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3 years ago

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julia puts her stickers into arrays in an album. some of her stickers are animal stickers. there are a different number of stick

ers on each page.the table at the right shows information about the stickers in julia's album

1 answer:

lina2011 [118]3 years ago

5 0

The total number of stickers :

Page 1 : 28

Page 2 : 24

Page 3 : 72

Page 4 : 48

<h3>Further explanation </h3>

There are several properties in integer multiplication operations

1. closed property

Multiplication between integers will produce integers too

2. commutative property

a x b = b x a

3. associative property

ax (bxc) = (axb) xc

4. identity

ax1 = 1 x a = a

5. distributive property

* addition

ax (b + c) = axb + axc

* substraction

ax (b-c) = axb - axc

We can use facts to solve multiplication problems

for example :

6 x 7 = (5 x 7) + ( 1 x 7) = 42

we can break facts with 6 into 5s and 1s facts from multiplication above

julia puts her stickers into arrays in an album

From picture (attached) we can find the total number of stickers on each page with 1s,2s,3s and 5s facts

Page 1 : 4 x 7 = (2 x 7) + ( 2 x 7) = 14 + 14 = 28
Page 2 : 4 x 6 = (1 x 6) + (3 x 6) = 6 + 18 = 24
Page 3 : 8 x 9 = ( 3 x 9) + (5 x 9) = 27 + 45 = 72
Page 4 : 8 x 6 = (3 x 6) + (5 x 6) = 18 + 30 = 48

<h3>Learn more</h3>

the multiplicative identity property

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Keywords : stickers, arrays, album, page, Julia

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Answer:

$\theta_{CAB}=128.316$

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$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

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$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

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we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

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$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

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Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

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$\theta_{BCA}=25.842$

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$25.842+128.316+25.842$

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