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Given that y = 2 − 3x, complete the table correctly. 30. Solve for K: (64)2k = (16)^(K+4). 31. Simplify: 0.042-0.012 / 0.5 X 0.2

Mathematics

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3 parts
28

Jedwalilililokamilikahapojuu\text{}Jedwali lililokamilika hapo juu\text{}

30

2\text{}2\text{}

31

0.3\text{}0.3\text{}

Graph of y = 2 − 3x

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Key points of y = 2 − 3x
Pointxy
y-intercept02
x-intercept0.670

Step-by-step solution

7 steps

Haya Ocen, twende kazi!

Part 28

Tunapewa y=2−3xy = 2 - 3x. Tunahitaji kukamilisha jedwali.

  • Wakati y=2y=2: 2=2−3x2 = 2 - 3x 0=−3x0 = -3x x=0x = 0

  • Wakati x=1x=1: y=2−3(1)y = 2 - 3(1) y=2−3y = 2 - 3 y=−1y = -1

  • Wakati y=−4y=-4: −4=2−3x-4 = 2 - 3x −6=−3x-6 = -3x x=2x = 2

  • Wakati x=5x=5: y=2−3(5)y = 2 - 3(5) y=2−15y = 2 - 15 y=−13y = -13

  • Wakati y=−3y=-3: −3=2−3x-3 = 2 - 3x −5=−3x-5 = -3x x=53x = \frac{5}{3}

  • Wakati x=0x=0: y=2−3(0)y = 2 - 3(0) y=2−0y = 2 - 0 y=2y = 2

  • Wakati y=−4y=-4 (rudia): −4=2−3x-4 = 2 - 3x −6=−3x-6 = -3x x=2x = 2

Jedwali lililokamilika ni:

y2−1−4−13−32−4x01255302\begin{array}{|c|c|c|c|c|c|c|c|} \hline y & 2 & -1 & -4 & -13 & -3 & 2 & -4 \\ \hline x & 0 & 1 & 2 & 5 & \frac{5}{3} & 0 & 2 \\ \hline \end{array}

Jibu ni Jedwalilililokamilikahapojuu\boxed{\text{}Jedwali lililokamilika hapo juu\text{}}

Part 30

2\text{}2\text{}

Tatua kwa KK: (64)2k=(16)(k+4)(64)^{2k} = (16)^{(k+4)}.

  1. Andika namba 64 na 16 kama nguvu za namba moja, kwa mfano 2.

    64=2664 = 2^6 na 16=2416 = 2^4.

    (26)2k=(24)(k+4)(2^6)^{2k} = (2^4)^{(k+4)}
  2. Tumia sheria ya vipeo (am)n=amn(a^m)^n = a^{mn} kurahisisha pande zote mbili.

    26×2k=24×(k+4)2^{6 \times 2k} = 2^{4 \times (k+4)} 212k=24k+162^{12k} = 2^{4k+16}
  3. Kwa kuwa besi (base) ni sawa, linganisha vipeo (exponents).

    12k=4k+1612k = 4k+16
  4. Tatua mlinganyo kwa KK.

    12k−4k=1612k - 4k = 16 8k=168k = 16 k=168k = \frac{16}{8} k=2k = 2

    Thamani ya KK ni 2\boxed{\text{}2\text{}}

Part 31

0.3\text{}0.3\text{}

Rahisisha: 0.042−0.0120.5×0.2\frac{0.042 - 0.012}{0.5 \times 0.2}.

  1. Rahisisha nambari (numerator).

    0.042−0.012=0.0300.042 - 0.012 = 0.030
  2. Rahisisha kinyume (denominator).

    0.5×0.2=0.100.5 \times 0.2 = 0.10
  3. Gawanya nambari kwa kinyume.

    0.0300.10=0.030.1\frac{0.030}{0.10} = \frac{0.03}{0.1} 0.030.1=0.3\frac{0.03}{0.1} = 0.3

    Thamani iliyorahisishwa ni 0.3\boxed{\text{}0.3\text{}}

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