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Dafna1 [17]
3 years ago
12

The triangles are congruent by the SSS congruence

Mathematics
1 answer:
Nostrana [21]3 years ago
6 0

Answer: rotation then translation

Step-by-step explanation:

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Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions calulator?
fgiga [73]

Answer:

Degree = 4

Step-by-step explanation:

For the given conditions:

n = 4

i and 5i are zeros

f(-2) = 145

For zeros, it means they are a quadratic factor of the expression

It means, we will have x = ± i and x = ± 5i

therefore, the given factors are (x - i)(x + i)(x - 5i)(x + 5i)

Hence, we have the function

given degree = 4

f(x) = a(x-i)(x+i)(x-5i)(x+5i)

f(x) = a(x² + 1)(x² + 25)

Hence, substituting -2 for x, we have

f(-2) = a(5)(29) = 145

Hence, a = 1

f(x) = x⁴ + 26x² + 25

Therefore, we can see that the given degree = 4

3 0
3 years ago
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
You can rent a paddleboat at Lake Isabel. The cost is $15 for the first hour - then $9 for each hour after that. Use this inform
murzikaleks [220]
You can rent a paddleboat at Lake Isabel. The cost is $15 for the first hour - then $9 for each hour after that. Use this information to complete the following: Write an equation in slope intercept form that represents the cost (y) of the rental based on the number of hours (x) you rent it. b) What is the y intercept of your equation? c) What does this mean in the context of the situation? d) What is the slope of your equation? e) What does this number mean in the context of the situation? f) Graph the line that is represented by your equation. Make sure to clearly label the axis. g) How much will it cost to rent the paddleboat for 4 hours? Show how you found your answer algebraically. Also show and explain where this information can be found on your graph.
5 0
3 years ago
Given segment AC and point B that lies on AC, if AB = 9 and BC= 49, find AC
Ipatiy [6.2K]

Answer:

58

Step-by-step explanation:

Let's draw this out (see attachment).

We know that since B lies on AC, we have the points in order from left to right: A, B, C.

AB = 9, which is the left portion. BC = 49, which is the right portion. Then AC is simply the sum:

AC = AB + BC = 9 + 49 = 58

The answer is thus 58.

<em>~ an aesthetics lover</em>

5 0
3 years ago
8 cm<br> 4 cm<br> 4 cm<br> 8 cm<br> The perimeter is<br> cm<br> What is the answer
dangina [55]

Answer:

24 cm

Step-by-step explanation:

8+8=16

4+4=8

8+16=24 cm

*Perimeter includes adding all sides, area is multiplying all sides.

8 0
3 years ago
Read 2 more answers
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