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2 years ago

Given: f(x) = 3x² - 2x +1 and g(x) =x -4

Mathematics

1 answer:

Alja [10]2 years ago

3 0

Answer:

For finding f(g(x)) ~ (x - 4) = 3x^2 - 26x + 57

For finding g(f(x)) ~ g (3x^2 - 2x + 1) = 3x^2 - 2x - 3

Step-by-step explanation:

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A sector of a circle of 7cm has an area of 44cm².calculate the angle of the sector,correct to the nearest degree π =22\7

Hitman42 [59]

Answer:

$\theta=102.85^{\circ}$

Step-by-step explanation:

Given that,

The radius of circle, r = 7 cm

The area of sector, A = 44cm²

We need to find the angle of the sector. The formula for the area of sector is given by :

$A=\dfrac{\theta}{360}\pi r^2$

Solve for $\theta$ .

$\theta=\dfrac{360A}{\pi r^2}\\\\\theta=\dfrac{360\times 44}{\dfrac{22}{7}\times 7^2}\\\\\theta=102.85^{\circ}$

So, the angle of the sector is equal to $102.85^{\circ}$ .

7 0

3 years ago

Reduce 2/8 to the smallest form and 3/12 to the smallest form

iris [78.8K]

Answer:

1/4 for both

Step-by-step explanation:

2/8 -- you divide 2 by 2 you get 1, 8 divided by 2 is 4 -- 1/4

3/12 -- you divide 3 by 3 you get 1, 12 divided by 3 is 4 -- 1/4

** tip: what you do to one half of the fraction you have to do to the other

hope this helps!

4 0

3 years ago

A linear function models the height of a burning candle. Candle A comes out of the mold at 211 mm and is expected to be at 187

DerKrebs [107]

Answer:

(11.4 - 22.8) / (26 - 7)

-11.4 / 19 this is the rate at which it burns - the slope

h = (-11.4/19)t + b

22.8 = (-11.4/19)7 + b

22.8 = (-79.8/19) + b

22.8 = -4.2 + b

27 = b

h = (-11.4/19)t + 27

Substitute 15 for t to determine the height of the candle.

6 0

3 years ago

The product of 2 and a number minus 9 is 13

algol13

<h3>The value of the number is equal to 11.</h3>

2x - 9 = 13

Add 9 to both sides.

2x = 22

Divide both sides by 2.

x = 11

5 0

3 years ago

Need help with my homework

Volgvan

Answer:

$\displaystyle y=\frac{16-9x^3}{2x^3 - 3}$

$\displaystyle y=-\frac{56}{13}$

Step-by-step explanation:

Equation Solving

We are given the equation:

$\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}$

To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.

We have to make it in steps like follows.

Cube both sides:

$\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3$

Simplify the radical with the cube:

$\displaystyle x^3=\frac{3y+16}{2y+9}$

Multiply by 2y+9

$\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)$

Simplify:

$\displaystyle x^3(2y+9)=3y+16$

Operate the parentheses:

$\displaystyle x^3(2y)+x^3(9)=3y+16$

$\displaystyle 2x^3y+9x^3=3y+16$

Subtract 3y and $9x^3$ :

$\displaystyle 2x^3y - 3y=16-9x^3$

Factor y out of the left side:

$\displaystyle y(2x^3 - 3)=16-9x^3$

Divide by $2x^3 - 3$ :

$\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}$

ii) To find y when x=2, substitute:

$\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}$

$\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}$

$\displaystyle y=\frac{16-72}{16- 3}$

$\displaystyle y=\frac{-56}{13}$

$\mathbf{\displaystyle y=-\frac{56}{13}}$

8 0

3 years ago