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Scilla [17]
2 years ago
10

2%20%7D%20%7D%20%7B%20%28%20%5Csqrt%20%7B%205%20%7D%20%29%20%5E%20%7B%202%20%7D%20%7D%20%5C%7D%20%5E%20%7B%20%5Cfrac%20%7B%201%20%7D%20%7B%202%20%7D%20%7D" id="TexFormula1" title="\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }" alt="\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }" align="absmiddle" class="latex-formula">solve this equation
​
Mathematics
1 answer:
ZanzabumX [31]2 years ago
3 0

Answer:

Step-by-step explanation:

Exponent law:

    \sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}

    \sf a^{-m}=\dfrac{1}{a^m}

       First convert radical form to exponent form and then apply exponent law.

 \sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}

\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}

                      = \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}

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Which expression is equivalent to 7(a+2) when a=6?<br> 7(6)<br> 9(6)<br> 7(6)+2<br> 7(6)+14
Pie

It is equivalent to 7(6) + 14

Step-by-step explanation:

  • Step 1: Solve 7(a + 2) when a = 6

⇒ 7 (6 + 2) = 7 × 8 = 56

  • Step 2: Find its equivalent

7(6) + 14 = 42 + 14 = 56

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Suppose M is the midpoint of Segment AB, P is the midpoint of Segment AM, and Q is the midpoint of segment PM.
DerKrebs [107]

The coordinates of M, P and Q in terms of a and b are M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b, P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b and Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b, respectively.

In this question we are going to use definitions of vectors and product of a vector by a scalar. Based on the information given on statement, we have the following vectorial formulas:

Location of M

\overrightarrow{AM} = \frac{1}{2}\cdot \overrightarrow{AB}

\vec M - \vec A = \frac{1}{2}\cdot \vec B - \frac{1}{2}\cdot \vec A

\vec M = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec B

M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b

Location of P

\overrightarrow{AP} = \frac{1}{2}\cdot \overrightarrow{AM}

\vec P - \vec A = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec A

\vec P = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec M

\vec P = \frac{3}{4}\cdot \vec A  + \frac{1}{4}\cdot \vec B

P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b

Location of Q

\overrightarrow{QM} = \frac{1}{2}\cdot \overrightarrow{PM}

\vec M - \vec Q = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec P

\vec Q = \frac{1}{2}\cdot \vec P - \frac{1}{2}\cdot \vec M

\vec Q = \frac{1}{2}\cdot \left(\frac{3}{4}\cdot \vec A + \frac{1}{4}\cdot \vec B\right) -\frac{1}{2}\cdot \left(\frac{1}{2}\cdot \vec A + \frac{1}{2}\cdot \vec B\right)

\vec Q = \frac{1}{8}\cdot \vec A -\frac{1}{8}\cdot \vec B

Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b

The coordinates of M, P and Q in terms of a and b are M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b, P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b and Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b, respectively.

We kindly invite to check this question on midpoints: brainly.com/question/4747771

4 0
2 years ago
-0.2x^2+0.9x+0.6=y<br>What's the vertex form for this equation?​
hjlf

Answer:   y = -0.2(x - 2.25)² + 1.6125

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

y = -0.2x^2 + 0.9x + 0.6\\\\y - 0.6 = -0.2x^2 + 0.9x\\\\y - 0.6 =-0.2(x^2-4.5x)\\\\y-0.6+\underline{(-0.2)(2.25)^2}=-0.2(x^2-4.5x+\underline{2.25^2})\\\\y-0.6-1.0125=-0.2(x-2.25)^2\\\\y-1.6125=-0.2(x-2.25)^2\\\\y=-0.2(x-2.25)^2+1.6125

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