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3 years ago

What is the measure of an angle that is eight times its supplement?

1 answer:

3 0

Remark
Supplementary angles = 180°

Givens
Let the supplement = x
Let the original angle = 8x

Formula
x + 8x = 180°

Solve
9x = 180° Divide by 9
x = 180/9
x = 20

Answer
The original angle = 8*20 = 160°
The Supplement = 20°

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

3 years ago

Find the solution of the square root of the quantity of x plus 2 plus 4 equals 8, and determine if it is an extraneous solution

Iteru [2.4K]

Consider the equation:

$\sqrt{x+2}+4 = 8$

Subtracting '4' from both the sides of the equation, we get as

$\sqrt{x+2}+4-4= 8-4$

$\sqrt{x+2}= 4$

Squaring on both the sides of the equation, we get

$(\sqrt{x+2})^2 = (4)^2$

$x+2 = 16$

Subtracting '2' from both the sides of the equation, we get

$x+2-2=16-2$

x=14

Since, An extraneous solution is a solution that arises from the solving process that is not really a solution at all. But, in this equation x=14 is the solution of the given equation.

Hence, it is not an extraneous solution.

4 0

3 years ago

Read 2 more answers

Please find angle q

mars1129 [50]

Hello!

75 + 90 + 79 + q = 360
q = 360 - 244 = 116

Stay safe!

4 0

3 years ago

Giving brainliest for help plz

Kryger [21]

Answer is B.

Thanks!!

5 0

3 years ago

Read 2 more answers

Ten less than 3 times a number is the same as that number increased by 4

Olenka [21]

3x - 10 = x + 4 <== ur equation

three times a number.....3x...with the x representing the number
ten less....3x - 10
is the same as...means =
that number (x) increased by 4....x + 4
so we have 3x - 10 = x + 4...

3x - 10 = x + 4
3x - x = 4 + 10
2x = 14
x = 14/2
x = 7....and that number is 7

3 0

3 years ago