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9966 [12]
3 years ago
10

Circle P is shown. Line segment P Q is a radius and has a length of 9. Line Q R is a tangent that intersects the circle at point

Q and has a length of 12. A line connects points R and P. The distance between point R and the circle is x, and the point on the circle to point P is a radius.
What value of x would make Line R Q tangent to circle P at point Q?

x =

Mathematics
2 answers:
gizmo_the_mogwai [7]3 years ago
8 0

Answer: six

Step-by-step explanation:

Eduardwww [97]3 years ago
5 0

Answer:

X=6

Step-by-step explanation:

We need to remember the theorem that Tangent always makes a right angle at the point of contact with the circle.

Given details-  

PQ=9= circle radius  

QR=12  

As given in the question  

PQ is the radius  

PQ=PY (since both are the radius to the circle)  

⇒If the line QR = tangent than ∠ PQR must be 90°  

Hence Δ PQR is a right-angled triangle with hypotenuse PR  

PQ²+QR²=PR² (Pythagoras theorem)  

∴Substituting the value of PQ, QR  

⇒We get (9)² +(12)² = PR²

PR²= 225  

⇒PR=15  

As clear in figure PR= PY+YR  

∴15=9+x  

⇒ YR(x)= 6cm  

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A student claims that 2i is the only imaginary root of a polynomial equation that has real coefficients. Explain the student's m
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Answer:

The Fundamental Theorem of Algebra assures that any polynomial  f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i

Step-by-step explanation:

1) This claim is mistaken.

2) The Fundamental Theorem of Algebra assures that any polynomial  f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i with real coefficients.

a_{0}x^{n}+a_{1}x^{2}+....a_{1}x+a_{0}

For example:

3) Every time a polynomial equation, like a quadratic equation which is an univariate polynomial one, has its discriminant following this rule:

\Delta < 0\\b^{2}-4*a*c

We'll have <em>n </em>different complex roots, not necessarily 2i.

For example:

Taking 3 polynomial equations with real coefficients, with

\Delta < 0

-4x^2-x-2=0 \Rightarrow S=\left \{ x'=-\frac{1}{8}-i\frac{\sqrt{31}}{8},\:x''=-\frac{1}{8}+i\frac{\sqrt{31}}{8} \right \}\\-x^2-x-8=0 \Rightarrow S=\left\{\quad x'=-\frac{1}{2}-i\frac{\sqrt{31}}{2},\:x''=-\frac{1}{2}+i\frac{\sqrt{31}}{2} \right \}\\x^2-x+30=0\Rightarrow S=\left \{ x'=\frac{1}{2}+i\frac{\sqrt{119}}{2},\:x''=\frac{1}{2}-i\frac{\sqrt{119}}{2} \right \}\\(...)

2.2) For other Polynomial equations with real coefficients we can see other complex roots ≠ 2i. In this one we have also -2i

x^5\:-\:x^4\:+\:x^3\:-\:x^2\:-\:12x\:+\:12=0 \Rightarrow S=\left \{ x_{1}=1,\:x_{2}=-\sqrt{3},\:x_{3}=\sqrt{3},\:x_{4}=2i,\:x_{5}=-2i \right \}\\

4 0
3 years ago
Frank turns his steering wheel a full circle of 360°. Which statement best represents the
enot [183]

Answer:

C. The wheel makes 360 one-degree turns.

Step-by-step explanation:

A full circle is 360°, that is, there are 360 degrees in a circle.

You can check how many total degrees the steering wheel is turned for each option by multiplying the number of turns by the number of degrees for each turn:

  • For A: 260 one-degree turns is (260 turns) × (1 degree per turn) = 260 degrees turned. This is not equal to the given fact that Frank turns a full circle of 360 degrees. So A is not correct.
  • For B: 360 ten-degree turns means a total of (360 turns) × (10 degrees per turn) = 3600 degrees turned, which does not equal one turn of 360 degrees. So B is not correct.
  • For C: 360 one-degree turns means a total of (360 turns) × (1 degree per turn) = 360 degrees turned, which is one full circle.
  • For D: 360 one-hundred degree turns means a total of (360 turns) × (100 degrees per turn) = 36000 degrees turned, which is not 360 degrees. So D is not correct.
8 0
3 years ago
What are the coordinates of the hole in the rational function? f(x)=x2+8x−9x2−1
Amanda [17]
The numerator factored is (x+9)(x-1)
The denominator factored is (x+1)(x-1)
The x coordinate for the hole comes from the like factor (x - 1).
Set it equal to zero.   x - 1 = 0  so x = 1
Plug the x value into the remaining fraction \frac{x+9}{x+1}
\frac{1+9}{1+1} = \frac{10}{2} =5
The answer is (1,5)
4 0
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cestrela7 [59]
I think a because if you add 8 to 1999 it is the year
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The area is about ____ square inches. ANYONE KNOW THIS!? I need the steps if possible:(
Anni [7]

Answer:

28.57

Step-by-step explanation:

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two half circles = one whole circle = \pi2²=12.566

16+12.57=28.57

3 0
3 years ago
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