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Svet_ta [14]
2 years ago
10

Write an equation of the circle given its center and radius

Mathematics
1 answer:
BlackZzzverrR [31]2 years ago
7 0

{(x + 4)}^{2}  +  {(y + 3)}^{2}  = 64

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Which algebraic expression is a polynomial with a degree of 3?
Irina18 [472]

Option a: 4x^{3} -\frac{2}{x}

Option b: 2y^{3} +5y^{2} -5y

Option c: 3y^{3} -\sqrt{4y}

Explanation:

The highest degree of a polynomial is the largest exponent of that variable.

Now, we shall determine the polynomial with degree 3.

Option a: 4x^{3} -\frac{2}{x}

From the expression 4x^{3} -\frac{2}{x}, the highest degree of the polynomial is 3.

Hence, 4x^{3} -\frac{2}{x} is a polynomial with a degree of 3.

Hence, Option a is the correct answer.

Option b: 2y^{3} +5y^{2} -5y

From the expression 2y^{3} +5y^{2} -5y, the highest degree of the polynomial is 3.

Hence, 2y^{3} +5y^{2} -5y is a polynomial with a degree of 3.

Hence, Option b is the correct answer.

Option c: 3y^{3} -\sqrt{4y}

From the expression 3y^{3} -\sqrt{4y}, the highest degree of the polynomial is 3.

Hence, 3y^{3} -\sqrt{4y} is a polynomial with a degree of 3.

Hence, Option c is the correct answer.

Option d: -xy\sqrt{6}

From the expression -xy\sqrt{6}, the highest degree of the polynomial is 1.

Hence, -xy\sqrt{6} is a polynomial with degree 1.

Hence, Option d is not the correct answer.

5 0
3 years ago
Read 2 more answers
What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?<br> units
pickupchik [31]

Answer:r=2

Step-by-step explanation:

6 0
3 years ago
How can I factor 5x^2 + 26x - 24 = 0 using the completing the square method.
kifflom [539]
<h2><u>QUADRATIC EQUATION</u></h2>

<h2>\mathbb{ANSWER:}</h2>
  • \bold{x = 0.8 \: } \:  \sf \:  {\color{grey}or} \:  \:  \:  \bold{ x=  \frac{4}{5} } \\

  • \bold{x =  - 6}

— — — — — — — — — —

<h3>Step-by-step explanation:</h3>

<u>How can </u><u>we</u><u> factor 5x^2 + 26x - 24 = 0 using the completing the square </u><u>method?</u>

Let's solve your equation step-by-step.

\bold{Given \:  Equation: \color{brown} 5x²+26x-24=0}

First, add 24 to both sides.

  • \bold{5x²+26x-24 - \purple{ 24} = 0 +  \purple{24}}

  • \bold{ \implies \: 5x²+26x = 24 }

Since the coefficient of 5x² is 5, divide both sides by 5.

  • \bold{ \frac{5 {x}^{2} + 26x }{5} =  \frac{24}{5}  } \\

  • \bold{ \implies \:  {x}^{2} +  \frac{26}{5} x =  \frac{24}{5}  } \\

The coefficient of 26/5x is 26/5. So, let b=26/5.

Then we need to add (b/2)²=169/25 to both sides to complete the square.

Add 169/25 to both sides.

  • \bold{ {x}^{2} +  \frac{26}{5} x +  \frac{  \purple{169}}{ \purple{25}}=  \frac{24}{5}    +  \frac{ \purple{169}}{ \purple{25}} } \\

  • \bold{ \implies \:\bold{ {x}^{2} +  \frac{26}{5} x +  \frac{  169}{ {25}}=  \frac{289}{25}  } } \\

Factor the left side.

  • \bold{(x +  \frac{13}{5} ) {}^{2} =  \frac{289}{25}  } \\

Take square root.

  • \bold{x +  \frac{13}{5} = ±  \:  \sqrt{ \frac{289}{25}  }} \\

Then, add (-13)/5 to both sides.

  • \bold{x +  \frac{13}{5} +  \frac{\purple{ - 13} }{\purple{ 5}} = \frac{{ - 13} }{{ 5}} ± \:      \sqrt{ \frac{289}{25}}} \\

  • \bold{  \: x =  \frac{ - 13}{5} ± \sqrt{ \frac{289}{25} } } \\

  • \implies \: \underline{ \boxed{ \bold{   \frac{4}{5}  } \sf  \:  \: or \:  \:  \bold{ x =  - 6}}} \\

_______________❖_______________

3 0
2 years ago
Read 2 more answers
A plane at an altitude of 7000 feet is flying in the direction of an island. If the angle of elevation is 21 degrees from the pl
sleet_krkn [62]

Answer:

6,535.06 feet

Step-by-step explanation:

The set up is right angles

hypotenuse = 7000feet

angle of elevation = 21 degrees

Required

horizontal distance (adjacent)

Using SOH, CAH TOA trig identity

cos theta = adj/hyp

cos 21 =  adj/7000

adj = 7000 cos 21

adj = 7000(0.9336)

adj =  6,535.06

Hence the HORIZONTAL distance until the plane flies over the island is 6,535.06 feet

5 0
2 years ago
What fraction of the whole are the blue piece, the orange piece, the red piece, and the purple piece. How do you know?
Rus_ich [418]
Red: 2/4
blue: 1/4
Purple: 1/4
6 0
2 years ago
Read 2 more answers
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