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ASHA 777 [7]
3 years ago
9

Complete the square in the following quadratic formula : x^2-3x

Mathematics
1 answer:
yanalaym [24]3 years ago
5 0
See attached solution

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Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)
Citrus2011 [14]

Answer:

<u>It</u><u> </u><u>is</u><u> </u><u>3</u><u>y</u><u> </u><u>=</u><u> </u><u>4</u><u>x</u><u> </u><u>+</u><u> </u><u>1</u><u>0</u>

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

{x}^{2}  - xy +  {y}^{2}  = 7

introduce dy/dx :

\frac{d}{dx} ( {x}^{2}  - xy +  {y}^{2} ) =  \frac{d}{dx} (7) \\  \\ 2x - (y +  \frac{dy}{dx} ) + 2y \frac{dy}{dx}  = 0

make dy/dx the subject:

2x - y -  \frac{dy}{dx}  + 2y \frac{dy}{dx}  = 0 \\  \\ 2y \frac{dy}{dx}  -  \frac{dy}{dx}  = y - 2x \\  \\  \frac{dy}{dx} (2y - 1) = y - 2x \\  \\  \frac{dy}{dx}  =  \frac{y - 2x}{2y - 1}

At point (-1, 2):

\frac{dy}{dx}  =  \frac{2 - 2( - 1)}{2(2) - 1}  \\  \\ slope =  \frac{4}{3}

but a tangent has the same slope as the curve:

y = mx + c

m is the slope

c is the y-intercept

At (-1, 2):

2 = ( - 1 \times  \frac{4}{3} ) + c \\  \\ c = 2 +  \frac{4}{3}  \\  \\ c =  \frac{10}{3}

equation:

y =  \frac{4}{3} x +  \frac{10}{3}  \\  \\ { \boxed{3y = 4x + 10}}

8 0
3 years ago
Read 2 more answers
If there are 21 values in a data set in order from smallest to largest, what is the first quartile of the data set?
jek_recluse [69]
I think the answer is B) The mean of the 5th and 6th values
4 0
4 years ago
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I need help on the last part!
stellarik [79]

Answer:

0; (0, 0); 144; (3, 144)

Step-by-step explanation:

Y = distance (m)

X = time (hr)

X = 48x

If a car travels for 0 hours, it will travel __ mile(s).

y = 48x

Plug in 0 hours for x (time in hours)

y = 48(0)

Any number mutliplied by 0 equals 0

y = 0

If a car travels for 0 hours, it will travel 0 miles. This means it will pass through the point (0, 0).

(0, 0) limits our options to graphs B and D

Car travels 144 miles in 3 hours

To find how many miles it travels in 1 hour, divide 144 miles by 3 hours

144 ÷ 3 = 48

In 1 hour, a car travels 48 miles

If 48 × 3 = 144, then 48 × 4 = ?

48 × 4 = 192

When looking at graph D, there are 4 lines above 0

Counting by 48, it perfectly fits 192 by the fourth line

From (0, 0), if we move 3 units to the right we can find the third vertical line intersecting

Since the lines are counted by 48 and we are looking at the third line: 48 × 3 = 144

Use the slope to move 3 units to the right of the origin and 144 unit(s) up to the find the point (3, 144) that can be used to graph the relationship

7 0
3 years ago
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Pllllzzzzz hellllpppp!!! What is an equation of the line that passes through the point (2,2) and is parallel to the line x-2y=4
tia_tia [17]

Answer:

-2y = 4 - x

2y = x - 4

y = 1/2x - 2

1/2 is the slope of both lines.

y = mx + b

Substitute the given point and the common slope

2 = 1/2 x 2 + b

2 = 1 + b

b = 1

y = 1/2x + 1

The equation of the line that passes through the point

(2, 2) and is parallel to the line x - 2y = 4 is y = 1/2x + 1 or 2y = x + 2.

hope this helps u

plz give me the brainliest i really need it

3 0
3 years ago
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Which object covers less area?
baherus [9]
Object A. You can use the area theorem to solve. Just do base x height to get the area of a shape.
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3 years ago
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