MATHEMATICS MIDDLE SCHOOL

Kaynard's first step in solving this rational equation is to simplify it by multiplying both sides by a common denominator. Which is the simplest expression he can use to do this?

Answers

Answer 1

Answer:

x^2 - 9 = (x + 3)(x -3)

3x - 9 = 3(x - 3)

and

Common denominator would be 6(x+3)(x - 3)

Answer: 6(x+3)(x - 3)

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Wats da anwser 4×70=4×7×_

Answers

10 will be your answer

it is 10 because 4*70 = 280 so 4*7 = 28*10 =280

Fun center rents popcorn machines for $20 per hour. In addition to the hourly charge, there is a fee of $32. Is the number if hours you rent the popcorn machine proportional to the total cost?

Answers

No... because the two can never collide mathematically. So no,

What is the slope and the y-intercept of each equation(1) 12x + 3y = 9
(2) 6x - 2y =2
(3) 2x + 5y = 10
(4) 9x - 3y = -1
(5) 4y + 6x =2
(6) 8y -2x = 5
(7) 5x + 5y = 3
(8) -4y = 16
(9) 6x = 12

Answers

$The\ slope-intercept\ form:y=mx+b\n\nm-the\ slope;\ b-y-intercept$

$(1)\n12x+3y=9\n3y=-12x+9\ \ \ \ |divide\ both\ sides\ by\ 3\ny=-4x+3\n\boxed{m=-4;\ b=3}\n\n(2)\n6x-2y=2\n-2y=-6x+2\ \ \ \ \ |divide\ both\ sides\ by\ (-2)\ny=3x-1\n\boxed{m=3;\ b=-1}$

$(3)\n2x+5y=10\n5y=-2x+10\ \ \ \ |divide\ both\ sides\ by\ 5\ny=-(2)/(5)x+2\n\boxed{m=-(2)/(5);\ b=2}\n\n(4)\n9x-3y=-1\n-3y=-9x-1\ \ \ \ |divide\ both\ sides\ by\ (-3)\ny=3x+(1)/(3)\n\boxed{m=3;\ b=(1)/(3)}$

$(5)\n4y+6x=2\n4y=-6x+2\ \ \ \ |divide\ both\ sides\ by\ 4\ny=-(6)/(4)x+(2)/(4)\ny=-(3)/(2)x+(1)/(2)\n\boxed{m=-(3)/(2);\ b=(1)/(2)}\n\n(6)\n8y-2x=5\n8y=2x+5\ \ \ \ |divide\ both\ sides\ by\ 8\ny=(2)/(8)x+(5)/(8)\ny=(1)/(4)x+(5)/(8)\n\boxed{m=(1)/(4);\ b=(5)/(8)}$

$(7)\n5x+5y=3\n5y=-5x+3\ \ \ \ |divide\ both\ sides\ by\ 5\ny=-x+(3)/(5)\n\boxed{m=-1;\ b=(3)/(5)}\n\n(8)\n-4y=16\ \ \ \ |divide\ both\ sides\ by\ (-4)\ny=-4\n\boxed{m=0;\ b=-4}\n\n(9)\n6x=12\ \ \ \ |divide\ both\ sides\ by\ 6\nx=2\n\boxed{m\ and\ b\ not\ exist}$

$y=mx+b\nm\ \ \rightarrow\ \ the\ slope\nb\ \ \rightarrow\ \ y-intercept\n---------------------------\n1)\ \ 12x+3y=9\ \ \ \Rightarrow\ \ \ 3y=-12x+9\ /:3\n.\ \ \ \ y=-4x+3\ \ \ \Rightarrow\ \ \ m=-4\ \ \ \ \ and\ \ \ \ \ b=3\n\n2)\ \ 6x-2y=2\ \ \ \Rightarrow\ \ \ -2y=-6x+2\ /:(-2)\n.\ \ \ \ y=3x-1\ \ \ \Rightarrow\ \ \ m=3\ \ \ \ \ and\ \ \ \ \ b=-1\n\n3)\ \ 2x+5y=10\ \ \ \Rightarrow\ \ \ 5y=-2x+10\ /:5\n.\ \ \ \ y=- (2)/(5) x+2\ \ \ \Rightarrow\ \ \ m=- (2)/(5)\ \ \ \ \ and\ \ \ \ \ b=2\n\n$

$4)\ \ 9x-3y=-1\ \ \ \Rightarrow\ \ \ -3y=-9x-1\ /:(-3)\n.\ \ \ \ y=3 x+ (1)/(3)\ \ \ \Rightarrow\ \ \ m= 3\ \ \ \ \ and\ \ \ \ \ b=(1)/(3)\n\n5)\ \ 4y+6x=2\ \ \ \Rightarrow\ \ \ 4y=-6x+2\ /:4\n.\ \ \ \ y=-(3)/(2) x+ (1)/(2)\ \ \ \Rightarrow\ \ \ m= -(3)/(2)\ \ \ \ \ and\ \ \ \ \ b=(1)/(2)\n\n6)\ \ 8y-2x=5\ \ \ \Rightarrow\ \ \ 8y=2x+5\ /:8\n.\ \ \ \ y=(1)/(4) x+ (5)/(8)\ \ \ \Rightarrow\ \ \ m=(1)/(4)\ \ \ \ \ and\ \ \ \ \ b=(5)/(8)\n\n$

$7)\ \ 5x+5y=3\ \ \ \Rightarrow\ \ \ 5y=-5x+3\ /:5\n.\ \ \ \ y= -x+ (3)/(5)\ \ \ \Rightarrow\ \ \ m=-1\ \ \ \ \ and\ \ \ \ \ b=(3)/(5)\n\n8)\ \ -4y=16\ /:(-4)\n.\ \ \ \ y= -4\ \ \ \Rightarrow\ \ \ m=0\ \ \ \ \ and\ \ \ \ \ b=-4\n\n8)\ \ 6x=12\ /:6\n.\ \ \ \ x=2\ \ \ \Rightarrow\ \ \ not\ exist:\ \ \ the\ slope\ \ \ and\ \ \ the\ y-intercept$

140% of what number is 48

Answers

1.4x = 48
Solve for x
x = 48/1.4

x = 34.2857

percent means parts out of 100
140%=140/100=1.4
'of' means multiply
'is' means =
140% of what is 48 means
1.4 times what=48
divide both sides by 1.4
what=34.285714285714285714285714...

HELP ME PLS!!!

What numbers do I multiply to find the volume

Answers

5x2x2 and 4x5x7 is the answer

hope i helped^-^

Length x width x height so 5x2x2 and 4x5x7

What is 13.8924439894 rounded to the nearest tenth

Answers

1st decimal place=tenth
2nd=hundreth

to round, you look at the place after it
so 13.8924439894 to tenth
look untill hundreth
13.89
if hundreth>5, round tenth up
if hundreth place<5 leave tenth as is

13.89
9>5
round up
8+1=9
13.9 is to theh tenth

the answer is 13. 90 if you round it to the nearest tenth. the nearest tenth is the 9 the first nine.( if the number is 0-5 then it will become a 0 but if the number is 5-9 you would add one to the number in front of it) since the number is 9 then the 8 would become a 9 so your answer would be 13.90

hope I explained it well enough.

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