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3 years ago

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Consider the sequence 8, 14, 20, 26, . . .. (a) What is the next term in the sequence? 2.2 Exercises 98 (b) Find a formula for t

he nth term of this sequence, assuming a1 8. (c) Find the sum of the first 100 terms of the sequence: P100 k1 ak

1 answer:

omeli [17]3 years ago

3 0

Answer:

Step-by-step explanation:

Each term of the given arithmetic sequence is 6 more than the previous one. Thus, the next term is 26+6, or 32.

a(n) = 8 + 6(n-1)

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Solve each equation (quadratic pattern)

dusya [7]

Answer: x = 2

<u>Step-by-step explanation:</u>

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Answer: x = 0

<u>Step-by-step explanation:</u>

$3^{2x}+3^{x+1}-4=0\\\\3^{2x}+3^x\cdot3^1-4=0\\\\\text{Let u = }3^x\\u^2+3u-4=0\\\\(u+4)(u-1)=0\\\\u+4=0\quad and\quad u-1=0\\u=-4\qquad and\quad u=1\\\\\text{Substitute u with }3^x\\3^x=-4\qquad and\quad 3^x=1\\\text{not possible}\ and\quad 3^x=3^0\\.\qquad \qquad \qquad \qquad \boxed{x=0}$

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Answer: No Solution

<u>Step-by-step explanation:</u>

$4^x+6\cdot 2^x+8=0\\\\2\cdot 2^x+6\cdot 2^x+8=0\\\\\text{Let u = }2^x\\2u+6u+8=0\\8u+8=0\\8u=-8\\u=-1\\\\\text{Substitute u with }2^x\\2^x=-1\\\text{not possible}$

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Answer: No Solution

<u>Step-by-step explanation:</u>

<u> $9^x=3^x-6\\\\3\cdot 3^x=1\cdot 3^x-6\\\\\text{Let u = }3^x\\\\3u=u-6\\2u=-6\\u=-3\\\\\text{Substitute u with }3^x\\3^x=-3\\\text{not possible}$ </u>

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3 years ago

Some one help me on this one

aleksandrvk [35]

The answer is III only, or D.

We can start to solve this by knowing what the HL theorem means. The HL theorem, like its name implies, shows says that if a hypotenuse and leg of a triangle are congruent to the hypotenuse and leg of a different triangle, then the triangles are congruent. The only triangle that we see a hypotenuse congruent in is in figure III. In figure II, those congruent sides are both legs while in figure I we just see 2 congruent angles. Now in figure III, we can also see that two legs are congruent because of the reflexive property. That means that the answer is III, or D.

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3 years ago

What is a 15% tip on a meal that costs $25.00

nataly862011 [7]

$25.00/ 10= 2.50
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As you've got 15%, the best thing to do is to find 10%, then multiply it by 1.5. Once you've found the tip, you add this onto the cost of the meal.
Therefore, the total cost of $25 meal with a 15% tip is $28.75
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3 years ago

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k0ka [10]

Answer:

625 ft^2

Step-by-step explanation:

Given

$P = 100$ --- perimeter

Required

The largest area

The perimeter is calculated as:

$P = 2 * ( L + W)$

So, we have:

$2 * ( L + W) = 100$

Divide both sides by 2

$L + W = 50$

Make L the subject

$L = 50 - W$

The area is calculated as:

$A= L * W$

Substitute $L = 50 - W$

$A= (50 - W) * W$

Open bracket

$A = 50W - W^2$

Differentiate with respect to W

$A' = 50 -2W$

Set to 0; to get the maximum value of W

$50 - 2W = 0$

Collect like terms

$-2W = -50$

Divide by -2

$W = 25$

So, the maximum area is:

$A = 50W - W^2$

$A = 50 * 25 - 25^2$

$A = 1250 - 625$

$A = 625$

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