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3 years ago

Write the quadratic function in vertex form. y=-3x^2+24x-50

Mathematics

1 answer:

castortr0y [4]3 years ago

4 0

Answer:

Step-by-step explanation:

y = -3x² + 24x - 50

factor out leading coefficient

y = -3(x² - 8x) - 50

complete the square

coefficient of the x term: -8

divide it in half: -4

square it: (-4)² = 4²

use 4² to complete the square and keep the equation balanced:

y = -3(x² - 8x + 4²) + 3(4²) - 50

y = -3(x-4)² - 2

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Find the equation for the circle with a diameter whose endpoints are (3,-1) and (-2,-1)

cricket20 [7]

Answer:

The equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Step-by-step explanation:

Here, let us assume the two end points of the diameter are:

P (3,-1) and Q (-2,-1)

Now, as we knew diameter is the chord that passer through the center of the circle.

⇒ Mid point of DIAMETER = Center coordinates of the Circle

Let us assume O(x,y) is the center of the line segment PQ.

So, by MID POINT FORMULA:

$(x,y)= (\frac{3 -2}{2} , \frac{-1-1}{2} ) =( \frac{1}{2},\frac{-2}{2}) \\\implies (x,y) =( 0.5 , -1)$

⇒ The center coordinates of the circle = O(0.5,-1) ...... (1)

Now, RADIUS = Half of DIAMETER

Using DISTANCE FORMULA:

$PQ = \sqrt{(3-(-2))^2 + (-1 - (-1))^2} = \sqrt{(5)^2 + 0} = 5$

So, Radius = 5/2 = 2.5 units

Now, the equation of circle with radius r and center coordinate ( h,k) is given as: $(x-h)^2 + (y-k)^2 = r^2$

Substitute r = 2.5 and (h,k) = (0.5,0) we get:

$(x-0.5)^2 + (y-0)^2 = (2.5)^2\\\implies (x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Hence the equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

5 0

4 years ago

What is an equation of the line that passes through the points (0, -4) and (-4, 6)?

Allushta [10]

I got this answer by first using the slope formula, which would result into $\frac{0 - 4}{6 - 0} \\$ for which the answer would be - ⅔ Then, the y-intercept could be found easily, since you already have it., which is (0,4). Since the format for all linear equations are y=mx+b , in which b means the y-intercept and m means the slope. So then, if you substitute - ⅔ for m and 4 for b , you would get

$y = - \frac{2}{3} x + 4 \\$

6 0

3 years ago

Fill in the blank. 6,399 is________2,911? Help mi please <br> *

Artemon [7]

Answer: If this is an equality problem then 6,399 > 2911.

4 0

3 years ago

Read 2 more answers

Maria is weiting a list of numbers. She asked susanne what the next number would be. After looking at the list susanne states, t

Tanzania [10]

Answer: Inductive Reasoning.

Had to complete the question first.

Maria is writing a list of numbers. She asked Susanne what the next number would be . After looking at the list: 7,14,21,28,35,42,_Susanne states,”the next number will be 49” inductive or deductive.

Step-by-step explanation:

inductive reasoning: This is known as a process of using observations and examples to reach a conclusion or decision.

When ever a pattern or trend is used to predict the next possible outcome, you are using inductive reasoning. Just like from Maria list Susanne was able to predict that the next number would be 49 because the sequence increases with an interval of 7. ( 7, 14, 21, 28, 35, 42, 49).

4 0

4 years ago

2 balls are rolling towards each other from the opposite ends of a straight tube that is

suter [353]

Answer:

6 seconds

Step-by-step explanation:

In second 1, the distance that separates them is 80 cm

Then, in second 2, it is an additional 76 cm which is 156

then 72, etc. etc.

From that, we can continue adding until we the total sum is 420.

80+76+72+68+64+60=420

That's 6 seconds

Not the most elegant solution but I think one of the simplest.

8 0

3 years ago

Read 2 more answers