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3 years ago

Simplifying Ratios 20:10 30:36 54:12

Mathematics

2 answers:

netineya [11]3 years ago

7 0

Answer:

Simplify

1. 20:10 = 2:1

2. 30:36 = 5:6

3. 54: 12 = 18:7

Step-by-step explanation:

Answer for Number 1

The GCF of 20 and 10 is 10

Divide both by the GCF, 10:

20 ÷ 10 = 2

10 ÷ 10 = 1

The ratio 20 : 10 can be reduced t by dividing both terms by the GCF = 10

20 : 10 = 2 : 1

docker41 [41]3 years ago

3 0

Answer:

20:10 is 2:1

30:36 is 5:6

54:12 is 9:2

Step-by-step explanation:

First one is Divide both terms by the GCF, 10:

20 ÷ 10 = 2

10 ÷ 10 = 1

The ratio 20 : 10 can be reduced to lowest terms by dividing both terms by the GCF = 10 :

20 : 10 = 2 : 1

Second is Divide both terms by the GCF, 6:

30 ÷ 6 = 5

36 ÷ 6 = 6

The ratio 30 : 36 can be reduced to lowest terms by dividing both terms by the GCF = 6 :

30 : 36 = 5 : 6

Third is Divide both terms by the GCF, 6:

54 ÷ 6 = 9

12 ÷ 6 = 2

The ratio 54 : 12 can be reduced to lowest terms by dividing both terms by the GCF = 6 :

54 : 12 = 9 : 2

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ki77a [65]

Answer:

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3 years ago

find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[-8,6]. B=[

just olya [345]

Answer:

49°

Step-by-step explanation:

Given vectors:

a = [-8, 6]

B = [√7, 3]

θ = ?

To find the angle between the two vectors, we will be using the formula,

a.B = |a||B|cosθ

For simplicity, it is good to first calculate the dot product, and the magnitudes. Then we will substitute the values of the dot product, and the magnitudes of the vectors to solve for the angle.

Calculating the dot product

a.B = (-8, 6) . (√7, 3)

= (-8 × √7) + (6 × 3)

= -8√7 + 18

= 18 - 8√7

= 10√7

Calculating the magnitude the vectors

1. The magnitude of vector (-8, 6)

$|a| = \sqrt{(-8)^{2} + 6^{2}}$

$|a| = \sqrt{64 + 36}$

$|a| = \sqrt{100}$

$|a| = 10$

2. The magnitude of vector (√7, 3)

$|B| = \sqrt{(\sqrt{7})^{2} + 3^{2}}$

$|B| = \sqrt{7 + 9}$

$|B| = \sqrt{16}$

$|B| = 4$

Calculating the angle between the vectors,

cosθ = $\frac{a.B}{|a||B|}$

cosθ = $\frac{10\sqrt{7}}{10 * 4}$

cosθ = 0.6614

θ = cos⁻¹0.6614

θ = 48.59°

θ = 49°

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Zanzabum

Answer:

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Step-by-step explanation:

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