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3 years ago

2x + y = 7

Mathematics

1 answer:

jolli1 [7]3 years ago

6 0

Answer:

(2/3, 17/3)

Step-by-step explanation:

put x and y coordinates value in given equation to check equality. it equality holds that's the coordinates we are looking for.

here 2nd coordinate holds the equality

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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

PLEASE HELP! In a film study, a sample of 300 movies was found to have an average runtime of 116 minutes with a standard deviati

BigorU [14]

Answer:

The answer is 1.42!!!!!!

Step-by-step explanation:

8 0

2 years ago

Convert (2, π) to rectangular form

blagie [28]

Answer: 0 . x=2⋅0.

Hope this helps!

3 0

2 years ago

A tree cast a shadow of 30m long and a 2m stick casts one that is 3m long. As show in the below diagram how tall is the tree?

PSYCHO15rus [73]

Answer:

20 m

Step-by-step explanation:

<u>We have similar triangles here.</u>

BC║DE, AB║AD and AC║AE ⇒ ΔADE ~ ΔABC

<u>The ratio of corresponding sides of similar triangles is same:</u>

BC/DE = AC/AE
BC / 2 = 30/3
BC / 2 = 10
BC = 2*10
BC = 20 m

6 0

3 years ago

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A rectangular box has length x and width 3. The volume of the box is given by y = 3x(8 – x). The greatest x-intercept of the gra

CaHeK987 [17]

Consider rectangular box with

length x units (x≥0);
width 3 units;
height (8-x) units (8-x≥0, then x≤8).

The volume of the rectangular box can be calculated as

$V_{box}=\text{length}\cdot \text{width}\cdot \text{height}.$

In your case,

$V_{box}=3\cdot x\cdot (8-x).$

Note that maximal possible value of the height can be 8 units (when x=0 - minimal possible length) and the minimal possible height can be 0 units (when x=8 - maximal possible length).

From the attached graph you can see that the greatest x-intercept is x=8, then the height will be minimal and lenght will be maximal.

Then the volume will be V=0 (minimal).

Answer: correct choices are B (the maximum possible length), C (the minimum possible height)

7 0

3 years ago