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2 years ago

14

(-4.25)0 to the power

1 answer:

guajiro [1.7K]2 years ago

6 0

Step-by-step explanation:

convert decimal to fraction which is -(17/4) 2 to the second power, use exponent rules which is raise a fraction to a power, raise the numerator and the denominator to that power, and you get 289/16 more effective use 18 1/6

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<img src="https://tex.z-dn.net/?f=z%20%3D%203%20%2B%20i%20%5C%5C%20%7Bz%7D%5E%7B5%7D%20%3D%20" id="TexFormula1" title="z = 3 + i

jarptica [38.1K]

Answer:

$z^{5}$ = - 12 + 316 i

Step-by-step explanation:

Given that -

z = 3 + i

<em> $z^{2}$ = $( 3 + i )^{2}$ </em>

<em> $z^{2}$ = 9 + $i^{2}$ + 6 i</em>

<em> $z^{2}$ = 9 - 1 + 6 i</em>

$z^{2}$ = 8 + 6 i

<em> $z^{3}$ = $z^{2}$ × z</em>

<em> $z^{3}$ = ( 8 + 6 i ) × ( 3 + i )</em>

<em> $z^{3}$ = 24 + 8 i + 18 i + 6 i²</em>

<em> $z^{3}$ = 24 + 26 i - 6</em>

$z^{3}$ = 18 + 26 i

$z^{5}$ = $z^{2}$ × $z^{3}$

<em> $z^{5}$ = ( 8 + 6 i ) × ( 18 + 26 i )</em>

<em> $z^{5}$ = 144 + 208 i + 108 i + 156 i²</em>

<em> $z^{5}$ = 144 + 316 i -156</em>

$z^{5}$ = - 12 + 316 i

6 0

2 years ago

Solve for x in the following equation.

WARRIOR [948]

$\huge\text{Hey there!}$

$\mathsf{5^{x - 2} = 5^8}$

$\mathsf{5^{x - 2} = 5\times5\times5\times5\times5\times5\times5\times5}$

$\mathsf{5^{x - 2} = 25\times25\times25\times25}$

$\mathsf{5^{x - 2} = 625\times625}$

$\mathsf{5^{x - 2} =390,625}$

$\large\textsf{Solving for the exponent:}$

$\mathsf{5^{x - 2} =390,625}$

$\large\textsf{Take the log (logarithm) to both of the sides:}$

$\mathsf{log(5^{x - 2} \rightarrow log(390,625)}$

$\large\textsf{Simplify it:}$

$\mathsf{(x - 2) \times(log (5)) \rightarrow log(390,625)}$

$\large\textsf{Simplify that as well:}$

$\mathsf{x - 2 = \dfrac{log(390,625)}{log(5)}}$

$\large\textsf{You get it: }\mathsf{x - 2 = 8}$

$\large\textsf{ADD by 2 to BOTH of the SIDES:}$

$\mathsf{x - 2 + 2 = 8 + 2}$

$\large\textsf{Simplify it:}$

$\mathsf{x = 8 + 2}$

$\mathsf{x = 10}$

$\huge\textsf{Therefore, your answer should be:}$

$\huge\boxed{\mathsf{x =} \frak{10}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

5 0

1 year ago

Read 2 more answers

Transformation for y=-2(x-1)2 + 2

Llana [10]

Answer:

Vertex = 1,2

it is shifted 2 units up and to the right 1 unit

it is a downward parabola (max at (1,2) going down

Step-by-step explanation:

5 0

2 years ago

A salesperson at a jewelry store earns 3% commission each week. Last week, Heidi sold $750

vampirchik [111]

She made $22.5 of commission

4 0

3 years ago

Need help with #1 #4 #7 plz giving 15 points

valentina_108 [34]

Answer:

Q1: p = - 33

Q2: d = - 99

Q3: t = - 13

Step-by-step explanation:

Q1: $$ \textbf{-} \frac{\textbf{p}}{\textbf{3}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{8} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{3}$

We solve this taking LCM.

We get: $\frac{-p - 24}{3} = 3$

$\implies - p - 24 = 9$

$\implies \textbf{p} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 33}$

Q4: $\frac{\textbf{d}}{\textbf{11}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{4} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13}$

Again we proceed like Q1 by taking LCM.

We get: $\frac{d - 44}{11} = - 13$

$\implies d - 44 = - 13 \times 11 = - 143$

$\implies d = - 143 + 44$

$\implies \textbf{d} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 99}$

Q7: 5t + 12 = 4t - 1

We club the like terms on either side.

$\implies 5t - 4t = - 1 - 12$

$\implies (5 -4)t = - 13$

$\implies \textbf{t} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13}$

Hence, the answer.

7 0

2 years ago