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Yakvenalex [24]

3 years ago

8

Is 3(–2) + 7(2) equivalent to (–3)(–3) + (–1)(1)? Let negative numbers be represented with a "–" symbol and positive numbers be

represented by "+" symbol. Use a pictorial model to justify your answer.

1 answer:

jek_recluse [69]3 years ago

3 0

3(-2) + 7(2) = 8
(-3)(-3) + (-1)(1) = 8
yes

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konstantin123 [22]

Answer:

1. 10 square yards

2. $9.10

3. 36 girls

4. 20 cherries

5. 159 bracelets

Step-by-step explanation:

1.

The area of this figure would be the area of the SQUARE minus the area of the RECTANGLE (taken out).

The middle part is taken out (this is a rectangle).

View this as a square with sides 4 by 4 with a rectangle portion taken out. So the area can be said as:

Area = Area of Whole Square - Area of Middle Rectangle Taken Out

Lets calculate:

Area of Whole Square:

side * side = 4 * 4 = 16

Now,

Area of Middle Rectangle Taken Out:

Length * Width

The length is given as 3

The width would be 4 - two 1 from two sides, that is 4 - 1 - 1 = 2

So, area = 3 * 2 = 6

Area of figure = 16 - 6 = 10 square yards

2.

We have to find 20% of the bill.

The bill was 45.50 and we have to find 20% of 45.50.

We first convert percentage to decimal by dividing by 100:

20% = 20/100 = 0.20

Now we multiply this decimal with the bill to get our desired answer:

0.20 * 45.50 = $9.10

The tip is $9.10

3.

The ratio of boys (b) to girls (g) would be 2 is to 3.

There are 24 boys.

We can set up a ratio (fraction) with boys on top and girls on bottom.

Then we equate it with actual number of boys and girls (let it be g). So the ratio set-up would be:

$\frac{2}{3}=\frac{24}{g}$

To solve for g, the number of girls, we have to cross multiply and use algebra to solve. The process is shown below:

$\frac{2}{3}=\frac{24}{g}\\2*g = 24*3\\2g=72\\g=\frac{72}{2}\\g=36$

There are 36 girls in sixth grade

4.

For every "9" lemon, there are "4" cherries.

There are 45 lemons

If we think of "9" lemons as a "box", how many boxes of lemons are there?

45/9 = 5

Similarly, there would be "5" boxes of cherries. But there are "4" cherries per box. So there are:

4 * 5 = 20 cherries

We can also set up a ratio of cherry to lemon as 4 is to 9 and equate it with actual cherries (let it be "c") and lemons (45). Cross multiply and use algebra to solve for cherries ("c"). Algebra process shown below:

$\frac{Cherries}{Lemons}=\frac{4}{9}=\frac{c}{45}\\9*c=4*45\\9c=180\\c=\frac{180}{9}\\c=20$

See, we have the same answer, 20 cherries!

5.

Number sold total = 14 + 27 + 45 = 86

She still has 73 in her stock

So, she basically started with whatever she now has (73) and whatever she has sold the 3 days (86), that would be:

73 + 86 = 159 bracelets

Tia started with 159 bracelets

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3 years ago