Mathematics Knowledge – Test 1

First, turn them into fractions.

12 2/5 = ((5*12) + 2)/ 5 = 62/5

8 1/9 = ((9*8) + 1)/9 = 73/9

(62/5) * (73/9) = (4526)/45

4526 divided by 45 = 100, remainder 26

That can be written as 100 26/45

PART 1:

If the ratio of the diameters is 1 : 2 : 3, then that means the diameters are 18 : 36 : 54. You can solve this with similar ratios:

1/18 = 2/x

x = 36

1/18 = 3/y

y = 54

So the respective diameters are 18", 36" and 54". (The radii would be half this or 9", 18", 27").

However, the answer is to be expressed in feet so divide by 12:

54 inches / 12 inches/ft = 4.5 feet.

PART 2:

Volume of the *middle* sphere. The radius is 18" (one half of 36"), so just plug this into the formula:

V = (4/3)(pi)(18)^3

V = 7,776 pi (cubic inches)

PART 3:

The volume of the *small* sphere = (4/3)(pi)(9)^3

The volume of the *middle* sphere = (4/3)(pi)(18)^3

To get the ratio between these two, just divide smallest / biggest

= (4/3)(pi)(9^3) / (4/3)(pi)(18^3)

The 4/3 and pi cancel out

= 9^3 / 18^3

= 729 / 5,832

= 1 : 8

This makes sense because the ratio of lengths is linear (1 : 2 : 3), the ratio of areas is squared (1 : 4 : 9) and the ratio of volumes is cubic (1 : 8 : 27).

PART 4:

We have the 3 diameters (18", 36", 54"). the total height is the sum:

18 + 36 + 54 = 108"

Convert this to feet (divide by 12):

108 inches / 12 inches/ft = 9 feet.

Since your book page is 8 3/4 inches already, just add together the lengths of the printed area (7 1/3 in) and the top margin (5/8 in) and subtract the sum from the length of your page.

the equation then would be:

8 3/4 - (7 1/3 + 5/8)

your final answer:

the bottom margin would be 19/24 inches long.

2x+5y=13 --- Equation 1

x=29-7y --- Equation 2

Substitute equation2 into equation 1, then we get

2(29-7y)+5y = 13

58-14y+5y = 13

-9y = -45

y = 5

Substitute y=5 into equation 2, then we get

x = 29-7*5

x = -6

So, the solution is x=-6 and y=5

If a number doesn't have a sign before it, it's positive.

So

9 - 3x = 36

Subtract 9 from both sides

-3x = 27

Divide by 3

-x = 9

so

x = -9

The area is 336 yd^2.

Area = length x width = L x W, and W = 5 + L

Therefore:

Area = (5+ L)L

336 = (5 + L)L

336 = L^2 + 5L

0 = L^2 + 5L - 336

Next, you solve like a quadratic equation using the quadratic formula, L = [-b + or - sqrt(b^2 - 4ac)]/2a.

[-b + or - sqrt(b^2 - 4ac)]/2a

= [-5 + or - sqrt(5^2 - 4(1 * -336)]/2(1)

=[-5 + or - sqrt(25 +1344)]/2

=[-5 + or - 37]/2 = 16 or 21

This means that the length is either 16 or 21.

Check them by plugging them back into the original

336 = (5 + L)L

336 = (5 + 21)21 = 546 Incorrect

336 = (5 + L)L = (5+16)(16) Correct, therefore, the length is 16.

5 + L = W

5+ 16 = W

21 = W

solve for SLOPE m = [4 - (-5)]/(4-2) = 9/2

Equation of the line solve for B:

y = mx +b

4 = (9/2) (4) + b

4 = 18 + b

b = -14

y = (9/2) (x) -14

y + 14 = (9/2) (x)

(9/2) (x) - y = 14, or

9x - 2y = 28

to do this as a fractions problem:

we can cancel.

(3/4)(156/1) =

(3/1) ( 39/1) = (3)(39) = 117 teachers

$155/775 = 1/5th, which is also 0.2 or 20%

(because 155 goes into 775 exactly 5 times, you can divide both the top/numerator and the bottom/denominator of the fraction by 155 and reduce it to 1/5)

x^(y) = 3

x^(3y)

= (x^y)^3

= 3^3

= 27

If we get the same denominators, she has 14/16 of a gallon. Each statue will require 1/16 of a gallon.

So she can paint 14 statues.

replace ''n'' with 10.

so

g(10)=3(10)-2

g(10)=30-2

g(10)=28

Let the initial side be 's' yards

initial area = s^2 ( s square) yards

new side = s+11

new area = (s+11)^2

acc. to question

(s+11)^2 =s^2 +451

s^2 + 121 + 22s = s^2 + 451

s =15 yards