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2 years ago

Plesse help me:) ive been stuck on this for a while

Mathematics

1 answer:

il63 [147K]2 years ago

3 0

Answer:

4th number line (the one of the bottom right)

Step-by-step explanation:

First, solve the inequality, then choose the number line that mathes the solution.

3x ≤ -6

Only step: Divide by 3.

x ≤ -6/3

x ≤ -2

But which number line matches the solution?

We know this is going left, so #1 & #3 are out. This also has a closed circle (because of ≤ (less than/equal to)), so #2 is also out.

Number line #4 matches the solution (x ≤ -2), so it is the answer.

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Which of the following expressions is equivalent to a3 + b3?

lubasha [3.4K]

ANSWER
${a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )$

EXPLANATION

To find the expression that is equivalent to
${a}^{3} + {b}^{3}$
we must first expand
${(a + b)}^{3}$
Then we rearrange to find the required expression.

So let's get started.

${(a + b)}^{3} = (a + b) {(a + b)}^{2}$

We expand the parenthesis on the right hand side to get,

${(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )$

We expand again to obtain,

${(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}$

Let us group the cubed terms on the right hand side to get,

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)$

We make the cubed terms the subject,

${(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}$

We factor to get,

$(a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We expand the bracket on the left hand side to get,

$(a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We finally simplify to get,

$(a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

5 0

3 years ago

Read 2 more answers

Find the 12th and 37th term for each arithmetic sequence.

shutvik [7]

Answer:

3. f(12) = -10; f(37) = -60

4. f(12) = -102; f(37) = -352

Step-by-step explanation:

3. Put the numbers in the formula and do the arithmetic:

f(12) = 12 -2(12-1) = 12 -22 = -10

f(37) = 12 -2(37-1) = 12 -72 = -60

4. The explicit formula for an arithmetic sequence with first term a1 and common difference d is ...

an = a1 +d(n -1)

Your sequence has a first term a1=8 and a common difference d=-10.

As above, fill in the numbers and do the arithmetic.

f(12) = 8 -10(12 -1) = -102

f(37) = 8 -10(37-1) = -352

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3 years ago

What is the formula for the pythagorem theory

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Answer:

C^2 = a^2 + b^2

The formula for the pythagorem theory

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Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal plac

worty [1.4K]

So here is the answer to the given equation above.
To find the answer, we can just factor this one.
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3 years ago

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Prime factorization of 212

Montano1993 [528]

212= 2 X 2 X 53
212= 4X 53

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