Mathematics Knowledge – Test 2

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.

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.

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.

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

Rewrite problem

14 = 7( X - 7 )

Distribute

14 = 7X - 49

Add 49 to each side

63 = 7X

Divide by 7

9 = X

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

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

14h - 42 = 56

add 42 to both sides

14h = 98

divide both sides by 14

h = 7

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

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

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

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.