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2 years ago

Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6?

Mathematics

1 answer:

wolverine [178]2 years ago

6 0

ANSWER

$9\: < x \leqslant0$

EXPLANATION

The given compound inequality is

$- 33 \: > - 3x - 6 \geqslant - 6$

We need to simplify this inequality so that we can obtain x standing alone between the inequality signs.

We add 6 through out the inequality.

$- 33 + 6\: > - 3x - 6 + 6 \geqslant - 6 + 6$

This simplifies to:

$- 27\: > - 3x \geqslant 0$

We now divide through by -3 and reverse the inequality sign.

$\frac{- 27}{ - 3} \: < \frac{ - 3x}{ - 3} \leqslant \frac{0}{ - 3}$

We now simplify to get:

$9\: < x \leqslant 0$

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T= 300 (d−15) 2 +20space, T, equals, start fraction, left parenthesis, d, minus, 15, right parenthesis, start superscript, 2,

stealth61 [152]

As can be read from your statement written "T, equals, start fraction, left parenthesis, d, minus, 15, right parenthesis, strt superscript, 2, end superscript, divided by, 300, end fraction, plus, 20", I hope your model equation is this :

$T = \frac{(d-15)^{2}}{300} + 20$

Hope this is your question, if not I think you will, still be able to find an answer of your question based on this solution

As we have to find lowest average temperature, So for minimum of a function its derivative is equal to 0 there.

So lets find derivative of T function first

So first expand $(d-15)^{2}$ as (d-15)(d-15)

we will use FOIL to multiply these

so $(d-15)(d-15) = d^{2} -15d -15d +225$

$= d^{2} -30d +225$

so we have $T = \frac{d^{2} -30d +225}{300} +20$

Now we will derivate each term here,300 in denominator is constant so that will come as it in in denominator.

To derivate terms in $dx^{2} -30d +225$ we will use power rule formula:

$(x^{n} )'= nx^{n-1}$

so derivative of $(d^{2} )'= 2d^{2-1} = 2d^{1} = 2d$

Then derivative of d will be 1

so that of -30d will be -30

then derivate of constant -225 will be 0

so we will have derivative as $\frac{2d-30}{300}$ for the fraction part and then derivative of +20 is again 0 as its constant term

$T' = \frac{2d-30}{300}$

For minimum we will put this derivative =0

$0 = \frac{2d-30}{300}$

Now solve for d

times both sides by 300

$0 \times 300 = \frac{2d-30}{300} \times 300$

$0 = 2d-30$

$0 +30 = 2d -30 +30$

$30 = 2d$

$\frac{30}{2} = \frac{2d}{2}$

$15 = d$

So now we have to find value of lowest temperature.

For that simply plug 15 in d place in original T function equation

$T = \frac{(d-15)^{2}}{300} + 20$

$T = \frac{(15-15)^{2}}{300} + 20$

$T = 20$

So T = 20 °C is the lowest average temperature and the answer.

6 0

2 years ago

Read 2 more answers

In an exam 35 out of 125 students failed. What percentage passed the exam?

kotegsom [21]

Answer:

28%

Step-by-step explanation:

To find the percentage, you first have to divide:

35 out of 125 Which is 35 ÷ 125 = 0.28

Then you must convert that into a percentage:

0.28 = 28%

Hope this helps you out! : )

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2 years ago

1. Write 3,876,943,000 using scientific notation.

Sunny_sXe [5.5K]

Answer:

3.876943x10^9

7.317x10^-4

Step-by-step explanation:

3,876,943,000

Put the decimal at the end

3,876,943,000.

Move it so only 1 number is before the decimal

3.876943000

We moved it 9 places, so that is the exponent

We moved it to the left, so the exponent is positive

The three zeros at the end can be dropped because they are the last numbers to the right of the decimal

3.876943x10^9

0.0007317

Move it so only 1 number is before the decimal

00007.317

We moved it 4 places, so that is the exponent

We moved it to the right, so the exponent is negative

The four zeros at the left can be dropped because they are the last numbers to the left of the whole number

7.317x10^-4

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ankoles [38]

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6x2y – 2x2y – 10x2y + 8x2y =

svp [43]

Answer:

4y is your answer........

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