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Oxana [17]
3 years ago
12

Select the correct answer. Which expression is equivalent to 8x^2^3 sqrt 375x + 2^3 sqrt 3x^7, if x=0?

Mathematics
2 answers:
natima [27]3 years ago
4 0

Answer:

(8x^3)^ \frac{2}{3} \sqrt{75x^3}  + 2^3 \sqrt{ 3x^7} =28x^3\sqrt{3x}

Step-by-step explanation:

The question is poorly formatted. The original question is:

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7

We have:

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7

Open bracket

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^{3* \frac{2}{3}}) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

Express 8 as 2^3

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^{3* \frac{2}{3}} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^2 *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =4x^2 \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

Express 2^3 as 8

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{75x^3} + 8\sqrt{ 3x^7}

Expand each exponent

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2 *3x} + 8\sqrt{ 3x * x^6}

Split

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2} *\sqrt{3x} + 8\sqrt{3x} * \sqrt{x^6}

(8x^3)^ \frac{2}{3} \sqrt{75x^3}  + 2^3 \sqrt{ 3x^7} =4x^2 *5x *\sqrt{3x} + 8\sqrt{3x} * x^3

(8x^3)^ \frac{2}{3} \sqrt{75x^3}  + 2^3 \sqrt{ 3x^7} =20x^3\sqrt{3x} + 8x^3\sqrt{3x}

Factorize

(8x^3)^ \frac{2}{3} \sqrt{75x^3}  + 2^3 \sqrt{ 3x^7} =28x^3\sqrt{3x}

Harlamova29_29 [7]3 years ago
4 0

Answer:

42x^2 ^3 square root 3x

Step-by-step explanation:

i got it right

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Step-by-step explanation:

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Hey there!

\\

  • Answer:

\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}

\\

  • Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be \: \sf{d_1} \: and the line that is parallel to \: \sf{d_1} \: be \: \sf{d_2} \: .

\sf{d_2} \: passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}

\\

⇒Subtitute the values :

\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}

\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}

\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}.

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \:  the \: line \: and \: b \: is \: the \: y-intercept.}

\implies \sf{y = \bold{\dfrac{7}{6}}x + b} \\

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line \: \sf{d_1} \:. Now, replace y with -3 and x with 0:

\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:

Therefore, the equation of the line \: \bold{d_1} \: is \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}

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▪️Learn more about finding the equation of a line that is parallel to another one here:

↣brainly.com/question/27497166

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