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Ivahew [28]
2 years ago
6

This figure is made up of two rectangular prisms.

Mathematics
1 answer:
Ber [7]2 years ago
4 0

Answer:

Answer:1134

Step-by-step explanation: first you do (21×7×2)+(12×10×7) then once you do that you'll get 1134 and that's your answer.

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Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}

Replace 180 with 36 * 5

\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

Further split the square roots

\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} *  \sqrt{x^{11}}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{11}}

Replace power of x; 11 with 10 + 1

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

From laws of indices; a^{m+n} = a^m * a^n

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x}

Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

So, we have

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

7 0
2 years ago
Read 2 more answers
Α + 4/5 = 3<br> Solve for a to make the proportion true
Natali5045456 [20]
4/15 should be your answer!
5 0
2 years ago
Read 2 more answers
Need help with these two percentages...<br>1) Increase 480 by 1 % <br>2) Decrease 180 by 13 %
solniwko [45]
1. 484.8
2.156.6

hope this helped :)

6 0
3 years ago
What is the vertex of the absolute value function defined by ƒ(x) = |x - 2| - 7?
inn [45]
<h3><u>Explanation</u></h3>
  • Modulus Function

y = a |x  - h|  + k

The structure or equation is similar to a quadratic function.

The value of a determines the slope of graph.

Tthe value of h determines the horizontal shift of graph.

The value of k determines the vertical shift of the graph.

From the given equation,

f(x) =  |x - 2|  - 7

We can say that the graph shifts to the right 2 units and shifts down 7 units. Hence the vertex would be at x = 2 and y = -7. It can be written in coordinate form as (2,-7).

<h3><u>Answer</u></h3>

<u>\large{(2,-7)}</u>

8 0
2 years ago
Suppose a linear transformation Upper T : Bold Upper R squared right arrow Bold Upper R squared is formed by taking a rotation c
kotykmax [81]

Answer:

All points on line x+y = 0 or x-y=0 will satisfy the transformation.

Step-by-step explanation:

Let (x, y) be the general such point.

Hence rotating it by 180 deg. counterclockwise will give us (-y,-x).

Reflecting (-y,-x) on x axis gives us (-y,x).

Hence if (x,y) = (-y,x) then all ( x, y) where x = -y or x+y = 0 or x=y or x-y=0 will satisfy this condition.

All points on line x+y = 0 or x-y=0 will satisfy the transformation.

8 0
3 years ago
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