =20,30 and 40. what conclusion can you draw

Mathematics

1 answer:

7nadin3 [17]3 years ago

6 0

15 (20)+6(60-20)= 240

15 (30)+6(60-30)=630

15(40)+6(60-40)=720

you can conclude that none of the numbers have anything in common except that they all end in a 0

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Please help.

denis23 [38]

9514 1404 393

Answer:

Angle 1 = 139°
Angle 2 = 41°
x = 29; exterior angle = 131°

Step-by-step explanation:

These problems let you make use of the fact that the sum of the remote interior angles is equal to the exterior angle.

1. 53° +86° = ∠1

139° = ∠1

2. ∠2 +92° = 133°

∠2 = 133° -92°

∠2 = 41°

3. (x +9)° +93° = (4x+15)°

87 = 3x . . . . . . . . . . . . . . . . subtract x+15°

29 = x . . . . . . . divide by 3

The exterior angle is ...

(4x +15)° = (4·29 +15)° = 131° . . . exterior angle

3 0

2 years ago

Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$