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Tresset [83]
3 years ago
6

Which of the following is a radical equation

Mathematics
1 answer:
Luden [163]3 years ago
3 0
Its b because yeah im just kidding idk im really stupid jk its b hahaha 

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The new length should be 9.5 inches and the new width should be 7 inches.
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What's the taxes on $1,500
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It depends on the percentage rate of said tax... is the tax rate 5%? 20%?
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How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0
2 years ago
What is 90 by 25% decreased
viva [34]

Answer:

- 22.5

Step-by-step explanation:

Answer:

90 decreased by 25% = 67.5

Absolute change (actual difference):

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While shopping, Dawn finds a backpack that she likes on the sale rack. Its original price is $60,
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No. Because 33 $ is the money deducted from the 60 $. Dawn bought everything for less than 60 $.

So, if Dawn purchases everything on the rack with a 30% discount and 15% coupon the total will indeed make 45%.

We have to take 100% - 45%= 55% to know the reduction number. Let's proceed to the calculations now.

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To find the amount at which she purchased everything, we need to do,

60 $ - 33 $ = 27 $

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3 years ago
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