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Yanka [14]
3 years ago
8

Replace ∗ with a monomial so that the result is an identity:

Mathematics
1 answer:
Mumz [18]3 years ago
7 0

QUESTION 1

Taking the right hand side we have;

4a^2-b^2

We can rewrite this as;

(2a)^2-b^2

We apply difference of two squares.

p^2-q^2=(p+q)(p-q)

(2a-b)(2a+b)

\therefore (2a-b)(2a+b)=4a^2-b^2

QUESTION 2

Taking the right hand side we have;

25x^2-0.16y^4

We can rewrite this as;

(5x)^2-(0.4y^2)^2

We apply difference of two squares.

p^2-q^2=(p+q)(p-q)

(5x-0.4y^2)(5x+0.4y^2)

\therefore (5x-0.4y^2)(5x+0.5y^2)=25x^2-0.16y^4

QUESTION 3

Taking the right hand side of the given equation, we have;

121a^{10}-b^8

We rewrite this as;

(11a^{5})^2-(b^4)^2

\therefore (11a^{5})^2-(b^4)^2=(11a^5-b^4)(11a^5+b^4)

QUESTION 4

From the RHS;

16y^2-9x^2

This implies that;

(4y)^2-(3x)^2

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

QUESTION 5

From the left hand side, we have

100m^4-4n^6

This implies that;

(10m^2)^2-(2n^3)^2

Using difference of two squares, we have;

(10m^2)^2-(2n^3)^2=(10m^2-2n^3)(2n^3+10m^2)

QUESTION 6

From the LHS;

m^4-225m^{10}

We rewrite to obtain;

(m^2)^2-(15c^5)^2

Using difference of two squares, we obtain;

(m^2)^2-(15c^5)^2=(m^2-15c^5)(15c^5+m^2)

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Is 5.78778777 a rational or irrational number?..
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3 years ago
You want to rent a car for the day.Prestige car rentals charges $47 plus $0.07 per mile to rent a midsize vehicle . Gateway Auto
jolli1 [7]

Answer:

240 miles

Step-by-step explanation:

Given that:

Charges offered by Prestige car rentals for renting a midsize vehicle:

Fixed charges = $47

Per mile charges for renting a midsize vehicle = $0.07

Charges offered by Gateway Auto for renting a midsize vehicle:

Fixed charges = $35

Per mile charges for renting a midsize vehicle = $0.12

To find:

Number of miles for which both the companies charge the same price?

Solution:

Let the number of miles for which both the companies will charge the same price = x miles

Charges for one mile by Prestige car rentals = $0.07

Charges for x miles by Prestige car rentals = $0.07x

Total charges by Prestige Car rentals = $47 + $0.07x

Charges for one mile by Gateway Auto = $0.12

Charges for x miles by Gateway Auto = $0.12x

Total charges by Gateway Auto = $35 + $0.12x

As per question statement, the charges are same:

\$47 + \$0.07x = \$35 + \$0.12x\\\Rightarrow 12=0.05x\\\Rightarrow x=\dfrac{1200}{5}\\\Rightarrow \bold{x=240\ miles}

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