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Which of the following is an equation of the circle with a center at (-1,4) and a radius of 2√5 units? plss pahelp naman

Ksivusya [100]

Answer:

Option A

Step-by-step explanation:

The standard form of an equation of a circle is represented by the formula $(x-h)^2+(y-k)^2 = r^2$ . Remember that $(h,k)$ is the center and $r^2$ is the radius squared.

So, the equation of the circle must be $(x+1)^2 +(y-4)^2 = 20$ . Complete the square to change the form of the equations listed in the options and find the one that is equal.

Let's try this with option A. Move the constants to the right side, then use the completing the square method to place the equation in standard form:

$x^2 + y^2 +2x -8y -3 = 0\\x^2 + y^2 +2x-8y = 3\\x^2 + 2x +y^2-8y = 3\\(x^2 +2x+1)+(y^2-8y +16)=3+1+16\\(x+1)^2 + (y-4)^2=20$

The end result matches with the equation determined before, so option A is the answer.

8 0

2 years ago

Best Buy is displaying 15 laptops for a big store sale. The laptops include 6 identical Dells, 4 identical Chromebooks, and 5

Alchen [17]

Answer:

630,630 different arrangements are possible for the given laptops.

Step-by-step explanation:

Total number of laptops = n = 15

Number of identical Dell laptops = 6

Number of identical Chromebooks = 4

Number of identical Mackbooks = 5

We have to find in how many ways can the laptops be arranged. Number of arrangement of objects is calculated using Permutations as the order of objects matter during the arrangement. The formula to calculate the number of possible arrangements when there are similar objects is given as:

$\frac{n!}{a!b!c!...}$

Here n is the total number of objects and a,b, and c represent the number of identical objects. Using the given values we get:

$\frac{15!}{6!4!5!} = 630630$

This means 630,630 different arrangements are possible for the given laptops.

4 0

2 years ago

Emily thought of a counting number, and then she added the next counting number to it. She got the sum of 57. What was Emily’s n

Dovator [93]

Let this number be x. The next number is (x+1). And their sum is 57. Then, we have to solve this equation x+x+1=57
$2x=56$
$x=28$
Emily's number was 28

8 0

2 years ago

Read 2 more answers

Jordan is making a beaded necklace two thirds of the beads she uses are red and 4/21 of the beads are blue she wants the rest to

stiks02 [169]

Answer:

2/3= 14/21....red beads...4/21 blue beads...14+4= 18/21...so you need 3/21 more to finish the necklace and 3/21=1/7 in white beads

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

If you add Natalie's age and Fred's age, the result is 39. If you add Fred's age to 4 times Natalie's age, the result is 78.

Darina [25.2K]

Step-by-step explanation:

We can write this word problem as two variables. Let us assume that:

x = Natalie's age

y = Fred's age

The first part of the word problem is that "If you add Natalie's age and Fred's age, the result is 39." Therefore:

Natalie's age + Fred's age = 39

x + y = 39

This will be our first equation. The second equation can be derived from the statement that "If you add Fred's age to 4 times Natalie's age, the result is 78." Therefore:

(4 times Natalie's age) + Fred's age = 78

4x + y = 78

We can now form a system of equations and solve for both x and y:

$\left \{ {{x + y = 39} \atop {4x + y = 78}} \right.$

The simplest way to solve would be using the Substitution method, as seen here:

x + y = 39

y = 39 - x

4x + y = 78

4x + (39 - x) = 78

3x + 39 = 78

3x = 39

x = 13

x + y = 39

13 + y = 39

y = 26

Remember that x = Natalie's age and y = Fred's age. Therefore, Natalie's age is 13 years old and Fred's age is 26 years old.

8 0

1 year ago