the first step is to expand the bracket and then make the new quadratic equation =0 by minusing 73 from both sides.

        5(x^2 + 2x) =73

         5x^2 + 10x =73
    (-73)                     (-73)

  5x^2 + 10x -73 = 0

at this point it is probably best to use the quadratic formula to solve the values of x. 

        -b +/- sqrt(b^2-4ac)
x=    —————————
                      2a

a=5      b=10      c=-73

       -10 +/- sqrt(10^2 - 4(5)(-73))
x= ——————————————
                         2 x 5



      -10 + sqrt(100+1460)
x= ——————————— = 2.95 (2dp)
                     10

                     or

      -10 - sqrt(100+1460)
x= ——————————– = -4.95 (2dp)
                     10

x= 2.95  or  x= -4.95
       

Maths

Solve 5(x^2+2x)=73

it may be easier to visualise 300 as a product of prime factors using a prime factor tree. 

             300
             /     \
           2     150
                   /   \
                 2     75
                        /   \
                      3    25
                            /   \
                          5     5

all the numbers with no further computations are the prime factors
2 x 2 x 3 x 5 x 5
= (2)^2 x 3 x (5)^2

What is 300 as a product of prime factors using index notation

to find the diameter of the sphere you have to find the diagonal of the cube by using the Pythagoras theorem twice. 

the first time is to find out the diagonal length of the base of the cube. 
sqrt(6^2 +6^2)=sqrt(72)

with this new information we can now find out the diagonal of the cube (diameter of the sphere)
sqrt(6^2 +(sqrt(72))^2)
=sqrt(36+72)
=sqrt(108)
=6root3

to fInd the volume of a sphere you have to use the formula: 4/3(pi)(r^3)
since the diameter is 6root3
the radius must be 3root3

4/3(pi)(3root3)^3=587.670994

the volume of the cube Is just 6^3=216

the space between the sphere and the cube is:
587.670994-216
=371.67
=372 inches^3 (to the nearest whole number) 


Can someone help me through this?: A cube with edges 6 inches long fits snugly inside a sphere. The diagonal of the cube is the diameter of the sphere. What is the volume, to the nearest whole number, of the space between the sphere and the cube.

(3^8 x 3^4)/(3^2 x 3^8)
= 3^(8+4)/3^(2+8)
= 3^12 / 3^10
= 3^2
= 9

when multiplying numbers with the same base number, you should add the powers. 
when dividing numbers with with the same base number, you should subtract the powers. 

3 to the power of 8 x 3 to the power of 4 divided by 3 to the power of 2 and 3 to the power of 8 simplified?

generally, to find the area you have to do length x width. but in this case you’ve been given the area and the length so you have to inverse the equation to find the width. 

width=area/length
          =53.75/12.5
          =4.3m

A group used 53.75m2 of groundsheet to cover 12.5m long campsite how wide was the campsite?

a rational surd is one that can be simplified into a rational number such as  sqrt(4)=2
sqrt(16)=4

an irrational surd is one that can not be simplified into a rational number such as 
sqrt(20)=sqrt(4) x sqrt(5)
               =2           x sqrt(5)
               =2sqrt(5)

the square root of 5 cannot be found as a rational number so the answer is irrational

What are irrational and rational surds?

interior angles are the angles found within a shape. For a regular polygon this can be worked out with a simple equation of: 

(no. of sides - 2) x 180°
_________________________________________

the exterior angle and its corresponding interior angle always add up to 180°. For a regular polygon there is also a formula for working out the exterior angle:

360°/no. of sides

What are interior and exterior angles

any number in the 7 times tables are a multiple of 7. Or any number that can be easily divided by 7 is a multiple of 7. 

A multiple of 7

12 - 28c

you have to multiply 4 by each golf the terms inside the brackets 

Expand 4(3-7c)

group all the similar terms together and keep the x on one side of the equal sign and the numbers on the other side. 

5 - x/2 - x - 1/3 = 1
(5-1/3) - (x + x/2) =1
(14/3) - 3/2x = 1
(14/3) - 1 = 3/2x
11/3 = 3/2x
2(11/3) = 3x
(22/3)/3 = x
22/9 = x

x= 22/9 = 2 4/9

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