Solve −3x+5<17 <br><br> If someone could do this fast it would really help!

3.3^(2x+1)-103^x+1=0 need value of x

photoshop1234 [79]

Answer:

The value of $x$ is approximately -1.531.

Step-by-step explanation:

Let $3.3^{2\cdot x + 1}-103^{x+1} = 0$ , we proceed to solve this expression by algebraic means:

1) $3.3^{2\cdot x + 1}-103^{x+1} = 0$ Given

2) $3.3^{2\cdot x}\cdot 3.3 -103^{x}\cdot 103 = 0$ $a^{b}\cdot a^{c} = a^{b+c}$

3) $(3.3^{x})^{2}\cdot 3.3 -\left[\left( \sqrt{103} \right)^{2}\right]^{x}\cdot 103 = 0$ $(a^{b})^{c} = a^{b\cdot c}$

4) $(3.3^{x})^{2}\cdot 3.3 - \left[\left(\sqrt{103}\right)^{x}\right]^{2}\cdot 103 = 0$ $(a^{b})^{c} = a^{b\cdot c}$ /Commutative property

5) $\left[\left(\frac{3.3}{\sqrt{103}}\right)^{x}\right] ^{2}-\frac{103}{3.3} = 0$ Existence of multiplicative inverse/Definition of division/Modulative property/ $a^{b}\cdot a^{c} = a^{b+c}$

6) $\left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\frac{103}{3.3}$ Existence of additive inverse/Modulative property/ $(a^{b})^{c} = a^{b\cdot c}$

7) $\log \left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\log \frac{103}{3.3}$ Definition of logarithm.

8) $2\cdot x\cdot \log \left(\frac{3.3}{\sqrt{103}} \right)= \log \frac{103}{3.3}$ $\log_{b} a^{c} = c\cdot \log_{b} a$

9) $2\cdot x \cdot [\log 3.3-\log \sqrt{103}] = \log 103 - \log 3.3$ $\log_{b} \frac{a}{d}$

10) $x\cdot (2\cdot \log 3.3-\log 103) = \log 103 - \log 3.3$ $\log_{b} a^{c} = c\cdot \log_{b} a$ /Associative property

11) $x = \frac{\log 103-\log 3.3}{2\cdot \log 3.3-\log 103}$ Existence of multiplicative inverse/Definition of division/Modulative property

12) $x \approx -1.531$ Result

The value of $x$ is approximately -1.531.

4 0

2 years ago

Five independent flips of a fair coin are made. Find the probability that(a) the first three flips are the same;(b) either the f

Korvikt [17]

Answer:

The answers to the question are

(a) 1/4

(b) 7/16

(c) 1/16

Step-by-step explanation:

To solve the question we note that

Total number of outcomes = 32

Probability of the event of first three flips are the same =P(F)

Probability of the event of last three flips are the same =P(L)

Total number of outcomes = 2⁵ = 32

The number of ways in which the frist three flips are the same is

F TTTTT, TTTTH, TTTHH, HHHTT, HHHHT, HHHHH, TTTHT, HHHTH = 8

L: TTTTT, HHTTT, HTTTT, THTTT, HHHHH, TTHHH, HTHHH, THHHH = 8

The probability that the first and the last three flips are the same that is

F ∩ L; TTTTT, HHHHH = 2

Therefore P(F ∩ L) = 2/32

(a) P(F) = 8/32 =1/4 also

P(L) = 8/32 =1/4

(b) P(LUF) = P(L) + P(F) - P(F ∩ L) = 1/4+1/4-1/16 =7/16

(c) Let the event of at least two heads among the first three flips be H

and the event of at least two tails among the last three flips be T

Then we have

H; HHHHH, HHHHT, HHHTT, HHHTH, HHTTT, HHTHH, THHTT, THHHT

= 8

T; TTTTT. HTTTT, HHTTT, THTTT, THHTT, HHHTT, THHTT, HTTTH =8

Also H∩T = TTTHH, HHTTT = 2

Therefore P(H ∩ T) = 2/32 = 1/16

5 0

2 years ago

A tree is 58 inches tall. how tall is it in feet and inches

mart [117]

A foot is 12 inches.
12 can go into 58 evenly 4 times, since 12• 4 equals 48 but 12 • 5 equals 60. This means that the tree is at least 4 feet. Then to find the leftover inches we do 58-48 equals 10, therefore the answer is 58 inches translates to 4 feet and 10 inches.

8 0

2 years ago

The area of a rectangle is 440 square inches. The length of the rectangle is 29 inches more than its width. What is the length o

Andreyy89

The length of regtangle is 40 inches

3 0

2 years ago

Please answer thanks. Come on its 30 points

VashaNatasha [74]

Be right there! Let's do this!

3 0

2 years ago

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Solve −3x+5<17 If someone could do this fast it would really help!