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Lady bird [3.3K]
3 years ago
5

A rectangular shoebox has a volume of 728 cubic inches. The base of the shoebox measures 8 inches by 6.5 inches. How long is the

shoe box?
Mathematics
1 answer:
bagirrra123 [75]3 years ago
8 0
Divide the volume by the two measures. 728 ÷ 8 = 91 ÷ 6.5 = 14 so, the shoe box is we inches long.
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If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
Dovator [93]

Keywords

quadratic equation, discriminant, complex roots, real roots

we know that

The formula to calculate the <u>roots</u> of the <u>quadratic equation</u> of the form  ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}

where

The <u>discriminant</u> of the <u>quadratic equation</u>  is equal to

b^{2}-4ac

if  (b^{2}-4ac)> 0 ----> the <u>quadratic equation</u> has two <u>real roots</u>

if  (b^{2}-4ac)=0 ----> the <u>quadratic equation</u> has one <u>real root</u>

if  (b^{2}-4ac)< 0 ----> the <u>quadratic equation</u> has two <u>complex roots</u>

in this problem we have that

the <u>discriminant</u> is equal to -8

so

the <u>quadratic equation</u> has two <u>complex roots</u>

therefore

the answer is the option A

There are two complex roots

5 0
3 years ago
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Pavel [41]

Answer:

1,3, and 7th option.

Step-by-step explanation:

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3 years ago
Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is
kodGreya [7K]

We're looking for a scalar function f(x,y) such that \nabla f(x,y)=\vec F(x,y). That is,

\dfrac{\partial f}{\partial x}=2x-6y

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Integrate the first equation with respect to x:

f(x,y)=x^2-6xy+g(y)

Differentiate with respect to y:

-6x+6y-7=-6x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=6y-7

Integrate with respect to y:

g(y)=3y^2-7y+C

So \vec F is indeed conservative with the scalar potential function

f(x,y)=x^2-6xy+3y^2-7y+C

where C is an arbitrary constant.

6 0
3 years ago
Write the following expression as the product of a repeated variable. X^5
klemol [59]

Answer:

25

Step-by-step explanation:

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3 years ago
If the sum of six consecutive even integers is 306, what is the smallest of the six integers
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3 years ago
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