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stich3 [128]
3 years ago
6

If 1/64=4^2s-1 times 16^2s+2 what is the value of s?

Mathematics
2 answers:
Irina18 [472]3 years ago
5 0

Answer: s=-1

Explanation:

We can re-write the equation as follows:

\frac{1}{64}=(4^{2s-1})(16^{2s+2})

Let's rewrite the terms on the left and on the right as follows:

2^{-6} = ((2^2)^{2s-1})((2^4)^{2s+2})

So we have

2^{-6} = (2^{2(2s-1)})(2^{4(2s+2)})

Now we can use the following rule:

x^{a+b}=x^a x^b

to rewrite the term on the right:

(2^{2(2s-1)})(2^{4(2s+2)})=2^{2(2s-1)+4(2s+2)}

So now we have

2^{-6}=2^{2(2s-1)+4(2s+2)}

and since the bases are the same, we can just equalize the exponents:

-6=2(2s-1)+4(2s+2)

-6=4s-2+8s+8\\-12 = 12 s\\s=-1

galina1969 [7]3 years ago
4 0
S=-1 see attachment for explanation

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S the following statement always, sometimes, or never true?
liubo4ka [24]

The statement <em>“The supplement of an acute angle is an obtuse angle.”</em> is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)

Step-by-step explanation:

Let us revise some facts about the supplementary angles

  • Supplementary angles are two angles the sum of their measure is 180°
  • The two angles could be right angles or one of them is acute and the other is obtuse
  • The two angles can not be acute angles or obtuse angles

Let us take some examples to explain the facts above

∵ One of two supplementary angles is a right angle

∵ The measure of the right angle is 90°

∵ The sum of the measures of the supplementary angles is 180°

∴ 90 + the measure of the supplement angle = 180

- Subtract 90 from both sides

∴ The measure of the supplement angle = 90°

∴ The supplement of a right angle <u><em>must be</em></u> a right angle

∵ One of two supplementary angles is 70°

∵ Its measure less than 90°

∴ This angle is an acute angle

∵ The sum of the measures of the supplementary angles is 180°

∴ 70 + the measure of the supplement angle = 180

- Subtract 70 from both sides

∴ The measure of the supplement angle = 110°

∵ Its measure greater than 90°

∴ The supplement angle is an obtuse angle

∴ The supplement of an acute angle <u><em>must be</em></u> an obtuse angle

The two supplementary angles can not be acute angles because their sum is less than 180°

The two supplementary angles can not be obtuse angles because their sum is greater than 180°

The statement <em>“The supplement of an acute angle is an obtuse angle.”</em> is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)

Learn more:

You can learn more about the supplementary angles in brainly.com/question/11175936

#LearnwithBrainly

4 0
3 years ago
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Mustafa’s soccer team is planning a school dance as a fundraiser. The dj charges $200 and decorations cost $100. The team deci
Kaylis [27]

Question is Incomplete;Complete question is given below.

Mustafa’s soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit?

5n - 300 = 1,500\\\\5n + 300 = 1,500\\ \\5n - 200 + 100n = 1,500\\\\5n - 100 -200n = 1,500

Answer:

5n - 300 = 1,500

Step-by-step explanation:

Given:

Charges of DJ = $200

Decoration charges = $100

Profit need to be made = $1500

Charges per student to attend the dance = $5

We need to write the equation to find the number of students for to attend the dance in order to make profit.

Solution:

Let the number of student be represented by 'n'.

Now we can say that;

Profit to be made should be equal to Charges per student to attend the dance multiplied by number of students minus sum of Charges of DJ and Decoration charges.

framing in equation form we get;

5n-(200+100)=1500\\\\5n-300=1500

Hence the equation to find the number of students attending the dance is 5n - 300 = 1,500

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Kendall is making greeting cards, which she will sell by the box at an arts fair. She paid $40
natta225 [31]

Answer:

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10 dollars made per sale

5 dollars lost per creation

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<em>$5 used up for material cost, $10 made from sales </em><em>-5+10= 5</em>

To pay the $40 dollar for the booth she would need to make 9 sales with her current profit

<em>40/5 = 9</em>

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Answer:

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Akimi4 [234]

Answer:

-2

Step-by-step explanation:

they are parallel so same slope but different y intercepts

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