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3 years ago

G(x)=-x^2-1-2x f(x)=x+5 Find (g-f)(x)

Mathematics

1 answer:

nikitadnepr [17]3 years ago

3 0

(g-f)(x) is x² - 3x - 6

<u>Step-by-step explanation:</u>

Step 1:

Given g(x) = x² - 1 - 2x, f(x) = x + 5. Find (g-f)(x)

(g-f)(x) = x² - 2x - 1 - (x + 5) = x² - 2x - 1 - x - 5 = x² - 3x - 6

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The perimeter of a rectangle is 30.8 km and it’s diagonal length is 11 km. Find it’s length and width

blsea [12.9K]

Answer:

Length of the rectangle is 15.0325 km and width is 0.3765 km.

Explanation:

Given:

Perimeter of a rectangle = 30.8 km

Length of diagonal of rectangle = 11 km

To find:

The length and width of rectangle=?

Solution:

Lets assume length of the rectangle = x km

And assume width of the rectangle = y km

Lets first create equation using given perimeter

perimeter of rectangle = 2 ( length + width )

=> 30.8 km = 2 ( x + y )

=> $x + y = \frac{30.8}{2}$

=> y = 15.4 – x ------(1)

As diagonal and two sides of rectangle forms right angle triangle whose hypoteneus is diagonal ,

=> $length^2 + width^2 = diagonal^2$

=> $x^2 + y^2 = 11^2$

=> $x^2 + y^2 = 121$

On substituting value of y from (1) in above equation we get

=> $x^2 + (15.4-x)^2 = 121$

=> $x^2 + (15.4)^2 + x^2 – 2 x 15.4 \times x = 121$

=> $2x^2-30.8x + 237.16 -121 = 0$

=> $2x^2-30.8x + 116.16 = 0$

Solving above quadratic equation using quadratic formula

General form of quadratic equation is

$ax^2 +bx +c = 0$

And quadratic formula for getting roots of quadratic equation is

$x= \frac{ -b\pm\sqrt{(b^2-4ac)}}{2a}$

As equation is $2x^2-30.8x + 116.16 = 0$ , in our case

a = 2 , b = -30.8 and c = 116.16

Calculating roots of the equation we get

$x=\frac{ -(-30.8)\pm\sqrt{(-30.8)^2-4(2)( 11)} } {(2\times2)}$

$x=\frac{30.8\pm\sqrt{(948.64-88)}}{4}$

$x=\frac{30.8\pm\sqrt{860.64}}{4}$

$x=\frac{(30.8\pm29.33)}4$

$x=\frac{(30.8+29.33)}{4}$

$x=\frac{(30.8-29.33)}{4}$

=> x = 15.0325 or x = 0.3675

As generally length is longer one ,

So x = 1.0325

From equation (1) y = 15.4 – x = 0.3765

Hence length of the rectangle is 15.0325 km and width is 0.3765 km.

6 0

3 years ago

Which expression is equivalent to (15²)(15^-7)?

Zanzabum

Answer:

there is no answer

Step-by-step explanation:

If you multiply 15^x by 15^y, the answer is 15^(x+y) so 2 plus -7 is negitive 5.

but there is no answer equal to this.

4 0

2 years ago

Will mark the brainliest

Sati [7]

Answer:

B. $60x^8$

Step-by-step explanation:

$4x^2\sqrt{5x^4} \cdot 3\sqrt{5x^8} =$

$= 4x^2 \times 3 \sqrt{5x^4 \times 5x^8}$

$= 12x^2 \sqrt{25x^{4+8}}$

$= 12x^2 \sqrt{25} \sqrt{x^{12}}$

$= 12x^2 \times 5 \times x^6$

$= 60x^8$

6 0

2 years ago

10 points

oee [108]

Answer:

x = 240 feet

Step-by-step explanation:

It is given that,

The angle of depression is 30 degrees from the bottom of the boat to a deep sea diver at the depth of 120 ft.

We need to find the distance x the diver must swim up to the boat. It can be calculate by applying trigonometry as follows :

$\sin30=\dfrac{120}{x}\\\\x=\dfrac{120}{\sin30}\\\\x=240\ \text{feet}$

So, the distance the diver must swim up to the boat is 240 feet.

6 0

3 years ago

Can someone help me with this problem please

salantis [7]

Domain: f (x) is the set of all values for which the function is defined
range: the set of all values that f takes
hope this helps

4 0

3 years ago

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