MATHEMATICS MIDDLE SCHOOL

Rationalize the denominator and simplify
12/√7+2

Answers

Answer 1

Answer:

Answer:

The answer is 4√7 - 8

Step-by-step explanation:

12/√7+2

Rationalize the denominator

=12/7+2 * √7-2/√7-2

=12√7-24/7-4

=12√7-24/3

By taking common from numerator we get

=12(√7-2)/3

=4√7-8

Answer 2

Answer:

Answer:

The answer is 4√7 - 8

Step-by-step explanation:

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Help me with this please I don't exactly get it

Answers

Answer:

P = 40.56 in (ANS)

Step-by-step explanation:

radius = 8/2 = 4 in

semi-circle perimeter = pi * R = 3.14 * 4 = 12.56 in

figure perimeter = 12.56 + 10 + 8 + 10 = 40.56 in (ANS)

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

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

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

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

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

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

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

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

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

Emily;s family drove 254.6 miles. Their car used 19 gallons of gasoline. Describe the car's gas mileage.

Answers

You take your miles driven divided by the gallons of gas used.

So,

254.6 miles/19 gallons = 13.4

The gas mileage of the car is 13.4

Hope this helps :D

Samantha bought 4.5 pounds of pears. Each pound cost $1.68. How much did Samantha spend in all?

Answers

we just need to multiply the amount of pounds and the cost of each one of them, that is:
spent = 4.5*1.68
= 7.56
so she spent $7.56

Solutions

Given --

1 pound = $ 1.68

Calculations

To find how much 4 pounds cost multiply by 4.

1.68 x 4 = 6.72

To find .5 divide 1.68 by 2 and add it to 6.72.

1.68 ÷ 2 = 0.84

6.72 + 0.84 = 7.56

She spent $ 7.56

What is straight part of a line and has two end points