On #10 i need help to solve this. please and thank you.

Answers

Answer 1

Answer: 10a. $f(x) = x - 4$
   $h(x) = √(x - 5)$
   $(f - h)(6) = (6 - 4) - (√(6 - 5))$
   $(f - h)(6) = 2 - √(1)$
   $(f - h)(6) = 2 - 1$
   $(f - h)(6) = 1$

10b. $f(x) = x - 4$
   $g(x) = (1)/(x - 3)$
   $(f * g)(x) = (x - 4)((1)/(x - 3))$
   $(f * g)(x) = (x - 4)/(x - 3)$
   Domain: (-∞, 3) ∨ (3, ∞) {x|x ≠ 3}
   Interval Notation: (3 < x < 3), (3 > x > 3)

10c. $g(x) = (1)/(x - 3)$
   $h(x) = √(x - 5)$
   $(g * h)(x) = ((1)/(x - 3))(√(x - 5))$
   $(g * h)(x) = (√(x - 5))/(x - 3)$

10d. $f(x) = x - 4$
   $g(x) = (1)/(x - 3)$
   $h(x) = \sqrt[3]{x - 7}$
   $h(x) = (f * g)(x)$
   $\sqrt[3]{x - 7} = (x - 4)((1)/(x - 3))$
   $\sqrt[3]{x - 7} = (x - 4)/(x - 3)$
   $(\sqrt[3]{x - 7})^(3) = ((x - 4)/(x - 3))^(3)$
   $x - 7 = ((x - 4)^(3))/((x - 3)^(3))$
   $(x - 3)^(3)(x - 7) = (x - 4)^(3)$
   $(x^(3) - 9x^2 + 27x + 27)(x - 7) = (x^(3) - 12x^(2) + 48x - 64)$
   $x^(4) - 16x^(3) + 90x^(2) - 216x + 189 = x^(3) - 12x^(2) + 48x - 64$
   $x^(4) + 90x^(2) - 216x + 189 = 17x^(3) - 12x^(2) + 48x - 64$
   $x^(4) + 102x^(2) - 216x + 189 = 17x^(3) + 48x - 64$
   $x^(4) + 102x^(2) + 189 = 17x^(3) + 264x - 64$
   $x^(4) + 102x^(2) + 253 = 17x^(3) + 264x$
   $x^(4) - 17x^(3) + 102x^(2) - 264x + 253 = 0$
   $x = 4\ or\ 8$

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I need help for algebra 2 for simplify form for example (3x-2i)(3x+2i)

Answers

Let's start...

$(3x-2i)*(3x+2i)$

$3x*3x+3x*2i-2i*3x-2i*2i$

$9x^2+6xi-6xi-4i^2$

$9x^2-4i^2$

we don't finish it yet...

$i^2=-1$

Let's replace it

$9x^2-4*(-1)$

$\boxed{\boxed{9x^2+4}}$

$(a+b)(a-b)=a^2-b^2\n\n (3x-2i)(3x+2i)=\n 9x^2-4i^2\n \n i=√(-1)\n i^2=-1\n \n 9x^2-4\cdot (-1)=9x^2+4$

Divide 7/24 by 35/48 and reduce the quotient to the lowest fraction

Answers

Given:
1st fraction - 7/24
2nd fraction - 34/48

Rules in dividing fractions:

1) Get the reciprocal of the 2nd fraction.
34/48 becomes 48/34

2) Multiply the 1st fraction to the reciprocal of the 2nd fraction
7/24 * 48/34 = 7*48 / 24*34 = 336/816

3) Simplify the fraction
336/816 ⇒ 112/272 ⇒ 56/136 ⇒ 14/34 ⇒ 7/17

336 ÷ 3 = 112
816 ÷ 3 = 272

112 ÷ 2 =   56
272 ÷ 2 = 136

56 ÷ 4 = 14
136 ÷ 4 =   34

14 ÷ 2 =    7
34 ÷ 2 =   17

7/24 ÷ 35/48 = 7/17

7/24 ÷ 35/48

= 7/24 × 48/35. 7 into 35 is 5. 24 into 48 is 2.

= 2/5

Please help with number 24 !!

Answers

The answer is F. y=2.5x. This is because if you multiply each pound (x) from the table by 2.5, you will get the cost (y). Hope this helps!

If y varies directly with respect to x, then
y = k*x
Solving for k, we get
k = y/x

Pick any column of (x,y) values and plug it into the equation
I'm going to pick (x,y) = (4,10)
k = y/x
k = 10/4
k = 5/2
k = 2.5

So the equation is y = 2.5*x or simply y = 2.5x
Answer is choice F

The diameter of a soccer ball is 8.65 inches what is the volume of the ball rounded to nearest hundredth

Answers

A soccer ball is an icosahedron with curved faces that is why it can be regarded as spherical. The volume of a sphere is calculated through,

Vs = 4πr^3/3

where Vs is the volume and r is radius. From the given, 8.65 in is the diameter which is 4.325 in in radius.

Vs = 4π(4.325^3)/3 = 338.88 in cubed.

Thus, the volume of the ball is 338. 88 in cubed.

Simplify 28 over 35