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Vanyuwa [196]
2 years ago
9

Twice the larger of two consecutive integers is equal to fifteen less than three times the smaller. Find the integers.

Mathematics
1 answer:
Alexxandr [17]2 years ago
7 0

Answer:

17,18

Step-by-step explanation:

let the smaller integer be "a" and the larger be "b"

Then 2b = 3a -15              ........................equ 1

but they are consecutive integers, b= a+1 ; substitute b into equ 1,thus,

2(a+1) = 3a - 15

2a + 2 = 3a-15

collect like terms,

2+15 =3a-2a

17 = a

b= a+1

b = 17+1

b=18.

The integers are 17,18

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Quentin is one third the age of his aunt. And 20% older than his sister. If Quentin's sister is 15 years old, how old is his aun
anastassius [24]

Answer:

54

Step-by-step explanation:

20% of 15 is 3 so Quentin is 18 years old

If Quentin is one thrid his Aunt's age that means his aunt is three times older.

18 * 3 = 54

So his Aunt is 54 years old

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3 years ago
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you have 160 yards of fencing to enclose a rectangular region. find the maximum area of the rectangular region
Dimas [21]
The maximum area of a rectangle when given perimeter is simply perimeter/sides.
To get the maximum area, simply divide 160 (perimeter) by 4 (sides in a rectangle) and then square the result:
160/4 = 40
40 x 40 = 1600
The maximum area, when the sides are all of the same length, is <u><em>1600 square yards.
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3 years ago
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Pythagorean Theorem with Known Legs
stepan [7]

you're given the pythagorean theorem, which is a^2 + b^2 = c^2.

what you're trying to find is ?, which is the number under the radical.

let's pretend one leg is a and the other is b.

a = 9

b = 10

so let's plug it into the equation. we get 9^2 + 10^2 = c^2

so that equals 81 + 100 = c^2

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Start at 10. Create a pattern that multiplies each number by 10
Yanka [14]

Pattern:

10, 100, 1,000, 10,000, 100,000, 1,000,000, 10,000,000, and so on.

Step-by-step explanation:

First, you must start by using 10 and multiplying it 10 times, 10 x 10 = 100.

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Countiue and you will get it.


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6 0
3 years ago
D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x
MA_775_DIABLO [31]
The solution depends on the value of k. To make things simple, assume k>0. The homogeneous part of the equation is

\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0

and has characteristic equation

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which admits the characteristic solution y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}.

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be y_p=ae^{4x}+be^x. Then

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and so the general solution would be

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8 0
2 years ago
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