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3 years ago

What is the side length of a cube with the volume 343cm3?

Mathematics

2 answers:

Oksi-84 [34.3K]3 years ago

7 0

The side length is 7 because 7*7*7 is 343 cm3

prohojiy [21]3 years ago

4 0

Volume is length times width times height so 343 divided by 7 so seven is the answer

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2) I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

Given function:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find a, compare the coefficients of x³:

$\implies a=3$

To find b, substitute the found value of a into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find c, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

Zero Product Property

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

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1 year ago

Write 2 in the form of a fraction (a/b).

Yuri [45]

Answer:

23/8

Step-by-step explanation:

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2 years ago

which statement couls be used to explain why the function h(x)=x³ has an inverse relation that is also a function

Gnom [1K]

Answer: Option 4

Step-by-step explanation:

The way to tell if a function has an inverse is to see if it passes the horizontal line test (if a horizontal line crosses the graph more than once).

P.S. I hope this helped! Feel free to tell me if I got it wrong, I'll try my best to fix it.

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2 years ago

If 6 teenagers can drink 6 ice cream sodas in 2 minutes. how many ice cream sodas can the same 6 teenagers drink in 2 hours

san4es73 [151]

Not sure if I’m correct, but 360 because I’m 1 minute they can drink 3 ice cream sodas, so multiply 3 by 60, the 60 is supposed to be 60 minutes, once you get that amount that you multiplied (180) add it again (180+180) the total should be your answer.

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3 years ago

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