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zvonat [6]
2 years ago
15

If the operation is defined for all integers a and b by

"35547557">[email protected] = a + b - ab, which of the following statements must be true for all integers a, b and c?
I. [email protected] = [email protected]
II. [email protected] = a
III. ([email protected])@c = [email protected]([email protected])

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II and III
Mathematics
1 answer:
leva [86]2 years ago
6 0

Answer:

(E) I, II and III

Step-by-step explanation:

Given,

[email protected] = a + b - ab ∀ a, b ∈ Z ( set of all integers ),

For solving this question we need to remember the following properties of integers:

  • Commutative property of addition
  • Additive identity property of addition
  • Commutative property of multiplication
  • Distributive property of multiplication over addition

I. [email protected] = a + b - ab,

[email protected] = b + a - ba = a + b - ab

Thus, [email protected] = [email protected]

II. [email protected] = a + 0 - a × 0

= a + 0 - 0  

= a

III. ([email protected])@c = ([email protected])+c - ([email protected])c

= (a + b - ab) + c - (a + b - ab)c

= a + b - ab + c - ac - bc + abc

= a + b + c - ab - bc - ac + abc,

Now, [email protected]([email protected]) = [email protected]( b + c - bc )

= a + (b + c - bc) - a(b+c - bc)

= a + b + c - bc - ab - ac + abc

= a + b + c - ab - bc - ac + abc.

Thus, ([email protected])@c = [email protected]([email protected])

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On a road trip, a family drives 350 miles per day. How many days, d, must they travel to reach a distance of at least 1,400 mile
Semenov [28]

Answer:

Inequality symbol = ≥

Solution = d≥4

Step-by-step explanation:

If a family drives 350 miles per day, then;

1 day = 350 miles

To determine the number of days they will use to reach at least 1400mles

d days = 1400miles

Divide both expressions

1/d = 350/1400

Cross multiply

350 * d = 1400

350d = 1400

Since we are told that it ia at least 1400miles, this means the total miles can be greater than 1400. Hence the correct inequality sign to use will be a greater than or equal to sign(≥).

The expression above becomes 350d ≥ 1400

Divide both sides by 3350

350d ≥ 1400/350

d≥ 4

Hence the solution that represent the situation is d≥ 4

8 0
3 years ago
Suppose the line of best fit for some data points has a slope of 4.915. If the mean of the x-coordinates of the data points is 1
aleksley [76]

The y-intercept of the linear equation of best fit, considering the slope and the means, is of -60.428.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For a line of best-fit, the y-intercept is given by:

b = \overline{y} - m\overline{x}

The parameters in this problem are given as follows:

m = 4.915, \overline{x} = 14.347, \overline{y} = 10.088

Then:

b = 10.088 - 4.915(14.347) = -60.428

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

5 0
1 year ago
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