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sladkih [1.3K]
3 years ago
8

Barbie is analyzing a circle, y2 + x2 = 16, and a linear function g(x). Will they intersect?

Mathematics
1 answer:
evablogger [386]3 years ago
4 0

Answer:

Yes, at positive x-coordinates.

Step-by-step explanation:

Finding the equation for g(x):

Slope = (3-6)/ (1-0) = -3

y-intercept =  y value when x = 0 = 6.

So g(x) = -3x + 6

Solve them simultaneously:

x^2 + y^2 = 16

g(x) : y =  -3x + 6

Substitute for y in the first equation:

x^2 + (-3x + 6)^2 = 16

x^2 + ( 9x^2 - 36x + 36) = 16

10x^2 - 36x + 20 = 0

5x^2 - 18x + 10 = 0

x = [-(-18) +/- sqrt ( (-18)^2 - 4 * -18 * 10)] / (5*2)

= ( 18 +/- sqrt 124 )/ 10

= (1.8) +/- 1,114

These 2 roots are both positive.

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Given:

The graph of a downward parabola.

To find:

The domain and range of the graph.

Solution:

Domain is the set of x-values or input values and range is the set of y-values or output values.

The graph represents a downward parabola and domain of a downward parabola is always the set of real numbers because they are defined for all real values of x.

Domain = R

Domain = (-∞,∞)

The maximum point of a downward parabola is the vertex. The range of the downward parabola is always the set of all real number which are less than or equal to the y-coordinate of the vertex.

From the graph it is clear that the vertex of the parabola is at point (5,-4). So, value of function cannot be greater than -4.

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Range =  (-∞,-4]

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3 years ago
5(4x-7) +3 (3x+3) can someone help me please
ivann1987 [24]

Answer:

The expression 5(4x - 7) + 3(3x + 3) can be simplified to 29x - 26

Step-by-step explanation:

The first step in solving this is to apply coefficients to the contents of the brackets:

5(4x - 7) + 3(3x + 3)

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Now you can group like terms:

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= (20 + 9)x - 26

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