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4 years ago

How do you work out? (step by step please) 2x-4≥6(x-1)

1 answer:

3 0

$2x-4 \geq 6(x-1)\\\\ 2x-4 \geq 6x-6 \\\\ 2x-6x \geq -6+4 \\\\-4x \geq -2 \ |:(-2) \\\\ 2x \leq 1 \\\\ x \leq \frac{1}{2} \\\\ \boxed{x= (-\infty; \frac{1}{2} ] }$

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A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

AURORKA [14]

Answer:

For maximum area, all of the wire should be used to construct the square.

The minimum total area is obtained when length of the wire is 10m

Step-by-step explanation:

For maximum, we use the whole length

For minimum,

supposed the x length was used for the square,

the length of the side of the square = x/4m

Area = $\frac{x^{2} }{16}$

For the equilateral triangle, the length of the side = $\frac{23 - x}{3}$

Area = $\frac{\sqrt{3} }{4} a^{2} = \frac{\sqrt{3} }{4} (\frac{23 - x}{3} )^{2}$

Total Area = $\frac{x^{2} }{16}$ + $\frac{\sqrt{3} }{36} (23-x)^{2}$

$\frac{dA}{dx} = \frac{x}{8} - \frac{\sqrt{3} }{18} (23 - x)\\$

$\frac{d^{2}A }{dx^{2} } = \frac{1}{8} + \frac{\sqrt{3} }{18} > 0$ , therefore it is minimum

$\frac{dA}{dx} = 0 \\\\$

$\frac{x}{8} - \frac{\sqrt{3} }{18} (23 - x) = 0\\$

x = 10.00m

3 0

3 years ago

Read 2 more answers

If one of the roots of the quadratice quation x2+kx-12=0is4,what is the value of k?

uysha [10]

<h3>Given Equation:</h3>

$\huge \purple {\rm { {x}^{2} + kx - 12 = 0}}$

<h3>Value:</h3>

$\huge \purple {\rm {x = 4}}$

$\huge \purple {\rm {The \: value \: of \: k.}}$

<h3>Solution:</h3>

$\huge \purple {\rm { {(4)}^{2} + k(4) - 12 = 0}}$

$\huge \purple {\rm {or, \: 16 + 4 k - 12 = 0}}$

$\huge \purple {\rm {or, \: 4k = - 4}}$

$\huge \purple {\rm {or, \: k = \frac{ - 4}{4} = - 1}}$

<h2>Answer:</h2>

$\huge \purple {\sf {The \: value \: of \: k \: is \: -1}}$

3 0

3 years ago

Read 2 more answers

What is the fourth row of Pascal’s triangle?

Anna [14]

Answer:

14641

Step-by-step explanation:

$formular \: for \: the \: digits \: in \: each \\ row \: of \: a \: pascal \: triangle \: is \: = 11 {}^{n} \\ row \: 0 = \: 11 {}^{0} = 1 \: \\ row \: 1 \: = 11 {}^{1} = 11 \\ row \: \: 2 \: = 11 {}^{2} = 121 \\ row \: 3 = \: 11 {}^{3} = 1331 \\ row \: 4 = 11 {}^{4} = 14641 \\ therefore \: the \: fourth \: row \: is \: 14641$

4 0

2 years ago

A store display shows two red shirts, four blue shirts, and

yulyashka [42]

Answer:

The probability is 3/5

Step-by-step explanation:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this question, we have that:

There are 2 + 4 + 4 + 4 + 2 + 4 = 20 itens.

Of those, 2 + 4 + 2 + 4 = 12 itens have white or red.

12/20 = 3/5

4 0

3 years ago

Orlando deposited $20 in his savings account. Find the additive inverse of 20 and write a real-world problem with these numbers,

eduard

Answer:

Loosing the $20, or spending $20

Step-by-step explanation:

Additive inverse of any number is that number, which when added with original number, gives 0.

i.e. Number + Its additive inverse = 0

Now, to find the additive inverse of $20.

Let that number be $a.

So, $20 + $a = 0

or, a = 0- 20 =$ -20

So, $(-20) is the additive inverse of 20.

Here, since the currency can not be negative, so the negative sign indicates the gain or loss or expenditure of the same amount.

So, if we have $20, and we loose or spend $20, we are at $0.

For example-

Sam has 17 candies. If he ate all 17 candies he is left with 0 candies.

Here, -17 represents the additive inverse of 17.

5 0

4 years ago