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3 years ago

What is the radius of the circle with equation x2 + y2 – 8x + 12y – 5 = 0?

Mathematics

1 answer:

kramer3 years ago

7 0

Answer:

radius: $\sqrt{52}$

Step-by-step explanation:

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Allisa [31]

Answer:

Step-by-step explanation:

18+12-6

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2 years ago

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Stella [2.4K]

Question:

Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0

Answer:

The number of real solutions for the equation $x^{2}+5 x+7=0$ is zero

Solution:

For a Quadratic Equation of form : $a x^{2}+b x+c=0$ ---- eqn 1

The solution is $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now , the given Quadratic Equation is $x^{2}+5 x+7=0$ ---- eqn 2

On comparing Equation (1) and Equation(2), we get

a = 1 , b = 5 and c = 7

In $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ , $b^2 - 4ac$ is called the discriminant of the quadratic equation

Its value determines the nature of roots

Now, here are the rules with discriminants:

1) D > 0; there are 2 real solutions in the equation

2) D = 0; there is 1 real solution in the equation

3) D < 0; there are no real solutions in the equation

Now let solve for given equation

$D= b^2 - 4ac\\\\D = 5^2 - 4(1)(7)\\\\D = 25 - 28 \\\\D = -3$

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

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4 years ago

What is the common difference in this sequence: 5, 17, 29, 41, 53?

irina1246 [14]

The common difference is 12.

5 0

3 years ago

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What is the distance around a triangle that has sides measuring 2 1/8 feet, 3 1/2 feet, and 2 1/2 feet?

Alex787 [66]

Hi!
A is the answer:⏬⏬⏬⏬⏬⏬⏬⏬

The distance around a triangle, better noun as de "perimeter of a triangle"

is the total distance around the outside, which can be found by adding together the length of each side.

Perimeter (P) = Length A + Length B + Lenght C

In this case, we know that each side measure 2 \frac{1}{8}81 feet, 3 \frac{1}{2}21 feet, and 2 \frac{1}{2}21feet but we have to rewrite each one of this mixed fractions as improper fractions:

2 \frac{1}{8}81 = \frac{16 + 1}{8}816+1 = \frac{17}{8}817

3 \frac{1}{2}21 = \frac{6 + 1}{2}26+1 = \frac{7}{2}27

2 \frac{1}{2}21 = \frac{4 + 1}{2}24+1 = \frac{5}{2}25

Then we just add all of them to find the perimeter:

= \frac{17 + 28 + 20}{8}817+28+20 = \frac{65}{8}865

A: The distance around a triangle is \frac{65}{8}865feet

3 0

3 years ago

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Leokris [45]

Independent variables are variables of a quantity that are not affected by any conditions.

Dependent variables are variables of a quantity that change if conditions relative to that variable changes.

For example, we generally we take x as independent variable by x variable and dependent variable by y variable.

To find the rate of change we get two values of independent variable (x's) and two values of dependent variables (y's) to get two coordinates in form of

(x,1,y1) and (x2,y2).

<h3>And we can find the rate of change by applying slope formula</h3>

$m= \frac{y_2-y_1}{x_2-x_1}$ .

3 0

3 years ago