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3 years ago

Find the quotient: (24xy^3-16x^2y^2+32x^2y)/8xy

Mathematics

1 answer:

kolbaska11 [484]3 years ago

5 0

$\cfrac{24xy^3-16x^2y^2+32x^2y}{8xy} = \\ \\ \\ = \cfrac{8xy(3y^2-2xy+4x)}{8xy} = \\ \\ \\ 3y^2-2xy+4x$

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When salt and water are combined, they form a salt or saline solution. How much ml of water must be added to 150 mL of an 80% sa

Vinvika [58]

Answer:

We must add 400 ml of water.

Step-by-step explanation:

We can use the following equation:

$C_{i}V_{i}=C_{f}V_{f}$

Where:

C(i) is the initial concentration of the solution (80%)
C(f) is the final concentration of the solution (30%)
V(i) is the initial volume (150 ml)
V(f) is the final volume

Now, we just need to solve the equation for V(f).

$V_{f}=\frac{C_{i}V_{i}}{C_{f}}$

$V_{f}=\frac{80*150}{30}$

$V_{f}=400\: ml$

Therefore, we must add 400 ml of water.

I hope it helps you!

3 0

3 years ago

What is the equation written in vertex from of a parabola with a vertex of (4, –2) that passes through (2, –14)?

vichka [17]

Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a = determines whether the graph opens up or down, and it also makes the parent function wider or narrower.

positive value of a = opens upward
negative value of a = opens downward
a is between 0 and 1, (0 < a < 1) the graph is wider than the parent function.
a > 1, the graph is narrower than the parent function.

h = determines how far left or right the parent function is translated.

h = positive, the function is translated h units to the right.
h = negative, the function is translated |h| units to the left.

k determines how far up or down the parent function is translated.

k = positive: translate k units up.
k = negative, translate k units down.

Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)² -2

-14 = a (-2)² -2

-14 = a4 + -2

Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)