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2 years ago

Ratios equilvalent to 3:11

Mathematics

2 answers:

kompoz [17]2 years ago

8 0

9 : 22

12 : 45

15 : 55

18 : 77

Snowcat [4.5K]2 years ago

4 0

6:22
9:33
12:44
15:55
18:66

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What is the equation of the quadratic graph with a focus of (4,3) and a directrix of y=-6

Rufina [12.5K]

Answer:

f(x) = (1/18)x^2 - (4/9)x - 65/18

Step-by-step explanation:

Since the focus (4,3) is higher up than is the directrix y = -6, the vertex is between y = -6 and y = 3, halfway between these values, to be exact: y = -3/2. Thus, the y-coordinate of the vertex is (-6 + 3/2), or -4.5. The x-coordinate of the vertex is 4, which comes from that 4 in (4,3). Thus, the vertex is (4, -4.5) or (4, -4 1/2).

The standard equation for a vertical parabola with vertex at (h,k) is:

4p(y-k) = (x-h)^2, where p is the distance between vertex and focus or between vertex and directrix. In this case p = 4.5. Thus, the equation of this quadratic is 4(4.5)(y - [-4.5]) = (x - 4)^2, or

18(y+4.5) = (x-4)^2, or y+4.5 = (1/18)(x-4)^2.

Let's expand this and rewrite the result as a quadratic equation in standard form y = ax^2 + bx + c:

y + 4.5 = (1/18)(x^2 - 8x + 16). Multiplying all terms by 18 to remove both fractions, we get:

18y + 81 = x^2 - 8x + 16. Rearranging these terms, we get:

18y = x^2 - 8x + 16 - 81, or

18y = x^2 - 8x - 65, or

y = f(x) = (1/18)x^2 - (4/9)x - 65/18.

5 0

3 years ago

Read 2 more answers

What is the slope-intercept equation of the line below?

Nataly [62]

Answer:

Step-by-step explanation:

We will use the 2 coordinates marked on the graph as the reference.

The coordinates are:

A(4,-2)

B(0,3)

We know that the standard form for equation of line is:

y = mx+c

where m is the slope of the equation

and c is the y-intercept.

Very clearly, the y-intercept is where the line intercepts the y line.

and in this case, y-intercept = c = 3.

Now we know that the equation of line is now

y = mx + 3

To find m, the slope, we can use the 2 above coordinates.

slope of line = $\frac{y1-y2}{x1-x2} \\=\frac{-2-3}{4-0} \\=\frac{-5}{4} \\=-\frac{5}{4}$

(Note: There is a 2nd way to find the slope in this case, let me know if you are interested to find out.)

Equation of line: $y=-\frac{5}{4} x+3$

Therefore the answer is D.

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Jerry has $558 to spend on dining room chairs. if each chair costs $58, does he have enough to purchase nine chairs

netineya [11]

Answer:

No because the chairs would have to be the price of $62.00

Step-by-step explanation:

divide 558 by 9

so if the chairs had been 62 dollars then he would have enough

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ivolga24 [154]

Answer:

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Step-by-step explanation:

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I think it is P because that is the intercecting point

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