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ANEK [815]
3 years ago
5

Determines the equation of the circumference passing through points A (-2; 0), B (6; 0) and having the center on the line x + 2y

+ 4 = 0. It then determines the line tangent to the circumference at point A .​
Mathematics
1 answer:
Alenkasestr [34]3 years ago
4 0

Answer:

y = 4/3 x + 8/3

Step-by-step explanation:

A (-2; 0), B (6; 0) on circle circumference, circle center O (h , k) and radius r

(-2 - h)² + (0 - k)² = r²

(6 - h)² + (0 - k)² = r²

(-2 - h)² = (6 - h)²

4 + 4h + h² = 36 - 12h + h²

16h = 32           h = 2

the center on the line x + 2y + 4 = 0, ∴ 2 + 2y + 4 = 0

y = -3   i.e.  k = -3         center O (2 , -3)

segment OA: (2 , -3) (-2 , 0)

slope OA = (-3 - 0) / (2 - (-2)) = -3 /4

tangent line through A (Lₐ) slope Lₐ = 4/3

y = mx + b    for A(-2 , 0)

b = y - mx = 0 - (4/3 x (-2)) = 8/3

line tangent to the circumference at point A: y = 4/3 x + 8/3

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Step-by-step explanation:

4x + 2xy=

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3 years ago
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A farmer needs to ship 71 pumpkins to a grocery store if each crates can hold 19 pumpkins how many crates Will the farmer need ?
Lesechka [4]

Answer:

The farmer will need 7 crates.

Step-by-step explanation:

<em>It is given that there are 71 pumpkins in total.</em>

<em>And each crate holds 19 pumpkins.</em>

Let the number of crates required be<em> "n".</em>

The total number of pumpkins can be calculated by multiplying number of pumpkins in each crate with total number of crates.

Thus, the equation is

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3 0
3 years ago
The length of a rectangle is 2 units more than the width. The area of the rectangle is 63 units. What is the length, in units, o
Keith_Richards [23]

Answer:

Length = 9units

Width = 7units

Step-by-step explanation:

It is said that the length is 2units more than the width

Assume that the width is x, then the length will be 2 + x

ie

Width = x

Length = 2 + x

Area of the rectangle = 63units

Area of rectangle = l * b

l - length of the rectangle

b - width of the rectangle

A = l * b

63 = (2 + x) * x

63 = ( 2 + x) x

63 = 2x + x^2

Let's rearrange it

x^2 + 2x - 63 = 0

Let's find the factor of 63

A factor that can be multiplied to give -63 and that can be added to give +2

Let's use -7 and +9

x^2 - 7x + 9x - 63 = 0

Separate with brackets

( x^2 - 7x) + ( 9x - 63) = 0

x( x - 7) + 9(x - 7) = 0

( x + 9)(x - 7) = 0

( x + 9) = 0

( x - 7) = 0

x + 9 = 0

x = -9

x - 7 = 0

x = 7

Note: the length of a rectangle can not be negative

So therefore,

x = 7

Length = 2 + x

= 2 + 7

= 9units

Width = x

= 7units

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Answer:54?

Step-by-step explanation:

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