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tangare [24]
3 years ago
11

what is the center and radius of the circle given the equation, 8x + x-squared - 2y + y-squared - 64 = 0?

Mathematics
1 answer:
RoseWind [281]3 years ago
7 0

Step-by-step explanation:

8x + x² - 2y + y² - 64 = 0

(x + 4)² + (y - 1)² - 81 = 0

(x + 4)² + (y - 1)² = 81

Hencr the center is (-4,1) and the radius is 9.

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Complete the work to find the dimensions of the rectangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 10 – 10 (x + 2)(x – 5) = 0
Norma-Jean [14]

Answer:

Length =5

Width = 2

Step-by-step explanation:

Given

Length =x

Width = x -3

Area = 10

x(x-3) =10

See comment for missing part of the question

Required

Complete the expression to determine the dimension of a rectangle

We have:

x(x-3) =10

Open bracket

x^2 -3x = 10

Equate to 0

x^2 -3x - 10 =0

Expand

x^2 + 2x - 5x - 10 = 0

Factorize

x(x + 2) - 5(x + 2) = 0

Factor out x + 2

(x  - 5)(x + 2) = 0

Solve for x

x - 5 = 0 or x + 2 = 0

x = 5 or x = -2

The value of x cannot be negative

So:

x  = 5

Recall that:

Length = x

Width = x - 3

So:

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Width = 2 ---- i.e. 5 - 3

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3 years ago
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Step-by-step explanation:

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Answer:

a. D and E are similar but not congruent.

Step-by-step explanation:

Let's analyse each statement and determine which is true about the 3 given quadrilaterals:

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D is similar to E because, every segment of D is proportional to the corresponding segments of E. The ratio of their corresponding segments are equal.

D and E are not congruent because their segments are not of equal length. Thus, they have the same shape but different sizes.

b. "E and F are similar and congruent." NOT TRUE.

E and F has the same size, hence they are congruent. However, they are not similar, because they don't have the same shape. Their corresponding lengths are not proportional.

c. "D and E are similar and congruent." NOT TRUE.

Since statement (a) is TRUE, statement (c) cannot be true.

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