1 _______=5,280 feet

If tanA = 1/2 then evaluate cos A/sinA +sinA /1+cosA

Deffense [45]

Answer:

√5.

Step-by-step explanation:

Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse = √(1^2 + 2^2) = √5 (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).

so cos A = adjacent / hypotenuse = 2/√5.

and sin A = opposite / hypotenuse = 1 / √5

cos A / sin A = 2/√5 / 1/ √5 = 2.

sin A / (1 + cos A) = 1/√5 (1 + 2/ √5)

= 1 / √5 ( (√5 + 2) /√5)

= 1 / (√5 + 2)

So the answer is:

2 + 1 /(√5 + 2).

We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.

2 + 1 / (√5 + 2)

= 2(√5 + 2) + 1 / (√5 + 2 )

= { 2(√5 + 2) + 1 } / (√5 + 2)

Multiplying this by √5 - 2 / √5 - 2 we get:

(2(5 - 4) + √5 - 2) / (5 -4)

= 2 + √5 - 2 / 1

= √5.

3 0

3 years ago

If b

lys-0071 [83]

Answer:

$46.2^o$

Step-by-step explanation:

The correct question is

If b = 9 and c = 13, what is the measure of ∠A? (round to the nearest tenth of a degree)

The picture in the attached figure

we know that

In the right triangle ABC

$cos(A)=\frac{b}{c}$ ---> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

$cos(A)=\frac{9}{13}$

using a calculator

$A=cos^{-1}(\frac{9}{13})=46.2^o$

7 0

3 years ago

The graph of the function f(x) = (x +2)(x + 6) is shown

dalvyx [7]

The true about the domain and the range of the function is:

The domain is all real numbers, and the range is all real numbers

greater than or equal to -4 ⇒ 1st answer

Step-by-step explanation:

f(x) = (x + 2)(x + 6) is a quadratic function with 2 factors (x + 2) and (x + 6)

By multiplying its two factors we will find the form of the quadratic function

∵ (x)(x) = x²

∵ (x)(6) = 6x

∵ (2)(x) = 2x

∵ (2)(6) = 12

∴ f(x) = x² + 6x + 2x + 12

- By adding like terms

∴ f(x) = x² + 8x + 12

The quadratic function represented graphically by a parabola

Look to the attached figure

The x-coordinate of the vertex point of the parabola h = $\frac{-b}{a}$

where b is the coefficient of x and a is the coefficient of x²

∵ f(x) = x² + 8x + 12

∴ a = 1 and b = 8

∴ h = $\frac{-8}{2*1}=-4$

The y-coordinate of the vertex point is k = f(h)

∵ h = -4

∴ k = f(-4)

∴ k = (-4)² + 8(-4) = 12 = 16 - 32 + 12

∴ k = -4

∴ The vertex point of the parabola is (-4 , -4)

∵ The parabola is opened upward

∴ Its vertex is minimum point

∴ The minimum value of f(x) is y = -4

∵ The domain of the function is the values of x

∵ The range of the function is the values of y corresponding to the

values of x

∵ x can be any real numbers

∴ x ∈ R, where R is the set of real numbers

∴ The domain of f(x) is all real numbers

∵ The minimum value of f(x) is y = -4

∴ y can be any real number greater than or equal to -4

∴ y ≥ -4

∴ The range is all real number greater than or equal to -4

The true about the domain and the range of the function is:

The domain is all real numbers, and the range is all real numbers

greater than or equal to -4

Learn more:

You can learn more about quadratic function in brainly.com/question/1332667

#LearnwithBrainly

7 0

3 years ago

Solve by completing the square ( need it asap pls) x2+18x+81=-4 -don’t send link-

Sholpan [36]

Answer:

x=2.17

Step-by-step explanation:

$x^2$ +18x+81=-4

-81 -81

$x^2$ +18x= -85

/18 /18

$x^2$ = -4.7

$\sqrt{x^2}$ = $\sqrt{-4.7}$

x= 2.17

I hope this helps :) (if it does, brainliest, please??)

6 0

3 years ago

Need help plzzzz will medal and fan

andriy [413]

The answer is f(x)=x²+2x when evaluated with -3 gives you the value of 3

Let's check all functions.
1. The function f(x)=x²+2x when evaluated with 3 gives you the value of 3:
Evaluated with x means that x = 3.
f(3) = 3² + 2 * 3 = 9 + 6 = 15
15 ≠ 3, so, this is not correct.

2. f(x)=x²-3x when evaulated with -3 give you the value of 3
Evaluated with -3 means that x = -3.
(f-3) = (-3)² - 3 * (-3) = 9 + 9 = 18
18 ≠ 3, so, this is not correct.

3. f(x)=x²+2x when evaluated with -3 gives you the value of 3
 Evaluated with -3 means that x = -3.
f(-3) = (-3)² + 2 * (-3) = 9 - 6 = 3
3 = 3, so this is correct.

4. f(x)=x²-3x when evaluated with -3 gives you the value of 3
Evaluated with 3 means that x = 3.
f(3) = (3)² - 3 * 3 = 9 - 9 = 0
0 ≠ 3, so this is not correct.

6 0

4 years ago

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