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notka56 [123]
3 years ago
13

Which equation has a graph with a vertex at (-1,-1)?

Mathematics
1 answer:
11111nata11111 [884]3 years ago
6 0

y =  {(x  + 1)}^{2}  - 1

The one is a vertical translation of the parent function to the left of one

f(x) =  {x}^{2}

making it -1.

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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
Can someone plz help me with this question
Nostrana [21]
10^2 is 10×10 which is 100
4^2 is 4×4 which is 16
so it simplifies to 100-16×2. By Order Of Operations, parentheses, exponents, multiply and divide, add and subtract 100-16×2 makes 100-32 which is 68
5 0
3 years ago
Which of the following is equivalent to 36 Superscript negative one-half?
taurus [48]

Answer:

1/6

Step-by-step explanation:

Negative one half power is the reciprocal of the square root, 1/6

5 0
3 years ago
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Given that (-3, 5) is on the graph of f(x), find the corresponding point for the function f(x) − 4.
sveticcg [70]
The graph of f(x) - 4 is obtained by translating the graph of f(x) 4 units down.
Therefore, the corresponding point for the function f(x) - 4 is (-3, 5 - 4) = (-3, 1).
7 0
3 years ago
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A customer owes $33.63 in transaction fees and he/she gives you $40.00. how much change should the customer receive back?
Nataliya [291]
The customer should receive $6.37 back
3 0
2 years ago
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