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yKpoI14uk [10]
3 years ago
13

Help Use the distributive property to demonstrate that the product of 10 and -(1)/(5) is a negative number. Make sure to include

all steps in your answer.
Mathematics
1 answer:
marissa [1.9K]3 years ago
3 0

Answer:

-2

Step-by-step explanation:

We have to multiply 10 and \frac{-(1)}{(5)}

Here we have to distribute the negative sign.

Distributive property = -(a) = -a

Using the above property, we get  \frac{-(1)}{(5)} = \frac{-1}{5}

Now we have to multiply 10 and  \frac{-1}{5}

= 10 ×  \frac{-1}{5}

= \frac{10 times -1}{5}

= \frac{-10}{5}

Now we have to divide -10 by 5.

= -2

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dexar [7]

Answer:

p = 32.32; A = 47.91  

Step-by-step explanation:

1. Calculate ∠B

∠A + ∠B + ∠C = 180°

60° + ∠B + 45° = 180°

       ∠B + 105° = 180°

                  ∠B =   75°

2. Find sides BC and AC

We can use the Law of Sines

\dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB}

(i) Find BC

\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.8660}{BC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.8661}{0.7071} = 11.02

(ii) Find AC

\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.9659}{AC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.9659}{0.7071} = 12.29

3. Find the perimeter

p = AB + AC + BC = 9 + 12.29 + 11.02 = 32.32

4. Find the area of the triangle

A general formula for the area of a triangle is

A = ½ab sinC

If we use ∠A, the formula becomes

A = ½ × 9 × 12.29 × sin60° = 55.30 × 0.8660 = 47.91

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