MATHEMATICS HIGH SCHOOL

A rectangular prism has a length of 2x^2+2x-24 over 4x^2+x, a width of x^2+x-6 over x+4, and a height of 8x^2+2x over x^2-9. For all values of x for which it is defined , express, in terms of x, the volume of the prism in simplest form.1. 4(x-2)
2. 2(x-2)
3.2(x+2)
4.4(x+2) please show work.

Answers

Answer 1
Answer: V=abc\n\nV=(2x^2+2x-24)/(4x^2+x)\cdot(x^2+x-6)/(x+4)\cdot(8x^2+2x)/(x^2-9)\nV=(2(x^2+x-12))/(x(4x+1))\cdot(x^2+3x-2x-6)/(x+4)\cdot(2x(4x+1))/((x-3)(x+3))\nV=2(x^2+4x-3x-12)\cdot(x(x+3)-2(x+3))/(x+4)\cdot(2)/((x-3)(x+3))\nV=2(x(x+4)-3(x+4))\cdot((x-2)(x+3))/(x+4)\cdot(2)/((x-3)(x+3))\nV=2(x-3)(x+4)\cdot(x-2)/(x+4)\cdot(2)/(x-3)\nV=2\cdot(x-2)\cdot2\nV=4(x-2)

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If y is the principal square root of 5 what must be true?

Answers

Since every square root has a positive and a negative solution, for example:

√(9) = -3 or +3

The principal square root defines only the positive solution (between the two);

Therefore: if y is the principal square root of 5, then it must be the positive square root of 5, not the negative square root of 5.

A box of candy weighs 340.23 grams and costs $18.99. if 1 gram is approximately 0.03527 ounces, what is the unit price per ounce of the candy?

Answers

340.23 / 0.03527 =9,646.44
$18.99 / 9,646.44 = .0019686
340.23 / 18.99 = 17.91
17.91 x .0019686 = .0352576

How many 2 inch segments are there in 12 ft

Answers

72 2's in 12 ft
Hope this helped :)

If Chris and Lisa went shopping and spent a total of $25.50 and Lisa spent $13.50 more then Chris spent. How much did Lisa spend?

Answers

x-\ Lisa\ny-\ Chris\n\nx+y=25.50\nx-13.5=y\n\nx+x-13.5=25.50\ \ \ | add\ 13.50\n\n2x=39\ \ \ | divide\ by\ 2\n\nx=19.50\n\n Lisa\ spent\ 19.50 \$


I think you just subtract the total - the money lisa spent

lets try it

25.50$-13.50$ = 12$

so we all know that its 12$

wanna PROVE IT , try adding 12$+13.50$ =

it will give us the total ;p

What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) – 4 = 0 as a quadratic equation? u = (x + 5) u = (x – 5) u = (x + 5)2 u = (x – 5)2

Answers

6(x+5)² + 5(x+5)-4 = 0

(x+5)(x+5) = x(x+5)+5(x+5) = x² + 5x + 5x + 25 = x² + 10x + 25

6(x²+10x+25) + 5(x+5) - 4 = 0
6x² + 60x + 150 + 5x + 25 - 4 = 0
6x² + 60x + 5x + 150 + 25 - 4 = 0
6x² + 65x + 171 = 0

u = (x + 5)

Answer:

A: u = (x + 5)

Edg 2020

Write the equation of the parabola with a focus (1,2) and directrix y = 1

Answers

since the y shifted and focus is above directix, parabola opens up
4P(y-k)=(x-h)^2
distance from focus to veretx=distance from vertex to directix=P

from focus to directix is
from 2 to 1 which is 1 distance
1/2=P since 1/2of 1=1/2
4(1/2)(y-k)=(x-h)^2
vertexis 1 higher than directix so add 1/2 to 1 to get 1.5
vertex=(1,1.5)
vertex=(h,k)

equation is
4(1/2)(y-1.5)=(x-1)^2
if you want vertex form
2(y-1.5)=(x-1)^2
divide 2
y-1.5=(1/2)(x-1)^2
add 1.5
y=(1/2)(x-1)^(2)+1.5
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