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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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Which expression are equivalent to -3-(7.5+4)
Hunter-Best [27]
-14.5

Basically, -(7.5+4) is -11.5 and then combine -3 with -11.5 which yields -14.5
3 0
3 years ago
You have a mean score of 84 after taking five 100-point tests. What do you need to score on the sixth 100-point test to have a m
kap26 [50]
The mean of n numbers is the sum of the numbers divided by n.

You have a mean score of 84 after taking 5 tests. Let x be the sum of scores.
\frac{x}{5}=84 \\
x=84 \times 5 \\
x=420
You scored a total of 420 points on five tests.

You need to have a mean score of 85 after taking 6 tests. Let y be the score you need to obtain. Your total score on 6 tests is 420+y.
\frac{420+y}{6}=85 \\
420+y=85 \times 6 \\
420+y=510 \\
y=510-420 \\
y=90

You need to score 90 points on the sixth test.
8 0
3 years ago
Read 2 more answers
In isosceles triangle ABC, AC=BC=20, the measure of angle A=68, and CD is the altitude to side AB. What is CD to the nearest 10t
antiseptic1488 [7]

Answer:

Step-by-step explanation:

Comment

The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.

Formula

Sin(A) = Sin(68 = opposite / hypotenuse     Substitute values.

Solution

sin(68) = altitude (side opposite) / 20       multiply both sides by 20

20*sin(68) = 20* altitude / 20                     substitute for sin(68)

20* 0.9272 = altitude

altitude = 18.5

Answer: 18.5 to the nearest tenth

3 0
2 years ago
Is 9+10=21? <br><br><br><br><br> this is free points, just say yes
Alex787 [66]

9+10=19 not 21, but ok

8 0
3 years ago
Read 2 more answers
1. Carter will install fencing all around the flat area of his
MariettaO [177]

Answer:

Amount of fencing required = 75 yards

Step-by-step explanation:

Distance between the two points (x_1,y_1) and (x_2,y_2) is given by the formula,

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Distance between A(3, 6) and B(3, -2) = \sqrt{(3-3)^2+(6+2)^2}

                                                               = 8 yards

Distance between B(3, -2) and C(-7, 4) = \sqrt{(3+7)^2+(-2-4)^2}

                                                                = \sqrt{136}

                                                                = 11.66 ≈ 12 yards

Distance between C(-7, 4) and D(-7, -2) = \sqrt{(-7+7)^2+(4+2)^2}

                                                                 = 6 yards

Distance between D(-7, -2) and E(-3, -2) = \sqrt{(-7+3)^2+(-2+2)^2}

                                                                   = 4 yards

Distance between E(-3, -2) and F(-3, -8) = \sqrt{(-3+3)^2+(-2+8)^2}

                                                                = 6 yards

Distance between F(-3, -8) and G(3, -8) = \sqrt{(-3-3)^2+(-8+8)^2}

                                                                 = 6 yards

Distance between G(3, -8) and H(10, -12) = \sqrt{(3-10)^2+(-8+12)^2}

                                                                   = \sqrt{49+16}

                                                                   = \sqrt{65}

                                                                   = 8.06 ≈ 8 yards

Distance between H(10, -12) and J(10, 6) = \sqrt{(10-10)^2+(-12-6)^2}

                                                                   = 18 yards

Distance between A(3, 6) and J(10, 6) = \sqrt{(10-3)^2+(6-6)^2}

                                                               = 7 yards

Since length of fence required = perimeter of the flat area

Perimeter of the given area = 8 + 12 + 6 + 4 + 6 + 6 + 8 + 18 + 7

                                              = 75 yards

Therefore, amount of fencing required = 75 yards

8 0
3 years ago
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