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1 year ago

100 POINTS PLS HELP

Mathematics

1 answer:

posledela1 year ago

5 0

The equations with parentheses added to make them true are;

(4 × (3 + 7 - 6) × 1) + 4 = 20
(60 - 18) ÷ (2 + 4) + 10÷2 = 12
80 - 36 ÷ (2 + 6 - 2) × (5 + 1) = 44
3 × (5 + 4) - (2 × (2 + 6) - 4) = 15

<h3>What is the effect of parentheses in a mathematical expression?</h3>

Parentheses indicate that operations within it should be completed first before those that are outside the parentheses.

The given terms of the equations can be regrouped with parentheses to make the equations true as follows;

1. 4 × 3 + 7 - 6 × 1 + 4 = 20

The above equation gives;

3 + 7 - 6 = 4

Therefore;

4 × 3 + 7 - 6 × 1 + 4 = 4 × (3 + 7 - 6) × 1 + 4

4 × (3 + 7 - 6) × 1 + 4 = (4 × 4) × 1 + 4

(4 × 4) × 1 + 4 = 16 × 1 + 4 = 16 + 4 = 20

Which gives;

(4 × (3 + 7 - 6) × 1) + 4 = 20

2. 60 - 18 ÷ 2 + 4 + 10 ÷ 2 = 12

60 - 18 = 42

2 + 4 = 6

The first four terms, therefore gives;

(60 - 18) ÷ (2 + 4) = 7

10÷2 = 5

Which gives;

60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2

(60 - 18) ÷ (2 + 4) + (10÷2) = 7 + 5 = 12

Which gives;

60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2 = 12

The expression is therefore;

(60 - 18) ÷ (2 + 4) + 10÷2 = 12

3. 80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 44

80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - 36 ÷ (2 + 6 - 2) × (5 + 1)

(2 + 6 - 2) = 6, and (5 + 1) = 6

Therefore;

80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - ((36 ÷ 6) × 6)

80 - ((36 ÷ 6) × 6) = 80 - ((36 × 6) ÷ 6)

80 - ((36 × 6) ÷ 6) = 80 - (36 × 1) = 44

Therefore;

80 - 36 ÷ (2 + 6 - 2) × (5 + 1) = 44

4. 3 × 5 + 4 - 2 × 2 + 6 - 4 = 15

3 × 5 + 4 - 2 × 2 + 6 - 4 = 3 × (5 + 4) - (2 × (2 + 6) - 4)

3 × (5 + 4) - (2 × (2 + 6) - 4) = 3 × 9 - (16 - 4)

3 × 9 - (16 - 4) = 27 - 12 = 15

Therefore;

3 × (5 + 4) - (2 × (2 + 6) - 4) = 15

Learn more about the order of mathematical operations here:

brainly.com/question/27146801

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Let width of the rectangular plot be x meters

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3 years ago

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Answer:

407 mi/h

Step-by-step explanation:

Given:

Speed of plane (s) = 470 mi/h

Height of plane above radar station (h) = 1 mi

Let the distance of plane from station be 'D' at any time 't' and let 'x' be the horizontal distance traveled in time 't' by the plane.

Consider a right angled triangle representing the above scenario.

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Speed of the plane is nothing but the rate of change of horizontal distance of plane. So, $s=\frac{dx}{dt}=470\ mi/h$

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Differentiating with respect to time 't', we get:

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Now, when the plane is 2 miles away from radar station, then D = 2 mi

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4 years ago

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Answer:

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Step-by-step explanation:

Given data

payment (P) = $100

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future payment and interest after 45 year

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3 years ago

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