Write an equation of the circle given its center and radius

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