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3 years ago

Someone, please help !! these are direct and inverse variations, algebra 2. i need them asap !

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

3 0

Answer:

3, 20, 2, and 2.5

Step-by-step explanation:

For each question, they gave you an x and y value. If you substitute them into the equation and then solve for k, you get your answer.

On the first one, x is 12 and y is 1/4. If you put those into the equation they gave you y = k/x, you get 1/4 = k/12

3/12 is 1/4 so the first k is 3.

Second one y = k/x. x is 4 and is 5. So 5 = k/4

20/4 is 5, so the second k is 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

Using first principle, this gives:

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

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

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

$S(1) = 1 + 1$

$S(1) = 2$

Hence, the smallest sum is 2

3 0

3 years ago

The function f is defined by f(x) = x + 3 / 4x - 5 . Find f(x+3).

natali 33 [55]

Answer:

x+6 / 4x-5

Step-by-step explanation:

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3 years ago

Tangent is positive in quadrants I and IV only. True or False

zhannawk [14.2K]

Answer:

The statement is false

Step-by-step explanation:

we know that

$tan(x)=\frac{sin(x)}{cos(x)}$

The tangent function will be positive when the sine function and the cosine function have the same sign

In the first quadrant the tangent function is positive

In the third quadrant the tangent function is positive

The statement is false

6 0

3 years ago

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What value of c makes the trinomial below a perfect square x2 + 7x + c?

Daniel [21]

We have that
x² + 7x + c
Group terms that contain the same variable
(x² + 7x )+ c
Complete the square. Remember to balance the equation
(x² + 7x+3.5² )+ c-3.5²

Rewrite as perfect squares

(x+3.5)²+ c-3.5²
so
c-3.5² must be zero
c-3.5²=0------- c=3.5²------> c=12.25

the answer is
the value of c must be 12.25

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3 years ago