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Nadya [2.5K]
2 years ago
14

Give the property that justifies each step.

Mathematics
1 answer:
frosja888 [35]2 years ago
3 0

Answer:

Please check the explanation below.

Step-by-step explanation:

Some of the properties are defined as:

  • <em>Distributive property</em>

a(b+c) = ab+ac

For example,

suppose a=3, b=4, c=5

3(4+5) = 3(4) + 3(5)

3(9) = 12+15

27 = 27

  • <em>Subtraction property of Equality</em>

if (a=b), then a-c = b-c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a-c = b-c ⇒ 2-5 = 2- 5 ⇒ -3 = -3

  • <em>Addition property of Equality</em>

if (a=b), then a+c = b+c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a+c = b+c ⇒ 2+3 = 2+3  ⇒ 5 = 5

  • <em>Multiplicative property of Equality</em>

if (a=b), then a×c = b×c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a×c = b×c ⇒ 2×5 = 2 × 5  ⇒ 10 = 10

  • <em>Division property of Equality</em>

if (a=b), then a÷c = b÷c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a÷c = b÷c ⇒ 2÷5 = 2 ÷ 3  ⇒ 2/5 = 2/5

Let us solve the given equation using the above properties.

7n-16=47                     Given

7n-16+16=47+16   1) Addtion property of Equality ∵ if (a=b), then a+c = b+c

7n=63                  2) simplify

n = 9                    3) Division property of Equality ∵ if (a=b), then a÷c = b÷c        

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-13 and -14

They both are consecutive negative integers that multiply to 182.
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No sure I used Photomath hope it’s a start

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The jug can hold 1500ml. The bucket can hold 2 litres. The barrel can hold 15 litres. Anisa wants to fill the barrel with water.
myrzilka [38]

Answer:

1. Using the jug 6 times and the bucket 3 times

2. Using the bucket 6 times, then using the jug two times

Step-by-step explanation:

Firstly, let’s remember that 1000 ml = 1l

Thus 2L = 2000 ml

And 15L = 15,000 ml

So the situation we are having now is that we want to fill a barrel of 15,000 ml using a jug of 1500 ml and a bucket with a capacity of 2000 ml

Firstly, the first way is using the bucket 6 times and the jug 2 times

What i mean by this is using the bucket 6 times bringing the total volume from the bucket as (6* 2000) = 12,000 ml

Then we are left with 15,000-12,000 = 3,000 ml

Now, she can fill the barrel with 2 times the full volume of the jug making 3,000

Secondly, she can also use the combination of both.

She can use the bucket 6 times and the jug 2 times

The total volume in each case here would be;

For the bucket; (2,000 * 6) = 12,000 ml

while for the jug, we have (1500 * 2) = 3,000 ml

And thus we shall be having a total of 12,000 + 3,000 = 15,000 ml this way

8 0
3 years ago
PLEASE HELP
s344n2d4d5 [400]
Let the length of the diameter be d and radius be r, thus to solve for d we proceed as follows:
r²+31²=(r+15)²
solving for d we solve for r
r²+961=r²+30r+225
putting like terms together we obtain:
r²-r²+961-225=30r
736=30r
solving for r
r=24.53
thus
d=24.5333×2
d=49.067~49.1
Answer is D. 49.1

7 0
3 years ago
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X^2-10x + y^2 + 6y – 30 = 0
pav-90 [236]

Answer:

(

5

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√

55

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0

)

,

(

5

−

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55

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0

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Step-by-step explanation:

4 0
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