Which of the following points is an equal distance (equidistant) from a(−4, 1) and b(2, −3)?

j(−3, −4)

k left parenthesis negative start fraction three over two end fraction comma negative start fraction one over two end fraction right parenthesis

l(−1, −2)

n(4, 1)

Using your answer choices, (3, 0) satisfies the resulting equation.

Step-by-step explanation:

Even if we did not know the choices, we can still use algebra to find the coordinate point(s).  We can use the distance formula.

d = √[(x1 - x2)2 + (y1 - y2)2]

where:

d = distance

(x1 , y1) and (x2 , y2) are given points.

Since we need to find the point that has he same distance between the points, we will use the distance formula and equated them.

Let (x3, y3) be the point we need to find. So by using the distance formula, we have

√[(0 - x3)2 + (-4 - y3)2] = √[(-2 - x3)2 + (0 - y3)2]

Squaring both sides of the equation leaves us with

x32 + (-4 - y3)2 = (-2 - x3)2 + y32

x32 + (-4 - y3)(-4 - y3) = (-2 - x3)(-2 - x3) + y32

x32 + 16 + 8y3 + y32 = 4 + 4x3 + x32 + y32

Eliminating x32 and y32

16 + 8y3 = 4 + 4x3

Move all the terms to the left side of equation to make the right side equal to zero.

16 + 8y3 - 4 - 4x3 = 0

12 + 8y3 - 4x3 = 0

Factoring, we get

4(3 + 2y3 - x3) = 0

3 + 2y3 - x3 = 0

2y3 - x3 = -3

Using your answer choices, (3, 0) satisfies the resulting equation.

the final price would be 29.6925

step-by-step explanation:

39.59 minus 25% equals 29.6925

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: