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Georgia [21]
3 years ago
8

Use properties of equality to simplify each of the following expressions so that you can simplify them in your head. Identify th

e properties used and describe how you used them.
1. 4 • (–3) • 5



2. (2.25 • 23) • 4





4. 5 • 12 • (–2)



5. 35(26)(0)
Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
4 0
Properties of equality have nothing to do with it. The associative and commutative properties of multiplication are used (along with the distributive property and the fact of arithmetic: 9 = 10 - 1).

All of these problems make use of the strategy, "look at what you have before you start work."


1. = (4·5)·(-3) = 20·(-3) = -60 . . . . if you know factors of 60, you can do this any way you like. It is convenient to ignore the sign until the final result.

2. = (2.25·4)·23 = 9·23 = 23·10 -23 = 230 -23 = 207 . . . . multiplication by 4 can clear the fraction in 2 1/4, so we choose to do that first. Multiplication by 9 can be done with a subtraction that is often easier than using ×9 facts.

4. = (2·5)·12·(-1) = 10·12·(-1) = (-1)·120 = -120 . . . . multiplying by 10 is about the easiest, so it is convenient to identify the factors of 10 and use them first. Again, it is convenient to ignore the sign until the end.

5. = 0 . . . . when a factor is zero, the product is zero
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4 0
3 years ago
Directed line segment has endpoints P(– 8, – 4) and Q(4, 12). Determine the point that partitions the directed line segment in a
larisa86 [58]

Answer:

Point (1,8)  

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

[x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}]

Let us substitute coordinates of point P and Q as:

x_1=-8,

y_1=-4

x_2=4

y_2=12

m=3

n=1

[x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}]

[x=\frac{12-8}{4},y=\frac{36-4}{4}]

[x=\frac{4}{4},y=\frac{32}{4}]

[x=1,y=8]

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

   

7 0
3 years ago
Which of the expressions below can be factored using the difference of<br> squares method?
zlopas [31]

Answer:

<em>The second choice is correct. It can be factored as:</em>

9x^2-16y^2=(3x-4y)(3x+4y)

Step-by-step explanation:

<u>The Difference of Squares Method for Factoring</u>

The expression:

a^2-b^2=(a-b)(a+b)

Is a widely used method to factor binomials that are expressed as the subtraction of two perfect squares.

The condition for a binomial to be factored by using this method is that both terms must have an exact square root and they must be subtracted.

The last two choices are not valid because they are not a subtraction but an addition.

The first choice is not valid because none of the terms is a perfect square.

The second choice is correct. It can be factored as:

9x^2-16y^2=(3x-4y)(3x+4y)

4 0
3 years ago
Julie earned 66 on the test. Describe how the scores of Julie’s classmates compared to Julie’s score.
Ne4ueva [31]
We would need the data of their classmates scores to complete this answer
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3 years ago
8 out of every 14 children in a school are boys. What is the ratio of boys to girls in the school?
DochEvi [55]

Answer:

8:6

Step-by-step explanation:

If 8 out of 14 students are boys then the remaining number of students must be girls

So

14-8= 6

There are 6 girls out of the 14

So as a ratio of boys to girls

8:6

7 0
3 years ago
Read 2 more answers
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