Mathematics Knowledge – Test 2

When you divide fractions, you multiply by the inverse of the second fraction. In simpler terms, you flip the second fraction and multiply. So, multiply 9/10 by 15/4 and you get 135/40. Simplify this down by dividing the numerator and denominator by 5 - you get 27/8.

14h - 42 = 56

add 42 to both sides

14h = 98

divide both sides by 14

h = 7

When you divide fractions, you multiply by the inverse of the second fraction. In simpler terms, you flip the second fraction and multiply. So, multiply 9/10 by 15/4 and you get 135/40. Simplify this down by dividing the numerator and denominator by 5 - you get 27/8.

Find the common denominator of 6

5/6+2/6=7/6

7/6 is the answer, or 1 1/6

1/4 + 1/6 + 1/2 + 6 years = total life

3/12 + 2/12 +6/12 + 6 years = total life

11/12 + 6 years = total life

so if the 6 years = 1/12 (the left overs to make 1 whole life) the other 11/12 would be 66 years.

66+ 6 = 72

so he died at 72

Rewrite problem

14 = 7( X - 7 )

Distribute

14 = 7X - 49

Add 49 to each side

63 = 7X

Divide by 7

9 = X

We have E = 2500 + 0.1s (i.e. Suzie gets a 10% sales commision over a $2500 base)

when s = $8000

E = 2500 + 0.1*8000 = $3300

1 1/5 = 6/5

3 3/4 = 15/4

6/5 + n = 15/4

n = 15/4 - 6/5

n = 75/20 - 24/20

n = 51/20

This is a problem with scale and ratio. It helps if you draw the two triangles out. But using the technique from #1, we can set up the ratio 24 ft (height)/20 ft (shadow) = x (height)/85 ft (shadow). Cross multiply as in #1. You find that 2040 = 85x, or x = 102 ft.

Let the vertex angle be A......then the exterior angle is (180-A)

It is given that the exterior angle is 3 times the measure of vertex angle i.e, A.....hence (180-A) = A

180 = 4A

A = 180/4 = 45

Hence the vertex angle is obtained as 45 degrees

Since in isoceles triangle the other two angles(say B) are equal....therefore A + B + B = 180

45 + 2B =180

2B = 135

B = 135/2 = 67.5

Hence the three angles of triangle are 45, 67.5 and 67.5 degrees.

A + a = 350....(1)

A = 4a.....(2)

=> (2) into (1) gives:

4a + a = 350

=> 5a = 350

i.e. a = 70 => A = 280

so, Austin drives 280 miles and Antonio drives 70 miles.

2^(x^2) = (8^x)/4

2^(x^2) = ((2^3)^x)/(2^2)

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

x^2 = 3x - 2

x^2 - 3x + 2 = 0

(x - 2)(x - 1) = 0

Hence x =2 or 1

When dividing fractions, you multiply the 1st fraction by the reciprocal of the 2nd fraction

9/10 divided by 6/1 = 9/10 x 1/6 = 9/60

Both 9 and 60 are divisible by 3, so reduce 9/60 to 3/20

Answer is 3/20 of a mile