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3 years ago

Given AC with A (4,-7) and (-4,11) if point B divides AC five-sixths of the way from A to C find the coordinates of B

Mathematics

1 answer:

Taya2010 [7]3 years ago

5 0

Answer:

B: (-8/3 , 8)

Step-by-step explanation:

A (x₁,y₁) (4,-7) and C (x₂,y₂) (-4,11), B (x,y)

AB (a):BC (b) = 5:1

x = (bx₁ + ax₂) / (a+b) = (1*4+5*-4) / (5+1) = -16/6 = - 8/3

y = (by₁ + ay₂) / (a+b) = (1*-7+5*11) / (5+1) = 48/6 = 8

B: (-8/3 , 8)

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Estimate how much MORE water it would take to completely FILL the vase to the top?

MariettaO [177]

Answer:

81πinc^3

Step-by-step explanation:

Volume of glass = π(3)^2(12) = 108πin^3

Volume of water in glass = π(3)^2(3) = 27πin^3

Volume needed to fill completely = 108π - 27π = 81π^3

Topic: Mensuration

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6 0

2 years ago

Stephan added 26 new contacts to his phone list. He had to delete 16 old contacts before he could add any more. Stefan now has a

bezimeni [28]

Answer: 26-16= c

c=10

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

5x4 – 7x3 – 5x2 + 5x + 1 = 0

olya-2409 [2.1K]

20 - 21 - 10 + 5x +1= 0
5x = 10
x = 2

5 0

2 years ago

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total

Katarina [22]

Answer:

t-shirts: 2790

profit: $12209

Step-by-step explanation:

Given the function:

p(x) = -x³ + 4x² + x

we want to maximize it.

The following criteria must be satisfied at the maximum:

dp/dx = 0

d²p/dx² < 0

dp/dx = -3x² + 8x + 1 = 0

Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}$

$x = \frac{-8 \pm \sqrt{8^2 -4(-3)(1)}}{2(-3)}$

$x = \frac{-8 \pm 8.72}{-6}$

$x_1 = \frac{-8 + 8.72}{-6}$

$x_1 = -0.12$

$x_2 = \frac{-8 - 8.72}{-6}$

$x_2 = 2.79$

d²p/dx² = -6x + 8

d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0

d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0

Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.

Replacing into profit equation:

p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209

that is, $12209

3 0

3 years ago

Determine whether the given equation has one solution, no solution, or infinitely many solutions: 4x+10=2(2x+5)

murzikaleks [220]

if we distribute 2(2x+5), we'll end up with 4x + 10, so in short, the right-hand-side, is really the left-hand-side in disguise.

and since 4x + 10 = 4x + 10, both equations are equal, meaning in short, the system has an infinite number of solutions.

4 0

2 years ago