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1 year ago

What is an equation of a circle whose center is at (2,-4) and is

Mathematics

1 answer:

Evgesh-ka [11]1 year ago

6 0

The equation of the circle with center at (2,-4) and tangent to the line x = -2 is given by:

(2) (x - 2)² + (y + 4)² = 16

<h3>What is the equation of a circle?</h3>

The equation of a circle of center $(x_0, y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

The circle has center at (2,-4), hence $x_0 = 2, y_0 = -4$ .

The center is tangent to the line x = -2, hence it has a point at x = -2, since |-2 - 2| = 4, r = 4 -> r² = 16.

Hence the equation of the circle is given by:

(2) (x - 2)² + (y + 4)² = 16

More can be learned about the equation of a circle at brainly.com/question/24307696

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The distance from Ari’s house, A, to Ben’s house, B, is equal to the distance from Ari’s house to Cal’s house, C. One day the bo

tresset_1 [31]

Answer:

they walked the same distance

Step-by-step explanation:

if you add cal's expression up which is 2(2+1)+(-4) you would have to use distributive property which means you would have to times 2 by 2 which is 4 and then times 2 by 1 and get two and then add them together and get 2 and if you do the same thing with Ari's expression you get 2.

3 0

2 years ago

Determine whether the set of vectors is a basis for ℛ3. Given the set of vectors , decide which of the following statements is t

schepotkina [342]

Answer:

(A) Set A is linearly independent and spans $R^3$ . Set is a basis for $R^3$ .

Step-by-Step Explanation

Definition (Linear Independence)

A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.

Definition (Span of a Set of Vectors)

The Span of a set of vectors is the set of all linear combinations of the vectors.

Definition (A Basis of a Subspace).

A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.

Given the set of vectors $A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right)$ , we are to decide which of the given statements is true:

In Matrix $A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right)$ , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. $R^3$ has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans $R^3$ .

Therefore Set A is linearly independent and spans $R^3$ . Thus it is basis for $R^3$ .

8 0

3 years ago

Gary earns $12 an hour plus $16 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week

hoa [83]

Part A.

Amount of money earned = Regular rate per hour * Number of working hours

M = 12 x

Part B.

Amount of wages earned = Regular rate per hour * Maximum number of regular working hours + Overtime rate per hour * Excess working hours

T = 12 * 30 + 16 * y

T = 360 + 16 y

T = 16 y + 360

Part C.

Given T = 408, find y:

408 = 16 y + 360

y = 3 hrs

Therefore the total hours Gary worked that week is,

x + y = 30 + 3 = 33 hrs

(x = 30 since that is the maximum limit for regular working hours)

7 0

3 years ago

Last year, James earned £1,100 per month. This year, he's had a 4% increase in his monthly pay. He worked 40 hours per week for

avanturin [10]

Answer:

A = £7.15 per hour

James' average pay per hour this year is £7.15 per hour

Step-by-step explanation:

Given;

Last year pay = £1,100 per month

This year, he's had a 4% increase in his monthly pay

This year pay P = 1,100 + 4% of 1,100 = 1,100 +1,100(0.04)

This year pay P = £1,144 per month

Yearly pay Tp= 12 × P = 12 × £1,144 = £13,728

Number of hours worked this year;

He worked 40 hours per week for 48 weeks in the year

N = 40 hours per week × 48 weeks per year

N = 1920 hours per year

Average pay per hour this year A;

A = Yearly pay/Number of hours worked this year

A = Tp/N

A = £13,728/1920hours

A = £7.15 per hour

James' average pay per hour this year is £7.15 per hour

5 0

3 years ago

Which of the following is not equivalent

dsp73

90/139 is the only fraction not equivalent to 45/70.

To find if a fractions are equivalent, divide the numerator by the denominator for each fraction.

45/70=0.642857
27/42=0.642857
9/14=0.642857
63/98=0.642857

Notice how all of these get you the same number. However, when you divide 90 by 137, you get 0.64748, which is not the same as the others. Therefore, 90/137 is the fraction that is not equivalent to 45/70.

6 0

3 years ago

Read 2 more answers